CP-violating asymmetries in top-quark production and decay in $e^+ e^-$ annihilation within

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The Subleading Isgur-Wise Form Factor $chi_3(vcdot v')$ to Order $alpha_s$ in QCD Sum Rules

a rXiv:h ep-ph/9212266v116Dec1992SLAC–PUB–6017WIS–92/99/Dec–PH December 1992T/E The Subleading Isgur-Wise Form Factor χ3(v ·v ′)to Order αs in QCD Sum Rules Matthias Neubert Stanford Linear Accelerator Center Stanford University,Stanford,California 94309Zoltan Ligeti and Yosef Nir Weizmann Institute of Science Physics Department,Rehovot 76100,Israel We calculate the contributions arising at order αs in the QCD sum rule for the spin-symmetry violating universal function χ3(v ·v ′),which appears at order 1/m Q in the heavy quark expansion of meson form factors.In particular,we derive the two-loop perturbative contribution to the sum rule.Over the kinematic range accessible in B →D (∗)ℓνdecays,we ﬁnd that χ3(v ·v ′)does not exceed the level of ∼1%,indicating that power corrections induced by the chromo-magnetic operator in the heavy quark expansion are small.(submitted to Physical Review D)I.INTRODUCTIONIn the heavy quark eﬀective theory(HQET),the hadronic matrix elements describing the semileptonic decays M(v)→M′(v′)ℓν,where M and M′are pseudoscalar or vector mesons containing a heavy quark,can be systematically expanded in inverse powers of the heavy quark masses[1–5].The coeﬃcients in this expansion are m Q-independent,universal functions of the kinematic variable y=v·v′.These so-called Isgur-Wise form factors characterize the properties of the cloud of light quarks and gluons surrounding the heavy quarks,which act as static color sources.At leading order,a single functionξ(y)suﬃces to parameterize all matrix elements[6].This is expressed in the compact trace formula[5,7] M′(v′)|J(0)|M(v) =−ξ(y)tr{(2)m M P+ −γ5;pseudoscalar meson/ǫ;vector mesonis a spin wave function that describes correctly the transformation properties(under boosts and heavy quark spin rotations)of the meson states in the eﬀective theory.P+=1g s2m Q O mag,O mag=M′(v′)ΓP+iσαβM(v) .(4)The mass parameter¯Λsets the canonical scale for power corrections in HQET.In the m Q→∞limit,it measures theﬁnite mass diﬀerence between a heavy meson and the heavy quark that it contains[11].By factoring out this parameter,χαβ(v,v′)becomes dimensionless.The most general decomposition of this form factor involves two real,scalar functionsχ2(y)andχ3(y)deﬁned by[10]χαβ(v,v′)=(v′αγβ−v′βγα)χ2(y)−2iσαβχ3(y).(5)Irrespective of the structure of the current J ,the form factor χ3(y )appears always in the following combination with ξ(y ):ξ(y )+2Z ¯Λ d M m Q ′ χ3(y ),(6)where d P =3for a pseudoscalar and d V =−1for a vector meson.It thus eﬀectively renormalizes the leading Isgur-Wise function,preserving its normalization at y =1since χ3(1)=0according to Luke’s theorem [10].Eq.(6)shows that knowledge of χ3(y )is needed if one wants to relate processes which are connected by the spin symmetry,such as B →D ℓνand B →D ∗ℓν.Being hadronic form factors,the universal functions in HQET can only be investigated using nonperturbative methods.QCD sum rules have become very popular for this purpose.They have been reformulated in the context of the eﬀective theory and have been applied to the study of meson decay constants and the Isgur-Wise functions both in leading and next-to-leading order in the 1/m Q expansion [12–21].In particular,it has been shown that very simple predictions for the spin-symmetry violating form factors are obtained when terms of order αs are neglected,namely [17]χ2(y )=0,χ3(y )∝ ¯q g s σαβG αβq [1−ξ(y )].(7)In this approach χ3(y )is proportional to the mixed quark-gluon condensate,and it was estimated that χ3(y )∼1%for large recoil (y ∼1.5).In a recent work we have reﬁned the prediction for χ2(y )by including contributions of order αs in the sum rule analysis [20].We found that these are as important as the contribution of the mixed condensate in (7).It is,therefore,worthwhile to include such eﬀects also in the analysis of χ3(y ).This is the purpose of this article.II.DERIV ATION OF THE SUM RULEThe QCD sum rule analysis of the functions χ2(y )and χ3(y )is very similar.We shall,therefore,only brieﬂy sketch the general procedure and refer for details to Refs.[17,20].Our starting point is the correlatord x d x ′d ze i (k ′·x ′−k ·x ) 0|T[¯q ΓM ′P ′+ΓP +iσαβP +ΓM+Ξ3(ω,ω′,y )tr 2σαβ2(1+/v ′),and we omit the velocity labels in h and h ′for simplicity.The heavy-light currents interpolate pseudoscalar or vector mesons,depending on the choice ΓM =−γ5or ΓM =γµ−v µ,respectively.The external momenta k and k ′in (8)are the “residual”oﬀ-shell momenta of the heavy quarks.Due to the phase redeﬁnition of the eﬀective heavy quark ﬁelds in HQET,they are related to the total momenta P and P ′by k =P −m Q v and k ′=P ′−m Q ′v ′[3].The coeﬃcient functions Ξi are analytic in ω=2v ·k and ω′=2v ′·k ′,with discontinuities for positive values of these variables.They can be saturated by intermediate states which couple to the heavy-light currents.In particular,there is a double-pole contribution from the ground-state mesons M and M ′.To leading order in the 1/m Q expansion the pole position is at ω=ω′=2¯Λ.In the case of Ξ2,the residue of the pole is proportional to the universal function χ2(y ).For Ξ3the situation is more complicated,however,since insertions of the chromo-magnetic operator not only renormalize the leading Isgur-Wise function,but also the coupling of the heavy mesons to the interpolating heavy-light currents (i.e.,the meson decay constants)and the physical meson masses,which deﬁne the position of the pole.1The correct expression for the pole contribution to Ξ3is [17]Ξpole 3(ω,ω′,y )=F 2(ω−2¯Λ+iǫ) .(9)Here F is the analog of the meson decay constant in the eﬀective theory (F ∼f M√m QδΛ2+... , 0|j (0)|M (v ) =iF2G 2tr 2σαβΓP +σαβM (v ) ,where the ellipses represent spin-symmetry conserving or higher order power corrections,and j =¯q Γh (v ).In terms of the vector–pseudoscalar mass splitting,the parameter δΛ2isgiven by m 2V −m 2P =−8¯ΛδΛ2.For not too small,negative values of ωand ω′,the coeﬃcient function Ξ3can be approx-imated as a perturbative series in αs ,supplemented by the leading power corrections in 1/ωand 1/ω′,which are proportional to vacuum expectation values of local quark-gluon opera-tors,the so-called condensates [22].This is how nonperturbative corrections are incorporated in this approach.The idea of QCD sum rules is to match this theoretical representation of Ξ3to the phenomenological pole contribution given in (9).To this end,one ﬁrst writes the theoretical expression in terms of a double dispersion integral,Ξth 3(ω,ω′,y )= d νd ν′ρth 3(ν,ν′,y )1Thereare no such additional terms for Ξ2because of the peculiar trace structure associated with this coeﬃcient function.possible subtraction terms.Because of theﬂavor symmetry it is natural to set the Borel parameters associated withωandω′equal:τ=τ′=2T.One then introduces new variables ω±=12T ξ(y) F2e−2¯Λ/T=ω0dω+e−ω+/T ρth3(ω+,y)≡K(T,ω0,y).(12)The eﬀective spectral density ρth3arises after integration of the double spectral density over ω−.Note that for each contribution to it the dependence onω+is known on dimensionalgrounds.It thus suﬃces to calculate directly the Borel transform of the individual con-tributions toΞth3,corresponding to the limitω0→∞in(12).Theω0-dependence can be recovered at the end of the calculation.When terms of orderαs are neglected,contributions to the sum rule forΞ3can only be proportional to condensates involving the gluonﬁeld,since there is no way to contract the gluon contained in O mag.The leading power correction of this type is represented by the diagram shown in Fig.1(d).It is proportional to the mixed quark-gluon condensate and,as shown in Ref.[17],leads to(7).Here we are interested in the additional contributions arising at orderαs.They are shown in Fig.1(a)-(c).Besides a two-loop perturbative contribution, one encounters further nonperturbative corrections proportional to the quark and the gluon condensate.Let usﬁrst present the result for the nonperturbative power corrections.WeﬁndK cond(T,ω0,y)=αs ¯q q TT + αs GG y+1− ¯q g sσαβGαβq√y2−1),δn(x)=1(4π)D×1dλλ1−D∞λd u1∞1/λd u2(u1u2−1)D/2−2where C F=(N2c−1)/2N c,and D is the dimension of space-time.For D=4,the integrand diverges asλ→0.To regulate the integral,we assume D<2and use a triple integration by parts inλto obtain an expression which can be analytically continued to the vicinity of D=4.Next we set D=4+2ǫ,expand inǫ,write the result as an integral overω+,and introduce back the continuum threshold.This givesK pert(T,ω0,y)=−αsy+1 2ω0dω+ω3+e−ω+/T(16)× 12−23∂µ+3αs9π¯Λ,(17)which shows that divergences arise at orderαs.At this order,the renormalization of the sum rule is thus accomplished by a renormalization of the“bare”parameter G2in(12).In the9π¯Λ 1µ2 +O(g3s).(18)Hence a counterterm proportional to¯Λξ(y)has to be added to the bracket on the left-hand side of the sum rule(12).To evaluate its eﬀect on the right-hand side,we note that in D dimensions[17]¯Λξ(y)F2e−2¯Λ/T=3y+1 2ω0dω+ω3+e−ω+/T(19)× 1+ǫ γE−ln4π+2lnω+−ln y+12T ξ(y) F2e−2¯Λ/T=αsy+1 2ω0dω+ω3+e−ω+/T 2lnµ6+ y r(y)−1+ln y+1According to Luke’stheorem,theuniversalfunction χ3(y )vanishes at zero recoil [10].Evaluating (20)for y =1,we thus obtain a sum rule for G 2(µ)and δΛ2.It reads G 2(µ)−¯ΛδΛ224π3ω00d ω+ω3+e −ω+/T ln µ12 +K cond (T,ω0,1),(21)where we have used that r (1)=1.Precisely this sum rule has been derived previously,starting from a two-current correlator,in Ref.[16].This provides a nontrivial check of our ing the fact that ξ(y )=[2/(y +1)]2+O (g s )according to (19),we ﬁnd that the µ-dependent terms cancel out when we eliminate G 2(µ)and δΛ2from the sum rule for χ3(y ).Before we present our ﬁnal result,there is one more eﬀect which has to be taken into account,namely a spin-symmetry violating correction to the continuum threshold ω0.Since the chromo-magnetic interaction changes the masses of the ground-state mesons [cf.(10)],it also changes the masses of higher resonance states.Expanding the physical threshold asωphys =ω0 1+d M8π3 22 δ3 ω032π2ω30e −ω0/T 26π2−r (y )−ξ(y ) δ0 ω096π 248T 1−ξ(y ).It explicitly exhibits the fact that χ3(1)=0.III.NUMERICAL ANALYSISLet us now turn to the evaluation of the sum rule (23).For the QCD parameters we take the standard values¯q q =−(0.23GeV)3,αs GG =0.04GeV4,¯q g sσαβGαβq =m20 ¯q q ,m20=0.8GeV2.(24) Furthermore,we useδω2=−0.1GeV from above,andαs/π=0.1corresponding to the scale µ=2¯Λ≃1GeV,which is appropriate for evaluating radiative corrections in the eﬀective theory[15].The sensitivity of our results to changes in these parameters will be discussed below.The dependence of the left-hand side of(23)on¯Λand F can be eliminated by using a QCD sum rule for these parameters,too.It reads[16]¯ΛF2e−2¯Λ/T=9T4T − ¯q g sσαβGαβq4π2 2T − ¯q q +(2y+1)4T2.(26) Combining(23),(25)and(26),we obtainχ3(y)as a function ofω0and T.These parameters can be determined from the analysis of a QCD sum rule for the correlator of two heavy-light currents in the eﬀective theory[16,18].Oneﬁnds good stability forω0=2.0±0.3GeV,and the consistency of the theoretical calculation requires that the Borel parameter be in the range0.6<T<1.0GeV.It supports the self-consistency of the approach that,as shown in Fig.2,weﬁnd stability of the sum rule(23)in the same region of parameter space.Note that it is in fact theδω2-term that stabilizes the sum rule.Without it there were no plateau.Over the kinematic range accessible in semileptonic B→D(∗)ℓνdecays,we show in Fig.3(a)the range of predictions forχ3(y)obtained for1.7<ω0<2.3GeV and0.7<T< 1.2GeV.From this we estimate a relative uncertainty of∼±25%,which is mainly due to the uncertainty in the continuum threshold.It is apparent that the form factor is small,not exceeding the level of1%.2Finally,we show in Fig.3(b)the contributions of the individual terms in the sum rule (23).Due to the large negative contribution proportional to the quark condensate,the terms of orderαs,which we have calculated in this paper,cancel each other to a large extent.As a consequence,ourﬁnal result forχ3(y)is not very diﬀerent from that obtained neglecting these terms[17].This is,however,an accident.For instance,the order-αs corrections would enhance the sum rule prediction by a factor of two if the ¯q q -term had the opposite sign. From thisﬁgure one can also deduce how changes in the values of the vacuum condensates would aﬀect the numerical results.As long as one stays within the standard limits,the sensitivity to such changes is in fact rather small.For instance,working with the larger value ¯q q =−(0.26GeV)3,or varying m20between0.6and1.0GeV2,changesχ3(y)by no more than±0.15%.In conclusion,we have presented the complete order-αs QCD sum rule analysis of the subleading Isgur-Wise functionχ3(y),including in particular the two-loop perturbative con-tribution.Weﬁnd that over the kinematic region accessible in semileptonic B decays this form factor is small,typically of the order of1%.When combined with our previous analysis [20],which predicted similarly small values for the universal functionχ2(y),these results strongly indicate that power corrections in the heavy quark expansion which are induced by the chromo-magnetic interaction between the gluonﬁeld and the heavy quark spin are small.ACKNOWLEDGMENTSIt is a pleasure to thank Michael Peskin for helpful discussions.M.N.gratefully acknowl-edgesﬁnancial support from the BASF Aktiengesellschaft and from the German National Scholarship Foundation.Y.N.is an incumbent of the Ruth E.Recu Career Development chair,and is supported in part by the Israel Commission for Basic Research and by the Minerva Foundation.This work was also supported by the Department of Energy,contract DE-AC03-76SF00515.REFERENCES[1]E.Eichten and B.Hill,Phys.Lett.B234,511(1990);243,427(1990).[2]B.Grinstein,Nucl.Phys.B339,253(1990).[3]H.Georgi,Phys.Lett.B240,447(1990).[4]T.Mannel,W.Roberts and Z.Ryzak,Nucl.Phys.B368,204(1992).[5]A.F.Falk,H.Georgi,B.Grinstein,and M.B.Wise,Nucl.Phys.B343,1(1990).[6]N.Isgur and M.B.Wise,Phys.Lett.B232,113(1989);237,527(1990).[7]J.D.Bjorken,Proceedings of the18th SLAC Summer Institute on Particle Physics,pp.167,Stanford,California,July1990,edited by J.F.Hawthorne(SLAC,Stanford,1991).[8]M.B.Voloshin and M.A.Shifman,Yad.Fiz.45,463(1987)[Sov.J.Nucl.Phys.45,292(1987)];47,801(1988)[47,511(1988)].[9]A.F.Falk,B.Grinstein,and M.E.Luke,Nucl.Phys.B357,185(1991).[10]M.E.Luke,Phys.Lett.B252,447(1990).[11]A.F.Falk,M.Neubert,and M.E.Luke,SLAC preprint SLAC–PUB–5771(1992),toappear in Nucl.Phys.B.[12]M.Neubert,V.Rieckert,B.Stech,and Q.P.Xu,in Heavy Flavours,edited by A.J.Buras and M.Lindner,Advanced Series on Directions in High Energy Physics(World Scientiﬁc,Singapore,1992).[13]A.V.Radyushkin,Phys.Lett.B271,218(1991).[14]D.J.Broadhurst and A.G.Grozin,Phys.Lett.B274,421(1992).[15]M.Neubert,Phys.Rev.D45,2451(1992).[16]M.Neubert,Phys.Rev.D46,1076(1992).[17]M.Neubert,Phys.Rev.D46,3914(1992).[18]E.Bagan,P.Ball,V.M.Braun,and H.G.Dosch,Phys.Lett.B278,457(1992);E.Bagan,P.Ball,and P.Gosdzinsky,Heidelberg preprint HD–THEP–92–40(1992).[19]B.Blok and M.Shifman,Santa Barbara preprint NSF–ITP–92–100(1992).[20]M.Neubert,Z.Ligeti,and Y.Nir,SLAC preprint SLAC–PUB–5915(1992).[21]M.Neubert,SLAC preprint SLAC–PUB–5992(1992).[22]M.A.Shifman,A.I.Vainshtein,and V.I.Zakharov,Nucl.Phys.B147,385(1979);B147,448(1979).FIGURESFIG.1.Diagrams contributing to the sum rule for the universal form factorχ3(v·v′):two-loop perturbative contribution(a),and nonperturbative contributions proportional to the quark con-densate(b),the gluon condensate(c),and the mixed condensate(d).Heavy quark propagators are drawn as double lines.The square represents the chromo-magnetic operator.FIG.2.Analysis of the stability region for the sum rule(23):The form factorχ3(y)is shown for y=1.5as a function of the Borel parameter.From top to bottom,the solid curves refer toω0=1.7,2.0,and2.3GeV.The dashes lines are obtained by neglecting the contribution proportional toδω2.FIG.3.(a)Prediction for the form factorχ3(v·v′)in the stability region1.7<ω0<2.3 GeV and0.7<T<1.2GeV.(b)Individual contributions toχ3(v·v′)for T=0.8GeV and ω0=2.0GeV:total(solid),mixed condensate(dashed-dotted),gluon condensate(wide dots), quark condensate(dashes).The perturbative contribution and theδω2-term are indistinguishable in thisﬁgure and are both represented by the narrow dots.11。

双语经验对大脑可塑性的影响

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monolingual peers. These ﬁndings suggest that L1 production in bimodal bilinguals involves an interaction 32
between L1 and L2, supporting the claim that learning a second language does, in fact, change the functional 33

超级对撞机之争

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子振荡和强作用介子物理方面做出了世界一流的结果，如 2012年在迄今中美最大的科技合作项目大亚湾中微子实验中就发现了一种新的中微子振荡，该结果在全球科学界引起热烈反响并被美国《科学》杂志评选为2012年十大科学突破。李政道、丁肇中等外籍科学家在人才培养、方案选定、开展国际合作等方面发挥了至关重要的作用。 30年过去了，北京正负电子对撞机已经穷尽了该能区的物理学，中国的高能物理研究必须考虑未来的出路。丘成桐认为，建造超级粒子对撞机将破解高能物理发展瓶颈，对中国科学的发展有突破性的促进。假如在对撞机里面能够发现超对称粒子的话，整个世界的物理前沿跟数学前沿都会改变。他还认为，超级对撞机将成为 “海纳百川”般吸引全球顶尖人才的平台，能使世界高能物理研究的重心移到中国来，就好像在中国建成了一个 “科学的联合国”。丘成桐预计，项目建成后，至少会有五六千名各国一流科学家为做实验举家迁往中国，且长期居住。高能所的王贻芳所长则认为，最近10年是中国建造大型对撞机的“窗口期”。 1993年美国宣布终止超导超级对撞机（SSC）计划后，1994年欧洲核子中心CERN批准了建造LHC的计划，世界高能物理研究中心从美国移到欧洲。但欧洲核子研究所的LHC正面临能级触顶的困局，美国和日本手头都有项
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枸橼酸爱地那非人肝微粒体代谢产物鉴定及性别差异

ＳｔｅｒｏｉｄＢｉｏｃｈｅｍꎬ２０２０ꎬ１９９:１０５５４８.[２]　ＴＡＭＡＵＣＨＩＳꎬＫＡＪＩＹＡＭＡＨꎬＵＴＳＵＭＩＦꎬｅｔａｌ.Ｅｆｆｉｃａｃｙｏｆｍｅｄｒｏｘｙｐｒｏｇｅｓｔｅｒｏｎｅａｃｅｔａｔｅｔｒｅａｔｍｅｎｔａｎｄｒｅｔｒｅａｔｍｅｎｔｆｏｒａｔｙｐｉｃａｌｅｎｄｏｍｅｔｒｉａｌｈｙｐｅｒｐｌａｓｉａａｎｄｅｎｄｏｍｅｔｒｉａｌｃａｎｃｅｒ[Ｊ].ＪＯｂｓｔｅｔＧｙｎａｅｃｏｌＲｅｓꎬ２０１８ꎬ４４(１):１５１－１５６.[３]　ＢＡＩＫＳꎬＭＥＨＴＡＦＦꎬＣＨＵＮＧＳＨ.Ｍｅｄｒｏｘｙｐｒｏｇｅｓｔｅｒｏｎｅａｃｅｔａｔｅｐｒｅｖｅｎｔｉｏｎｏｆｃｅｒｖｉｃａｌｃａｎｃｅｒｔｈｒｏｕｇｈｐｒｏｇｅｓｔｅｒｏｎｅｒｅｃｅｐｔｏｒｉｎａｈｕｍａｎｐａｐｉｌｌｏｍａｖｉｒｕｓｔｒａｎｓｇｅｎｉｃｍｏｕｓｅｍｏｄｅｌ[Ｊ].ＡｍＪＰａｔｈｏｌꎬ２０１９ꎬ１８９(１２):２４５９－２４６８.[４]　ＳＵＮＲꎬＧＵＯＹꎬＹＩＮＮꎬｅｔａｌ.Ｐｒｅｐａｒａｔｉｏｎｏｆｓｔｅｒｉｌｅｌｏｎｇ￣ａｃｔｉｎｇｉｎｊｅｃｔａｂｌｅｍｅｄｒｏｘｙｐｒｏｇｅｓｔｅｒｏｎｅａｃｅｔａｔｅｍｉｃｒｏｃｒｙｓｔａｌｓｂａｓｅｄｏｎａｎｔｉ￣ｓｏｌｖｅｎｔｐｒｅｃｉｐｉｔａｔｉｏｎａｎｄｃｒｙｓｔａｌｈａｂｉｔｃｏｎｔｒｏｌ[Ｊ].ＥｘｐｅｒｔＯｐｉｎＤｒｕｇＤｅｌꎬ２０１９ꎬ１６(１０):１１３３－１１４４.[５]　杨梦瑞ꎬ李鹏ꎬ简凌波ꎬ等.甲砜霉素纯度标准物质定值研究及其不确定度评估[Ｊ].农产品质量与安全ꎬ２０１９ꎬ(５):６３－６８.[６]　ＹＡＮＧＤＺꎬＳＵＢꎬＢＩＹＣꎬｅｔａｌ.Ｐｒｅｐａｒａｔｉｏｎａｎｄｃｅｒｔｉｆｃａ￣ｔｉｏｎｏｆａｎｅｗｓａｌｖｉａｎｏｌｉｃａｃｉｄａｒｅｆｅｒｅｎｃｅｍａｔｅｒｉａｌｆｏｒｆｏｏｄａｎｄｄｒｕｇｒｅｓｅａｒｃｈ[Ｊ].ＮａｔｕｒＰｒｏｄＢｉｏｐｒｏｓｐꎬ２０２０ꎬ１０(２):６７－７５.[７]　ＴＡＮＧＰＡＩＳＡＲＮＫＵＬＮꎬＴＵＣＨＩＮＤＡＰꎬＷＩＬＡＩＲＡＴＰꎬｅｔａｌ.Ｄｅｖｅｌｏｐｍｅｎｔｏｆｐｕｒｅｃｅｒｔｉｆｉｅｄｒｅｆｅｒｅｎｃｅｍａｔｅｒｉａｌｏｆｓｔｅｖｉｏｓｉｄｅ[Ｊ].ＦｏｏｄＣｈｅｍꎬ２０１８ꎬ２５５:７５－８０.[８]　刘金涛ꎬ李玲ꎬ董家吏ꎬ等.柚皮素标准物质的研制及不

O(alpha) QED Corrections to Polarized Elastic $mu e$ and Deep Inelastic l N Scattering

a r X i v :h e p -p h /9711228v 1 4 N o v 1997hep-ph/9711228October 1997O (α)QED Corrections to Polarized Elastic µe and Deep Inelastic lN ScatteringDima Bardin a,b,c ,Johannes Bl¨u mlein a ,Penka Christova a,d ,and Lida Kalinovskaya a,caDESY–Zeuthen,Platanenallee 6,D–15735Zeuthen,GermanybINFN,Sezione di Torino,Torino,ItalycJINR,ul.Joliot-Curie 6,RU–141980Dubna,RussiadBishop Konstantin Preslavsky University of Shoumen,9700Shoumen,BulgariaAbstractTwo computer codes relevant for the description of deep inelastic scattering oﬀpolarized targets are discussed.The code µe la deals with radiative corrections to elastic µe scattering,one method applied for muon beam polarimetry.The code HECTOR allows to calculate both the radiative corrections for unpolarized and polarized deep inelastic scattering,including higher order QED corrections.1IntroductionThe exact knowledge of QED,QCD,and electroweak (EW)radiative corrections (RC)to the deep inelastic scattering (DIS)processes is necessary for a precise determination of the nucleon structure functions.The present and forthcoming high statistics measurements of polarized structure functions in the SLAC experiments,by HERMES,and later by COMPASS require the knowledge of the RC to the DIS polarized cross-sections at the percent level.Several codes based on diﬀerent approaches for the calculation of the RC to DIS experiments,mainly for non-polarized DIS,were developped and thoroughly compared in the past,cf.[1].Later on the radiative corrections for a vast amount of experimentally relevant sets of kinematic variables were calculated [2],including also semi-inclusive situations as the RC’s in the case of tagged photons [3].Furthermore the radiative corrections to elastic µ-e scattering,a process to monitor (polarized)muon beams,were calculated [4].The corresponding codes are :•HECTOR 1.00,(1994-1995)[5],by the Dubna-Zeuthen Group.It calculates QED,QCD and EW corrections for variety of measuremets for unpolarized DIS.•µe la 1.00,(March 1996)[4],calculates O (α)QED correction for polarized µe elastic scattering.•HECTOR1.11,(1996)extends HECTOR1.00including the radiative corrections for polarized DIS[6],and for DIS with tagged photons[3].The beta-version of the code is available from http://www.ifh.de/.2The Programµe laMuon beams may be monitored using the processes ofµdecay andµe scattering in case of atomic targets.Both processes were used by the SMC experiment.Similar techniques will be used by the COMPASS experiment.For the cross section measurement the radiative corrections to these processes have to be known at high precision.For this purpose a renewed calculation of the radiative corrections toσ(µe→µe)was performed[4].The diﬀerential cross-section of polarized elasticµe scattering in the Born approximation reads,cf.[7],dσBORNm e Eµ (Y−y)2(1−P e Pµ) ,(1)where y=yµ=1−E′µ/Eµ=E′e/Eµ=y e,Y=(1+mµ/2/Eµ)−1=y max,mµ,m e–muon and electron masses,Eµ,E′µ,E′e the energies of the incoming and outgoing muon,and outgoing electron respectively,in the laboratory frame.Pµand P e denote the longitudinal polarizations of muon beam and electron target.At Born level yµand y e agree.However,both quantities are diﬀerent under inclusion of radiative corrections due to bremsstrahlung.The correction factors may be rather diﬀerent depending on which variables(yµor y e)are used.In the SMC analysis the yµ-distribution was used to measure the electron spin-ﬂip asymmetry A expµe.Since previous calculations,[8,9],referred to y e,and only ref.[9]took polarizations into account,a new calculation was performed,including the complete O(α)QED correction for the yµ-distribution,longitudinal polarizations for both leptons,theµ-mass eﬀects,and neglecting m e wherever possible.Furthermore the present calculation allows for cuts on the electron re-coil energy(35GeV),the energy balance(40GeV),and angular cuts for both outgoing leptons (1mrad).The default values are given in parentheses.Up to order O(α3),14Feynman graphs contribute to the cross-section forµ-e scattering, which may be subdivided into12=2×6pieces,which are separately gauge invariantdσQEDdyµ.(2) One may express(2)also asdσQEDdyµ+P e Pµdσpol kk=1−Born cross-section,k=b;2−RC for the muonic current:vertex+bremsstrahlung,k=µµ;3−amm contribution from muonic current,k=amm;4−RC for the electronic current:vertex+bremsstrahlung,k=ee;5−µe interference:two-photon exchange+muon-electron bremsstrahlung interference,k=µe;6−vacuum polarization correction,runningα,k=vp.The FORTRAN code for the scattering cross section(2)µe la was used in a recent analysis of the SMC collaboration.The RC,δA yµ,to the asymmetry A QEDµeshown inﬁgures1and2is deﬁned asδA yµ=A QEDµedσunpol.(4)The results may be summarized as follows.The O(α)QED RC to polarized elasticµe scattering were calculated for theﬁrst time using the variable yµ.A rather general FORTRAN codeµe la for this process was created allowing for the inclusion of kinematic cuts.Since under the conditions of the SMC experiment the corrections turn out to be small our calculation justiﬁes their neglection. 3Program HECTOR3.1Diﬀerent approaches to RC for DISThe radiative corrections to deep inelastic scattering are treated using two basic approaches. One possibility consists in generating events on the basis of matrix elements including the RC’s. This approach is suited for detector simulations,but requests a very hughe number of events to obtain the corrections at a high precision.Alternatively,semi-analytic codes allow a fast and very precise evaluation,even including a series of basic cuts andﬂexible adjustment to speciﬁc phase space requirements,which may be caused by the way kinematic variables are experimentally measured,cf.[2,5].Recently,a third approach,the so-called deterministic approach,was followed,cf.[10].It treats the RC’s completely exclusively combining features of fast computing with the possibility to apply any cuts.Some elements of this approach were used inµe la and in the branch of HECTOR1.11,in which DIS with tagged photons is calculated.Concerning the theoretical treatment three approaches are in use to calculate the radiative corrections:1)the model-independent approach(MI);2)the leading-log approximation(LLA); and3)an approach based on the quark-parton model(QPM)in evaluating the radiative correc-tions to the scattering cross-section.In the model-independent approach the QED corrections are only evaluated for the leptonic tensor.Strictly it applies only for neutral current processes.The hadronic tensor can be dealt with in its most general form on the Lorentz-level.Both lepton-hadron corrections as well as pure hadronic corrections are neglected.This is justiﬁed in a series of cases in which these corrections turn out to be very small.The leading logarithmic approximation is one of the semi-analytic treatments in which the diﬀerent collinear singularities of O((αln(Q2/m2l))n)are evaluated and other corrections are neglected.The QPM-approach deals with the full set of diagrams on the quark level.Within this method,any corrections(lepton-hadron interference, EW)can be included.However,it has limited precision too,now due to use of QPM-model itself. Details on the realization of these approaches within the code HECTOR are given in ref.[5,11].3.2O (α)QED Corrections for Polarized Deep Inelastic ScatteringTo introduce basic notation,we show the Born diagramr rr r j r r r r l ∓( k 1,m )l ∓( k 2,m )X ( p ′,M h )p ( p ,M )γ,Z ¨¨¨¨B ¨¨¨¨£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡z r r r r r r r r r r r r r rr ¨¨¨¨B ¨¨¨¨r r r r j r r r r and the Born cross-section,which is presented as the product of the leptonic and hadronic tensordσBorn =2πα2p.k 1,x =Q 2q 2F 1(x,Q 2)+p µ p ν2p.qF 3(x,Q 2)+ie µνλσq λs σ(p.q )2G 2(x,Q 2)+p µ s ν+ s µ p νp.q1(p.q )2G 4(x,Q 2)+−g µν+q µq νp.qG 5(x,Q 2),(8)wherep µ=p µ−p.qq 2q µ,and s is the four vector of nucleon polarization,which is given by s =λp M (0, n )in the nucleonrest frame.The combined structure functions in eq.(8)F1,2(x,Q2)=Q2e Fγγ1,2(x,Q2)+2|Q e|(v l−p eλl a l)χ(Q2)FγZ1,2(x,Q2)+ v2l+a2l−2p eλl v l a l χ2(Q2)F ZZ1,2(x,Q2),F3(x,Q2)=2|Q e|(p e a l−λl v l)χ(Q2)FγZ3(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)F ZZ3(x,Q2),G1,2(x,Q2)=−Q2eλl gγγ1,2(x,Q2)+2|Q e|(p e a l−λl v l)χ(Q2)gγZ1,2(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)g ZZ1,2(x,Q2),G3,4,5(x,Q2)=2|Q e|(v l−p eλl a l)χ(Q2)gγZ3,4,5(x,Q2),+ v2l+a2l−2p eλl v l a l χ2(Q2)g ZZ3,4,5(x,Q2),(9) are expressed via the hadronic structure functions,the Z-boson-lepton couplings v l,a l,and the ratio of the propagators for the photon and Z-bosonχ(Q2)=Gµ2M2ZQ2+M2Z.(10)Furthermore we use the parameter p e for which p e=1for a scattered lepton and p e=−1for a scattered antilepton.The hadronic structure functions can be expressed in terms of parton densities accounting for the twist-2contributions only,see[12].Here,a series of relations between the diﬀerent structure functions are used in leading order QCD.The DIS cross-section on the Born-leveld2σBorndxdy +d2σpol Borndxdy =2πα2S ,S U3(y,Q2)=x 1−(1−y)2 ,(13) and the polarized partdσpol BornQ4λp N f p S5i=1S p gi(x,y)G i(x,Q2).(14)Here,S p gi(x,y)are functions,similar to(13),and may be found in[6].Furthermore we used the abbrevationsf L=1, n L=λp N k 12πSy 1−y−M2xy2π1−yThe O(α)DIS cross-section readsd2σQED,1πδVRd2σBorndx l dy l=d2σunpolQED,1dx l dy l.(16)All partial cross-sections have a form similar to the Born cross-section and are expressed in terms of kinematic functions and combinations of structure functions.In the O(α)approximation the measured cross-section,σrad,is deﬁne asd2σraddx l dy l +d2σQED,1dx l dy l+d2σpol radd2σBorn−1.(18)The radiative corrections calculated for leptonic variables grow towards high y and smaller values of x.Theﬁgures compare the results obtained in LLA,accounting for initial(i)andﬁnal state (f)radiation,as well as the Compton contribution(c2)with the result of the complete calculation of the leptonic corrections.In most of the phase space the LLA correction provides an excellent description,except of extreme kinematic ranges.A comparison of the radiative corrections for polarized deep inelastic scattering between the codes HECTOR and POLRAD[17]was carried out.It had to be performed under simpliﬁed conditions due to the restrictions of POLRAD.Corresponding results may be found in[11,13,14].3.3ConclusionsFor the evaluation of the QED radiative corrections to deep inelastic scattering of polarized targets two codes HECTOR and POLRAD exist.The code HECTOR allows a completely general study of the radiative corrections in the model independent approach in O(α)for neutral current reac-tions including Z-boson exchange.Furthermore,the LLA corrections are available in1st and2nd order,including soft-photon resummation and for charged current reactions.POLRAD contains a branch which may be used for some semi-inclusive DIS processes.The initial state radia-tive corrections(to2nd order in LLA+soft photon exponentiation)to these(and many more processes)can be calculated in detail with the code HECTOR,if the corresponding user-supplied routine USRBRN is used together with this package.This applies both for neutral and charged current processes as well as a large variety of diﬀerent measurements of kinematic variables. Aside the leptonic corrections,which were studied in detail already,further investigations may concern QED corrections to the hadronic tensor as well as the interference terms. References[1]Proceedings of the Workshop on Physics at HERA,1991Hamburg(DESY,Hamburg,1992),W.Buchm¨u ller and G.Ingelman(eds.).[2]J.Bl¨u mlein,Z.Phys.C65(1995)293.[3]D.Bardin,L.Kalinovskaya and T.Riemann,DESY96–213,Z.Phys.C in print.[4]D.Bardin and L.Kalinovskaya,µe la,version1.00,March1996.The source code is availablefrom http://www.ifh.de/~bardin.[5]A.Arbuzov,D.Bardin,J.Bl¨u mlein,L.Kalinovskaya and T.Riemann,Comput.Phys.Commun.94(1996)128,hep-ph/9510410[6]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,DESY96–189,hep-ph/9612435,Nucl.Phys.B in print.[7]SMC collaboration,D.Adams et al.,Phys.Lett.B396(1997)338;Phys.Rev.D56(1997)5330,and references therein.[8]A.I.Nikischov,Sov.J.Exp.Theor.Phys.Lett.9(1960)757;P.van Nieuwenhuizen,Nucl.Phys.B28(1971)429;D.Bardin and N.Shumeiko,Nucl.Phys.B127(1977)242.[9]T.V.Kukhto,N.M.Shumeiko and S.I.Timoshin,J.Phys.G13(1987)725.[10]G.Passarino,mun.97(1996)261.[11]D.Bardin,J.Bl¨u mlein,P.Christova,L.Kalinovskaya,and T.Riemann,Acta Phys.PolonicaB28(1997)511.[12]J.Bl¨u mlein and N.Kochelev,Phys.Lett.B381(1996)296;Nucl.Phys.B498(1997)285.[13]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,Preprint DESY96–198,hep-ph/9609399,in:Proceedings of the Workshop‘Future Physics at HERA’,G.Ingelman,A.De Roeck,R.Klanner(eds.),Vol.1,p.13;hep-ph/9609399.[14]D.Bardin,Contribution to the Proceedings of the International Conference on High EnergyPhysics,Warsaw,August1996.[15]M.Gl¨u ck,E.Reya,M.Stratmann and W.Vogelsang,Phys.Rev.D53(1996)4775.[16]S.Wandzura and F.Wilczek,Phys.Lett.B72(1977)195.[17]I.Akushevich,A.Il’ichev,N.Shumeiko,A.Soroko and A.Tolkachev,hep-ph/9706516.-20-18-16-14-12-10-8-6-4-200.10.20.30.40.50.60.70.80.91elaFigure 1:The QED radiative corrections to asymmetry without experimental cuts.-1-0.8-0.6-0.4-0.200.20.40.60.810.10.20.30.40.50.60.70.80.91elaFigure 2:The QED radiative corrections to asymmetry with experimental cuts.-50-40-30-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 3:A comparison of complete and LLA RC’s in the kinematic regime of HERMES for neutral current longitudinally polarized DIS in leptonic variables.The polarized parton densities [15]are used.The structure function g 2is calculated using the Wandzura–Wilczek relation.c 2stands for the Compton contribution,see [6]for details.-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 4:The same as in ﬁg.3,but for energies in the range of the SMC-experiment.-20-10010203040500.10.20.30.40.50.60.70.80.91HectorFigure 5:The same as in ﬁg.4for x =10−3.-200-150-100-5005010015020000.10.20.30.40.50.60.70.80.91HectorFigure 6:A comparison of complete and LLA RC’s at HERA collider kinematic regime for neutral current deep inelastic scattering oﬀa longitudinally polarized target measuring the kinematic variables at the leptonic vertex.。

C.parvum全基因组序列

DOI: 10.1126/science.1094786, 441 (2004);304Science et al.Mitchell S. Abrahamsen,Cryptosporidium parvum Complete Genome Sequence of the Apicomplexan, (this information is current as of October 7, 2009 ):The following resources related to this article are available online at/cgi/content/full/304/5669/441version of this article at:including high-resolution figures, can be found in the online Updated information and services,/cgi/content/full/1094786/DC1 can be found at:Supporting Online Material/cgi/content/full/304/5669/441#otherarticles , 9 of which can be accessed for free: cites 25 articles This article 239 article(s) on the ISI Web of Science. cited by This article has been /cgi/content/full/304/5669/441#otherarticles 53 articles hosted by HighWire Press; see: cited by This article has been/cgi/collection/genetics Genetics: subject collections This article appears in the following/about/permissions.dtl in whole or in part can be found at: this article permission to reproduce of this article or about obtaining reprints Information about obtaining registered trademark of AAAS.is a Science 2004 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m3.R.Jackendoff,Foundations of Language:Brain,Gram-mar,Evolution(Oxford Univ.Press,Oxford,2003).4.Although for Frege(1),reference was established rela-tive to objects in the world,here we follow Jackendoff’s suggestion(3)that this is done relative to objects and the state of affairs as mentally represented.5.S.Zola-Morgan,L.R.Squire,in The Development andNeural Bases of Higher Cognitive Functions(New York Academy of Sciences,New York,1990),pp.434–456.6.N.Chomsky,Reﬂections on Language(Pantheon,New York,1975).7.J.Katz,Semantic Theory(Harper&Row,New York,1972).8.D.Sperber,D.Wilson,Relevance(Harvard Univ.Press,Cambridge,MA,1986).9.K.I.Forster,in Sentence Processing,W.E.Cooper,C.T.Walker,Eds.(Erlbaum,Hillsdale,NJ,1989),pp.27–85.10.H.H.Clark,Using Language(Cambridge Univ.Press,Cambridge,1996).11.Often word meanings can only be fully determined byinvokingworld knowledg e.For instance,the meaningof “ﬂat”in a“ﬂat road”implies the absence of holes.However,in the expression“aﬂat tire,”it indicates the presence of a hole.The meaningof“ﬁnish”in the phrase “Billﬁnished the book”implies that Bill completed readingthe book.However,the phrase“the g oatﬁn-ished the book”can only be interpreted as the goat eatingor destroyingthe book.The examples illustrate that word meaningis often underdetermined and nec-essarily intertwined with general world knowledge.In such cases,it is hard to see how the integration of lexical meaning and general world knowledge could be strictly separated(3,31).12.W.Marslen-Wilson,C.M.Brown,L.K.Tyler,Lang.Cognit.Process.3,1(1988).13.ERPs for30subjects were averaged time-locked to theonset of the critical words,with40items per condition.Sentences were presented word by word on the centerof a computer screen,with a stimulus onset asynchronyof600ms.While subjects were readingthe sentences,their EEG was recorded and ampliﬁed with a high-cut-off frequency of70Hz,a time constant of8s,and asamplingfrequency of200Hz.14.Materials and methods are available as supportingmaterial on Science Online.15.M.Kutas,S.A.Hillyard,Science207,203(1980).16.C.Brown,P.Hagoort,J.Cognit.Neurosci.5,34(1993).17.C.M.Brown,P.Hagoort,in Architectures and Mech-anisms for Language Processing,M.W.Crocker,M.Pickering,C.Clifton Jr.,Eds.(Cambridge Univ.Press,Cambridge,1999),pp.213–237.18.F.Varela et al.,Nature Rev.Neurosci.2,229(2001).19.We obtained TFRs of the single-trial EEG data by con-volvingcomplex Morlet wavelets with the EEG data andcomputingthe squared norm for the result of theconvolution.We used wavelets with a7-cycle width,with frequencies ranging from1to70Hz,in1-Hz steps.Power values thus obtained were expressed as a per-centage change relative to the power in a baselineinterval,which was taken from150to0ms before theonset of the critical word.This was done in order tonormalize for individual differences in EEG power anddifferences in baseline power between different fre-quency bands.Two relevant time-frequency compo-nents were identiﬁed:(i)a theta component,rangingfrom4to7Hz and from300to800ms after wordonset,and(ii)a gamma component,ranging from35to45Hz and from400to600ms after word onset.20.C.Tallon-Baudry,O.Bertrand,Trends Cognit.Sci.3,151(1999).tner et al.,Nature397,434(1999).22.M.Bastiaansen,P.Hagoort,Cortex39(2003).23.O.Jensen,C.D.Tesche,Eur.J.Neurosci.15,1395(2002).24.Whole brain T2*-weighted echo planar imaging bloodoxygen level–dependent(EPI-BOLD)fMRI data wereacquired with a Siemens Sonata1.5-T magnetic reso-nance scanner with interleaved slice ordering,a volumerepetition time of2.48s,an echo time of40ms,a90°ﬂip angle,31horizontal slices,a64ϫ64slice matrix,and isotropic voxel size of3.5ϫ3.5ϫ3.5mm.For thestructural magnetic resonance image,we used a high-resolution(isotropic voxels of1mm3)T1-weightedmagnetization-prepared rapid gradient-echo pulse se-quence.The fMRI data were preprocessed and analyzedby statistical parametric mappingwith SPM99software(http://www.ﬁ/spm99).25.S.E.Petersen et al.,Nature331,585(1988).26.B.T.Gold,R.L.Buckner,Neuron35,803(2002).27.E.Halgren et al.,J.Psychophysiol.88,1(1994).28.E.Halgren et al.,Neuroimage17,1101(2002).29.M.K.Tanenhaus et al.,Science268,1632(1995).30.J.J.A.van Berkum et al.,J.Cognit.Neurosci.11,657(1999).31.P.A.M.Seuren,Discourse Semantics(Basil Blackwell,Oxford,1985).32.We thank P.Indefrey,P.Fries,P.A.M.Seuren,and M.van Turennout for helpful discussions.Supported bythe Netherlands Organization for Scientiﬁc Research,grant no.400-56-384(P.H.).Supporting Online Material/cgi/content/full/1095455/DC1Materials and MethodsFig.S1References and Notes8January2004;accepted9March2004Published online18March2004;10.1126/science.1095455Include this information when citingthis paper.Complete Genome Sequence ofthe Apicomplexan,Cryptosporidium parvumMitchell S.Abrahamsen,1,2*†Thomas J.Templeton,3†Shinichiro Enomoto,1Juan E.Abrahante,1Guan Zhu,4 Cheryl ncto,1Mingqi Deng,1Chang Liu,1‡Giovanni Widmer,5Saul Tzipori,5GregoryA.Buck,6Ping Xu,6 Alan T.Bankier,7Paul H.Dear,7Bernard A.Konfortov,7 Helen F.Spriggs,7Lakshminarayan Iyer,8Vivek Anantharaman,8L.Aravind,8Vivek Kapur2,9The apicomplexan Cryptosporidium parvum is an intestinal parasite that affects healthy humans and animals,and causes an unrelenting infection in immuno-compromised individuals such as AIDS patients.We report the complete ge-nome sequence of C.parvum,type II isolate.Genome analysis identiﬁes ex-tremely streamlined metabolic pathways and a reliance on the host for nu-trients.In contrast to Plasmodium and Toxoplasma,the parasite lacks an api-coplast and its genome,and possesses a degenerate mitochondrion that has lost its genome.Several novel classes of cell-surface and secreted proteins with a potential role in host interactions and pathogenesis were also detected.Elu-cidation of the core metabolism,including enzymes with high similarities to bacterial and plant counterparts,opens new avenues for drug development.Cryptosporidium parvum is a globally impor-tant intracellular pathogen of humans and animals.The duration of infection and patho-genesis of cryptosporidiosis depends on host immune status,ranging from a severe but self-limiting diarrhea in immunocompetent individuals to a life-threatening,prolonged infection in immunocompromised patients.Asubstantial degree of morbidity and mortalityis associated with infections in AIDS pa-tients.Despite intensive efforts over the past20years,there is currently no effective ther-apy for treating or preventing C.parvuminfection in humans.Cryptosporidium belongs to the phylumApicomplexa,whose members share a com-mon apical secretory apparatus mediating lo-comotion and tissue or cellular invasion.Many apicomplexans are of medical or vet-erinary importance,including Plasmodium,Babesia,Toxoplasma,Neosprora,Sarcocys-tis,Cyclospora,and Eimeria.The life cycle ofC.parvum is similar to that of other cyst-forming apicomplexans(e.g.,Eimeria and Tox-oplasma),resulting in the formation of oocysts1Department of Veterinary and Biomedical Science,College of Veterinary Medicine,2Biomedical Genom-ics Center,University of Minnesota,St.Paul,MN55108,USA.3Department of Microbiology and Immu-nology,Weill Medical College and Program in Immu-nology,Weill Graduate School of Medical Sciences ofCornell University,New York,NY10021,USA.4De-partment of Veterinary Pathobiology,College of Vet-erinary Medicine,Texas A&M University,College Sta-tion,TX77843,USA.5Division of Infectious Diseases,Tufts University School of Veterinary Medicine,NorthGrafton,MA01536,USA.6Center for the Study ofBiological Complexity and Department of Microbiol-ogy and Immunology,Virginia Commonwealth Uni-versity,Richmond,VA23198,USA.7MRC Laboratoryof Molecular Biology,Hills Road,Cambridge CB22QH,UK.8National Center for Biotechnology Infor-mation,National Library of Medicine,National Insti-tutes of Health,Bethesda,MD20894,USA.9Depart-ment of Microbiology,University of Minnesota,Min-neapolis,MN55455,USA.*To whom correspondence should be addressed.E-mail:abe@†These authors contributed equally to this work.‡Present address:Bioinformatics Division,Genetic Re-search,GlaxoSmithKline Pharmaceuticals,5MooreDrive,Research Triangle Park,NC27009,USA.R E P O R T S SCIENCE VOL30416APRIL2004441o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mthat are shed in the feces of infected hosts.C.parvum oocysts are highly resistant to environ-mental stresses,including chlorine treatment of community water supplies;hence,the parasite is an important water-and food-borne pathogen (1).The obligate intracellular nature of the par-asite ’s life cycle and the inability to culture the parasite continuously in vitro greatly impair researchers ’ability to obtain purified samples of the different developmental stages.The par-asite cannot be genetically manipulated,and transformation methodologies are currently un-available.To begin to address these limitations,we have obtained the complete C.parvum ge-nome sequence and its predicted protein com-plement.(This whole-genome shotgun project has been deposited at DDBJ/EMBL/GenBank under the project accession AAEE00000000.The version described in this paper is the first version,AAEE01000000.)The random shotgun approach was used to obtain the complete DNA sequence (2)of the Iowa “type II ”isolate of C.parvum .This isolate readily transmits disease among numerous mammals,including humans.The resulting ge-nome sequence has roughly 13ϫgenome cov-erage containing five gaps and 9.1Mb of totalDNA sequence within eight chromosomes.The C.parvum genome is thus quite compact rela-tive to the 23-Mb,14-chromosome genome of Plasmodium falciparum (3);this size difference is predominantly the result of shorter intergenic regions,fewer introns,and a smaller number of genes (Table 1).Comparison of the assembled sequence of chromosome VI to that of the recently published sequence of chromosome VI (4)revealed that our assembly contains an ad-ditional 160kb of sequence and a single gap versus two,with the common sequences dis-playing a 99.993%sequence identity (2).The relative paucity of introns greatly simplified gene predictions and facilitated an-notation (2)of predicted open reading frames (ORFs).These analyses provided an estimate of 3807protein-encoding genes for the C.parvum genome,far fewer than the estimated 5300genes predicted for the Plasmodium genome (3).This difference is primarily due to the absence of an apicoplast and mitochondrial genome,as well as the pres-ence of fewer genes encoding metabolic functions and variant surface proteins,such as the P.falciparum var and rifin molecules (Table 2).An analysis of the encoded pro-tein sequences with the program SEG (5)shows that these protein-encoding genes are not enriched in low-complexity se-quences (34%)to the extent observed in the proteins from Plasmodium (70%).Our sequence analysis indicates that Cryptosporidium ,unlike Plasmodium and Toxoplasma ,lacks both mitochondrion and apicoplast genomes.The overall complete-ness of the genome sequence,together with the fact that similar DNA extraction proce-dures used to isolate total genomic DNA from C.parvum efficiently yielded mito-chondrion and apicoplast genomes from Ei-meria sp.and Toxoplasma (6,7),indicates that the absence of organellar genomes was unlikely to have been the result of method-ological error.These conclusions are con-sistent with the absence of nuclear genes for the DNA replication and translation machinery characteristic of mitochondria and apicoplasts,and with the lack of mito-chondrial or apicoplast targeting signals for tRNA synthetases.A number of putative mitochondrial pro-teins were identified,including components of a mitochondrial protein import apparatus,chaperones,uncoupling proteins,and solute translocators (table S1).However,the ge-nome does not encode any Krebs cycle en-zymes,nor the components constituting the mitochondrial complexes I to IV;this finding indicates that the parasite does not rely on complete oxidation and respiratory chains for synthesizing adenosine triphosphate (ATP).Similar to Plasmodium ,no orthologs for the ␥,␦,or εsubunits or the c subunit of the F 0proton channel were detected (whereas all subunits were found for a V-type ATPase).Cryptosporidium ,like Eimeria (8)and Plas-modium ,possesses a pyridine nucleotide tran-shydrogenase integral membrane protein that may couple reduced nicotinamide adenine dinucleotide (NADH)and reduced nico-tinamide adenine dinucleotide phosphate (NADPH)redox to proton translocation across the inner mitochondrial membrane.Unlike Plasmodium ,the parasite has two copies of the pyridine nucleotide transhydrogenase gene.Also present is a likely mitochondrial membrane –associated,cyanide-resistant alter-native oxidase (AOX )that catalyzes the reduction of molecular oxygen by ubiquinol to produce H 2O,but not superoxide or H 2O 2.Several genes were identified as involved in biogenesis of iron-sulfur [Fe-S]complexes with potential mitochondrial targeting signals (e.g.,nifS,nifU,frataxin,and ferredoxin),supporting the presence of a limited electron flux in the mitochondrial remnant (table S2).Our sequence analysis confirms the absence of a plastid genome (7)and,additionally,the loss of plastid-associated metabolic pathways including the type II fatty acid synthases (FASs)and isoprenoid synthetic enzymes thatTable 1.General features of the C.parvum genome and comparison with other single-celled eukaryotes.Values are derived from respective genome project summaries (3,26–28).ND,not determined.FeatureC.parvum P.falciparum S.pombe S.cerevisiae E.cuniculiSize (Mbp)9.122.912.512.5 2.5(G ϩC)content (%)3019.43638.347No.of genes 38075268492957701997Mean gene length (bp)excluding introns 1795228314261424ND Gene density (bp per gene)23824338252820881256Percent coding75.352.657.570.590Genes with introns (%)553.9435ND Intergenic regions (G ϩC)content %23.913.632.435.145Mean length (bp)5661694952515129RNAsNo.of tRNA genes 454317429944No.of 5S rRNA genes 6330100–2003No.of 5.8S ,18S ,and 28S rRNA units 57200–400100–20022Table parison between predicted C.parvum and P.falciparum proteins.FeatureC.parvum P.falciparum *Common †Total predicted proteins380752681883Mitochondrial targeted/encoded 17(0.45%)246(4.7%)15Apicoplast targeted/encoded 0581(11.0%)0var/rif/stevor ‡0236(4.5%)0Annotated as protease §50(1.3%)31(0.59%)27Annotated as transporter ࿣69(1.8%)34(0.65%)34Assigned EC function ¶167(4.4%)389(7.4%)113Hypothetical proteins925(24.3%)3208(60.9%)126*Values indicated for P.falciparum are as reported (3)with the exception of those for proteins annotated as protease or transporter.†TBLASTN hits (e Ͻ–5)between C.parvum and P.falciparum .‡As reported in (3).§Pre-dicted proteins annotated as “protease or peptidase”for C.parvum (CryptoGenome database,)and P.falciparum (PlasmoDB database,).࿣Predicted proteins annotated as “trans-porter,permease of P-type ATPase”for C.parvum (CryptoGenome)and P.falciparum (PlasmoDB).¶Bidirectional BLAST hit (e Ͻ–15)to orthologs with assigned Enzyme Commission (EC)numbers.Does not include EC assignment numbers for protein kinases or protein phosphatases (due to inconsistent annotation across genomes),or DNA polymerases or RNA polymerases,as a result of issues related to subunit inclusion.(For consistency,46proteins were excluded from the reported P.falciparum values.)R E P O R T S16APRIL 2004VOL 304SCIENCE 442 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mare otherwise localized to the plastid in other apicomplexans.C.parvum fatty acid biosynthe-sis appears to be cytoplasmic,conducted by a large(8252amino acids)modular type I FAS (9)and possibly by another large enzyme that is related to the multidomain bacterial polyketide synthase(10).Comprehensive screening of the C.parvum genome sequence also did not detect orthologs of Plasmodium nuclear-encoded genes that contain apicoplast-targeting and transit sequences(11).C.parvum metabolism is greatly stream-lined relative to that of Plasmodium,and in certain ways it is reminiscent of that of another obligate eukaryotic parasite,the microsporidian Encephalitozoon.The degeneration of the mi-tochondrion and associated metabolic capabili-ties suggests that the parasite largely relies on glycolysis for energy production.The parasite is capable of uptake and catabolism of mono-sugars(e.g.,glucose and fructose)as well as synthesis,storage,and catabolism of polysac-charides such as trehalose and amylopectin. Like many anaerobic organisms,it economizes ATP through the use of pyrophosphate-dependent phosphofructokinases.The conver-sion of pyruvate to acetyl–coenzyme A(CoA) is catalyzed by an atypical pyruvate-NADPH oxidoreductase(Cp PNO)that contains an N-terminal pyruvate–ferredoxin oxidoreductase (PFO)domain fused with a C-terminal NADPH–cytochrome P450reductase domain (CPR).Such a PFO-CPR fusion has previously been observed only in the euglenozoan protist Euglena gracilis(12).Acetyl-CoA can be con-verted to malonyl-CoA,an important precursor for fatty acid and polyketide biosynthesis.Gly-colysis leads to several possible organic end products,including lactate,acetate,and ethanol. The production of acetate from acetyl-CoA may be economically beneficial to the parasite via coupling with ATP production.Ethanol is potentially produced via two in-dependent pathways:(i)from the combination of pyruvate decarboxylase and alcohol dehy-drogenase,or(ii)from acetyl-CoA by means of a bifunctional dehydrogenase(adhE)with ac-etaldehyde and alcohol dehydrogenase activi-ties;adhE first converts acetyl-CoA to acetal-dehyde and then reduces the latter to ethanol. AdhE predominantly occurs in bacteria but has recently been identified in several protozoans, including vertebrate gut parasites such as Enta-moeba and Giardia(13,14).Adjacent to the adhE gene resides a second gene encoding only the AdhE C-terminal Fe-dependent alcohol de-hydrogenase domain.This gene product may form a multisubunit complex with AdhE,or it may function as an alternative alcohol dehydro-genase that is specific to certain growth condi-tions.C.parvum has a glycerol3-phosphate dehydrogenase similar to those of plants,fungi, and the kinetoplastid Trypanosoma,but(unlike trypanosomes)the parasite lacks an ortholog of glycerol kinase and thus this pathway does not yield glycerol production.In addition to themodular fatty acid synthase(Cp FAS1)andpolyketide synthase homolog(Cp PKS1), C.parvum possesses several fatty acyl–CoA syn-thases and a fatty acyl elongase that may partici-pate in fatty acid metabolism.Further,enzymesfor the metabolism of complex lipids(e.g.,glyc-erolipid and inositol phosphate)were identified inthe genome.Fatty acids are apparently not anenergy source,because enzymes of the fatty acidoxidative pathway are absent,with the exceptionof a3-hydroxyacyl-CoA dehydrogenase.C.parvum purine metabolism is greatlysimplified,retaining only an adenosine ki-nase and enzymes catalyzing conversionsof adenosine5Ј-monophosphate(AMP)toinosine,xanthosine,and guanosine5Ј-monophosphates(IMP,XMP,and GMP).Among these enzymes,IMP dehydrogenase(IMPDH)is phylogenetically related toε-proteobacterial IMPDH and is strikinglydifferent from its counterparts in both thehost and other apicomplexans(15).In con-trast to other apicomplexans such as Toxo-plasma gondii and P.falciparum,no geneencoding hypoxanthine-xanthineguaninephosphoribosyltransferase(HXGPRT)is de-tected,in contrast to a previous report on theactivity of this enzyme in C.parvum sporo-zoites(16).The absence of HXGPRT sug-gests that the parasite may rely solely on asingle enzyme system including IMPDH toproduce GMP from AMP.In contrast to otherapicomplexans,the parasite appears to relyon adenosine for purine salvage,a modelsupported by the identification of an adeno-sine transporter.Unlike other apicomplexansand many parasitic protists that can synthe-size pyrimidines de novo,C.parvum relies onpyrimidine salvage and retains the ability forinterconversions among uridine and cytidine5Ј-monophosphates(UMP and CMP),theirdeoxy forms(dUMP and dCMP),and dAMP,as well as their corresponding di-and triphos-phonucleotides.The parasite has also largelyshed the ability to synthesize amino acids denovo,although it retains the ability to convertselect amino acids,and instead appears torely on amino acid uptake from the host bymeans of a set of at least11amino acidtransporters(table S2).Most of the Cryptosporidium core pro-cesses involved in DNA replication,repair,transcription,and translation conform to thebasic eukaryotic blueprint(2).The transcrip-tional apparatus resembles Plasmodium interms of basal transcription machinery.How-ever,a striking numerical difference is seenin the complements of two RNA bindingdomains,Sm and RRM,between P.falcipa-rum(17and71domains,respectively)and C.parvum(9and51domains).This reductionresults in part from the loss of conservedproteins belonging to the spliceosomal ma-chinery,including all genes encoding Smdomain proteins belonging to the U6spliceo-somal particle,which suggests that this par-ticle activity is degenerate or entirely lost.This reduction in spliceosomal machinery isconsistent with the reduced number of pre-dicted introns in Cryptosporidium(5%)rela-tive to Plasmodium(Ͼ50%).In addition,keycomponents of the small RNA–mediatedposttranscriptional gene silencing system aremissing,such as the RNA-dependent RNApolymerase,Argonaute,and Dicer orthologs;hence,RNA interference–related technolo-gies are unlikely to be of much value intargeted disruption of genes in C.parvum.Cryptosporidium invasion of columnarbrush border epithelial cells has been de-scribed as“intracellular,but extracytoplas-mic,”as the parasite resides on the surface ofthe intestinal epithelium but lies underneaththe host cell membrane.This niche may al-low the parasite to evade immune surveil-lance but take advantage of solute transportacross the host microvillus membrane or theextensively convoluted parasitophorous vac-uole.Indeed,Cryptosporidium has numerousgenes(table S2)encoding families of putativesugar transporters(up to9genes)and aminoacid transporters(11genes).This is in starkcontrast to Plasmodium,which has fewersugar transporters and only one putative ami-no acid transporter(GenBank identificationnumber23612372).As a first step toward identification ofmulti–drug-resistant pumps,the genome se-quence was analyzed for all occurrences ofgenes encoding multitransmembrane proteins.Notable are a set of four paralogous proteinsthat belong to the sbmA family(table S2)thatare involved in the transport of peptide antibi-otics in bacteria.A putative ortholog of thePlasmodium chloroquine resistance–linkedgene Pf CRT(17)was also identified,althoughthe parasite does not possess a food vacuole likethe one seen in Plasmodium.Unlike Plasmodium,C.parvum does notpossess extensive subtelomeric clusters of anti-genically variant proteins(exemplified by thelarge families of var and rif/stevor genes)thatare involved in immune evasion.In contrast,more than20genes were identified that encodemucin-like proteins(18,19)having hallmarksof extensive Thr or Ser stretches suggestive ofglycosylation and signal peptide sequences sug-gesting secretion(table S2).One notable exam-ple is an11,700–amino acid protein with anuninterrupted stretch of308Thr residues(cgd3_720).Although large families of secretedproteins analogous to the Plasmodium multi-gene families were not found,several smallermultigene clusters were observed that encodepredicted secreted proteins,with no detectablesimilarity to proteins from other organisms(Fig.1,A and B).Within this group,at leastfour distinct families appear to have emergedthrough gene expansions specific to the Cryp-R E P O R T S SCIENCE VOL30416APRIL2004443o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mtosporidium clade.These families —SKSR,MEDLE,WYLE,FGLN,and GGC —were named after well-conserved sequence motifs (table S2).Reverse transcription polymerase chain reaction (RT-PCR)expression analysis (20)of one cluster,a locus of seven adjacent CpLSP genes (Fig.1B),shows coexpression during the course of in vitro development (Fig.1C).An additional eight genes were identified that encode proteins having a periodic cysteine structure similar to the Cryptosporidium oocyst wall protein;these eight genes are similarly expressed during the onset of oocyst formation and likely participate in the formation of the coccidian rigid oocyst wall in both Cryptospo-ridium and Toxoplasma (21).Whereas the extracellular proteins described above are of apparent apicomplexan or lineage-specific in-vention,Cryptosporidium possesses many genesencodingsecretedproteinshavinglineage-specific multidomain architectures composed of animal-and bacterial-like extracellular adhe-sive domains (fig.S1).Lineage-specific expansions were ob-served for several proteases (table S2),in-cluding an aspartyl protease (six genes),a subtilisin-like protease,a cryptopain-like cys-teine protease (five genes),and a Plas-modium falcilysin-like (insulin degrading enzyme –like)protease (19genes).Nine of the Cryptosporidium falcilysin genes lack the Zn-chelating “HXXEH ”active site motif and are likely to be catalytically inactive copies that may have been reused for specific protein-protein interactions on the cell sur-face.In contrast to the Plasmodium falcilysin,the Cryptosporidium genes possess signal peptide sequences and are likely trafficked to a secretory pathway.The expansion of this family suggests either that the proteins have distinct cleavage specificities or that their diversity may be related to evasion of a host immune response.Completion of the C.parvum genome se-quence has highlighted the lack of conven-tional drug targets currently pursued for the control and treatment of other parasitic protists.On the basis of molecular and bio-chemical studies and drug screening of other apicomplexans,several putative Cryptospo-ridium metabolic pathways or enzymes have been erroneously proposed to be potential drug targets (22),including the apicoplast and its associated metabolic pathways,the shikimate pathway,the mannitol cycle,the electron transport chain,and HXGPRT.Nonetheless,complete genome sequence analysis identifies a number of classic and novel molecular candidates for drug explora-tion,including numerous plant-like and bacterial-like enzymes (tables S3and S4).Although the C.parvum genome lacks HXGPRT,a potent drug target in other api-complexans,it has only the single pathway dependent on IMPDH to convert AMP to GMP.The bacterial-type IMPDH may be a promising target because it differs substan-tially from that of eukaryotic enzymes (15).Because of the lack of de novo biosynthetic capacity for purines,pyrimidines,and amino acids,C.parvum relies solely on scavenge from the host via a series of transporters,which may be exploited for chemotherapy.C.parvum possesses a bacterial-type thymidine kinase,and the role of this enzyme in pyrim-idine metabolism and its drug target candida-cy should be pursued.The presence of an alternative oxidase,likely targeted to the remnant mitochondrion,gives promise to the study of salicylhydroxamic acid (SHAM),as-cofuranone,and their analogs as inhibitors of energy metabolism in the parasite (23).Cryptosporidium possesses at least 15“plant-like ”enzymes that are either absent in or highly divergent from those typically found in mammals (table S3).Within the glycolytic pathway,the plant-like PPi-PFK has been shown to be a potential target in other parasites including T.gondii ,and PEPCL and PGI ap-pear to be plant-type enzymes in C.parvum .Another example is a trehalose-6-phosphate synthase/phosphatase catalyzing trehalose bio-synthesis from glucose-6-phosphate and uridine diphosphate –glucose.Trehalose may serve as a sugar storage source or may function as an antidesiccant,antioxidant,or protein stability agent in oocysts,playing a role similar to that of mannitol in Eimeria oocysts (24).Orthologs of putative Eimeria mannitol synthesis enzymes were not found.However,two oxidoreductases (table S2)were identified in C.parvum ,one of which belongs to the same families as the plant mannose dehydrogenases (25)and the other to the plant cinnamyl alcohol dehydrogenases.In principle,these enzymes could synthesize protective polyol compounds,and the former enzyme could use host-derived mannose to syn-thesize mannitol.References and Notes1.D.G.Korich et al .,Appl.Environ.Microbiol.56,1423(1990).2.See supportingdata on Science Online.3.M.J.Gardner et al .,Nature 419,498(2002).4.A.T.Bankier et al .,Genome Res.13,1787(2003).5.J.C.Wootton,Comput.Chem.18,269(1994).Fig.1.(A )Schematic showing the chromosomal locations of clusters of potentially secreted proteins.Numbers of adjacent genes are indicated in paren-theses.Arrows indicate direc-tion of clusters containinguni-directional genes (encoded on the same strand);squares indi-cate clusters containingg enes encoded on both strands.Non-paralogous genes are indicated by solid gray squares or direc-tional triangles;SKSR (green triangles),FGLN (red trian-gles),and MEDLE (blue trian-gles)indicate three C.parvum –speciﬁc families of paralogous genes predominantly located at telomeres.Insl (yellow tri-angles)indicates an insulinase/falcilysin-like paralogous gene family.Cp LSP (white square)indicates the location of a clus-ter of adjacent large secreted proteins (table S2)that are cotranscriptionally regulated.Identiﬁed anchored telomeric repeat sequences are indicated by circles.(B )Schematic show-inga select locus containinga cluster of coexpressed large secreted proteins (Cp LSP).Genes and intergenic regions (regions between identiﬁed genes)are drawn to scale at the nucleotide level.The length of the intergenic re-gions is indicated above or be-low the locus.(C )Relative ex-pression levels of CpLSP (red lines)and,as a control,C.parvum Hedgehog-type HINT domain gene (blue line)duringin vitro development,as determined by semiquantitative RT-PCR usingg ene-speciﬁc primers correspondingto the seven adjacent g enes within the CpLSP locus as shown in (B).Expression levels from three independent time-course experiments are represented as the ratio of the expression of each gene to that of C.parvum 18S rRNA present in each of the infected samples (20).R E P O R T S16APRIL 2004VOL 304SCIENCE 444 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m。

《粒子物理学教学讲义》6.4－节重夸克和重夸克偶素

6
确定了J/Ψ粒子子的夸克组分——正反粲夸克对，我们就可以解
释它的窄宽度了：
质量最轻的含粲D介子子质量为1870MeV，两个D介子子的阈能
为3740MeV，所以J/Ψ不能衰变到D介子子末态，它的强衰变末
态只能是由u,d,s夸克组成的轻强子子。
J/Ψ的强子子衰变的费曼图可以画作，
u d
c
d
c
c
d
c
d
它和J/Ψ粒子子类似, 也只能通过把b 和 b 湮没掉的Zweig禁戒过程做强衰变，衰变概率被大大大大地压低，表现出突出的“重质量，窄宽度”性质．同样ϒ (2S), ϒ(3S)也具有同样的性质。ϒ (4S)以及更高高质量的态则可以衰变到两个B介子子。因而而具有很大大的宽度。
17
对前3个ϒ共振态, ϒ→ 2B 的衰变道没有打开,他们所有的强衰变道都是OZI禁戒过程而受到压低, 衰变宽度很窄。但对下面更高质量的ϒ高激发态, 均可以衰变到两个B介子,因而具有很大的几十个MeV的宽度
16
ϒ粒子子所有的强衰变道都是OZI 禁戒过程而而受到压低，
分支支比比最大大的衰变道也是二二级电磁衰变的 e+e− 道，µ +µ − 道和 τ +τ − 道．
含底夸克b的最轻的粒子子是 B+(bu) 和 B0 (bd) 粒子子，其质量为
m = (5279)MeV，因此ϒ粒子子不可能衰变为一一对正反B介子子。
14
如果粲夸克存在，那么可以将u，d，s的SU(3) 味道对称性扩充到u,d,s,c的SU(4) 对称性，则应该存在含有若干（反）粲夸克的重子子和介子子多重态，
1976年发现了含粲介子子态（ D0 = cu , D+ = cd ）， 1977年又又发现了含粲奇异介子子 Ds+ = cs ，

Evolution of Ge and SiGe Quantum Dots under Excimer Laser Annealing

CHIN.PHYS.LETT.Vol.25,No.1(2008)242 Evolution of Ge and SiGe Quantum Dots under Excimer Laser Annealing∗HAN Gen-Quan(韩根全)1∗∗,ZENG Yu-Gang(曾玉刚)1,YU Jin-Zhong(余金中)1,CHENG Bu-Wen(成步文)1,YANG Hai-Tao(杨海涛)21State Key Laboratory on Integrated Optoelectronics,Institute of Semiconductors,Chinese Academy of Sciences,Beijing1000832Tsinghua-Foxconn Nanotechnology Research Center,Department of Physics,Tsinghua University,Beijing100084(Received15September2007)We present diﬀerent relaxation mechanisms of Ge and SiGe quantum dots under excimer laser annealing.Inves-tigation of the coarsening and relaxation of the dots shows that the strain in Ge dots on Geﬁlms is relaxed by dislocation since there is no interface between the Ge dots and the Ge layer,while the SiGe dots on Si0.77Ge0.23ﬁlm relax by lattice distortion to coherent dots,which results from the obvious interface between the SiGe dots and the Si0.77Ge0.23ﬁlm.The results are suggested and sustained by Vanderbilt and Wickham’s theory,and also demonstrate that no bulk diﬀusion occurs during the excimer laser annealing.PACS:68.65.Hb,68.35.Fx,68.35.Md,68.37.PsGe and SiGe self-assembled quantum dots (SAQDs)are widely studied for their promis-ing application in optoelectronics due to three-dimensional(3D)quantum conﬁnement.[1]Many works have focused on the growth mechanism,[2,3] shape transition,[4,5]and the coarsening process under thermal annealing[6]of the SAQDs in S-K mode.Re-cently,we obtained SiGe quantum dots with small size and high density by excimer laser annealing(ELA).[7] The nanosecond pulse duration of the excimer,which induces rapid heating and cooling of the sample sur-face,ensuring that the laser induced quantum dots (LIQDs)are formed only by surface atoms diﬀusion.[8] We obtained Ge and SiGe laser induced quantum dots by ELA of the Ge and SiGeﬁlms,respectively.In this Letter,we report that the laser-induced Ge and SiGe quantum dots undergo diﬀerent relax-ation mechanisms.Atomic-force-microscopy(AFM) measurements indicate that the Ge LIQDs on the Ge ﬁlm relax by formation of dislocation,while the SiGe LIQDs on the Si0.77Ge0.23ﬁlm release the strain by the lattice tetragonal distortion and then form coher-ent dots.The theory developed by Vanderbilt and Wickham has shown[9]that the interface between the dots and the wetting layer plays a pivotal role in the relaxation process of the strained dots.For the SiGe LIQDs on the Si0.77Ge0.23ﬁlm,our calculation shows that SiGe quantum dots with the Ge composition of about83%are formed on the Si0.77Ge0.23ﬁlm,which indicates an obvious interface between the dots and the Si0.77Ge0.23ﬁlm.The interface leads to the for-mation of the coherent SiGe relaxed dots.However, for the Ge LIQDs on the Geﬁlm,no interface between the dots and the wetting layer results in the formation of the dislocated dots.These are suggested and sus-tained by Vanderbilt and Wickham’s theory,and also demonstrates that no bulk diﬀusion occurs during the excimer laser annealing.The Ge and SiGeﬁlms were grown by an ultra-high-vacuum chemical vapour deposition(UHV-CVD) system on(001)-oriented Si substrates at500◦C and 550◦C,respectively.The Geﬁlm is in thickness of about1nm(8monolayers),and the SiGeﬁlm is about 20nm.The sources of Si and Ge are disilane and ger-mane,respectively.The Si substrates were cleaned in an ex-situ chemical etch process and loaded into an UHV growth chamber with basic pressure lower than 10−7Pa,and then heated up to950◦C to deoxidize. The thickness and Ge composition of the Si0.77Ge0.23ﬁlm are determined by double-crystal x-ray diﬀraction (XRD).A193nm ArF excimer laser operating frequency in 40Hz,was used to ex-situ anneal the samples,which were annealed in argon ambient.A top-ﬂat beam proﬁle of10×10mm2with the energy density of about180mJ/cm2was obtained by using a homog-enizer.This was carried out to ensure uniform an-nealing of samples’surface.The surface morphology of the samples was measured by an SPA-300HV AFM, performed in tapping mode.Figure1shows the AFM images of Ge and SiGe LIQDs obtained by ELA of Ge and Si0.77Ge0.23ﬁlms, respectively.The height proﬁles of the dots are also in Fig.1.The diameters of the Ge and SiGe LIQDs are20–25nm and15–20nm,respectively.The ther-mal process induced by the excimer laser pulse is only several tens nanoseconds,so during the ELA,only surface diﬀusion occurs.The dot energy can be ex-pressed by E=4ΓV2/3tan1/3θ−6AV tanθ,[2]where Γ=γd cscθ−γs cotθis the increase of surface energy,∗Supported by the National Natural Science Foundation of China under Grant No60576001.∗∗Email:hgquan@c 2008Chinese Physical Society and IOP Publishing LtdNo.1HANGen-Quan et al.243γs and γd are the surface energy per unit area of the wetting layer and dot facet,respectively,θis the facet angle with respect to the surface of the wetting layer,V is the volume of the dot,A =σ2(1−ν)/(2πG )where σis the in-plane misﬁt strain,and νand G are Poisson’s ratio and shear modulus,respectively.For the LIQDs,only surface energy should be stud-ied,and the second term on the right can be con-sidered as the eﬀect of strain on the surface energy.From the formula,we can see that the slightly strained dots are not stable during the ELA.We speculate that the heavily strained LIQDs will grow,relax the strainin them with longer annealing time.To investigate the relaxation of the LIQDs,we prolong the anneal-ing time with the laser energy density of 180mJ/cm 2.As the ELA continues,We observe the relaxation and the shrinking of the LIQDs,while it is surprisingly found that Ge quantum dots on the Ge wetting layer and SiGe dots on the Si 0.77Ge 0.23layer underwent the diﬀerent relaxation modes:the Ge dots relax through the formation of the dislocation,while the strain in the SiGe quantum dots on the Si 0.77Ge 0.23wetting layer is released by lattice tetragonal distortion.Fig.1.AFM images (500nm ×500nm)of LIQDs:(a)Ge LIQDs on the Ge ﬁlm and the height proﬁles along the line marked,(b)SiGe LIQDs on the Si 0.77Ge 0.23ﬁlm and the height proﬁles along the line marked.Figure 2shows a series of AFM images of the mor-phology of Ge LIQDs on the Ge ﬁlm at diﬀerent an-nealing times.When the annealing time is prolonged to 3.5hours,coarsening of the quantum dot,as shown in Fig.2(a),occurs.The contacting of the small and large dots in Fig.2(a)and 2(b)can be interpreted to be the losing materials of small dots to the near large dots,which is analogous to the anomalous coarsening in the SAQDs.[10]As the ELA proceeds,the density of the dots further decreases,and when the annealing time is up to 5hours,almost all the LIQDs disappear (shown in Fig.2(c)).After 7-h ELA,no new LIQDs are observed.We speculate that the relaxation of the laser induced Ge dots is by the dislocations and the strained ﬁlm is also relaxed by the dislocations.Fig-ure 3shows the schematic of the relaxation process ofthe Ge quantum dots on the Ge ﬁlm.Figure 4(a)shows the coarsening and the growth of the SiGe dots on the Si 0.77Ge 0.23ﬁlm.After 4-h an-nealing,the SiGe dots become larger and the density decreases.As the annealing continues (5h),some new LIQDs appear.This indicates that the growth and disappearing of the SiGe dots give rise to the restora-tion of the strain in the Si 0.77Ge 0.23ﬁlm.This will decrease the surface energy and increase the strain en-ergy.The recovered stress in the ﬁlm drives the new LIQDs under ELA.This reveals that the SiGe dots grow and relax to be the coherent dots,i.e.,the strain in the SiGe dots is relaxed by the lattice distortion.Figure 5shows the schematic of the relaxation process of the SiGe quantum dots on the Si 0.77Ge 0.23ﬁlm.244HAN Gen-Quan et al.Vol.25Fig.2.AFM images (1µm ×1µm)of the Ge LIQDs on the Ge ﬁlm with diﬀerent annealing times:(a)annealed for 3.5h,(b)annealed for 4h,(c)annealed for 5h,(d)annealed for 7h.Fig.3.Schematic diagram of the relaxation mode of the Ge quantum dots on the Ge ﬁlm.Fig.4.AFM images (1µm ×1µm)of the SiGe LIQDs on the Si 0.77Ge 0.23ﬁlm for diﬀerent annealing times:(a)annealed for 4h,(b)annealed for 5h.These results reveal the existence of two diﬀerent relaxation mechanisms:generation dislocation in the dots and formation coherent relaxed dots.When the quantum dots grow,the relaxation of quantum dots is the competing of the lattice distortion (coherent re-laxed dots)with the formation of the dislocation (dis-located relaxed dots).The theory developed by Van-derbilt and Wickham [9]compares the two mechanisms of elastic relaxation and yields a phase diagram of a lattice mismatched system in which all possible mor-phologies are present,i.e.,uniform ﬁlms,dislocated dots,and coherent dots.No.1HAN Gen-Quan et al.245It was shown by Vanderbilt and Wickham that morphology of the mismatched system is determined by the ratio of the energy of interface between dots and the wetting layer (E interface )to the change of the sur-face energy (∆E surf ).[9]The deposited material wets the substrate ﬁrstly,and then the 2D strained ﬁlm transforms to the 3D quantum dots.If ∆E surf is posi-tive and large,or if the energy of the interface between the dots and the wetting layer is relatively small,the formation of coherently strained dots is not favoured.With an increase in the amount of deposited material,a transition occurs from uniform ﬁlm to dislocated dots,and the coherently strained dots are not formed.If ∆E surf is positive and small,or if the energy of the dislocated interface is relatively large,with an increase in the amount of deposited material,a transition oc-curs from a uniform ﬁlm to coherent dots.Further de-position may cause the onset of dislocations.The de-tailed calculation and the phase diagram can be found in Ref.[9].Fig.5.Schematic diagram of the relaxation process of the SiGe quantum dots on the Si 0.77Ge 0.23ﬁlm.This theory can be used to interpret the diﬀer-ent relaxation modes of the Ge and SiGe dots.It is sure that the pyramidal laser induced Ge dots,with the diameter of about 20–25nm and density of about 6×1010cm −2,do not exhaust the Ge ﬁlm with the thickness more than 1nm (8monolayers).Because no bulk diﬀusion occurs during the annealing,atoms intermixing between the dots and the wetting layer need not be considered.We think that the pure Ge LIQDs are formed on the Ge ﬁlm,i.e.,there is no in-terface between the dots and the wetting layer.For the SiGe LIQDs on the Si 0.77Ge 0.23ﬁlm,based on the surface chemical potential calculation,we show that the heavily strained SiGe quantum dots must have a misﬁt above 0.035corresponding to a Ge composi-tion of about 83%,to promise E surf <0(the dots stable under ELA).[7]This indicates the SiGe dots are Ge richer than the Si 0.77Ge 0.23ﬁlm,which also results from that the surface diﬀusion coeﬃcient of Ge is 102–103times greater than that of Si.[11]If the atoms interdiﬀusion is neglected,there should be an obvious interface between the SiGe quantum dots and the Si 0.77Ge 0.23wetting layer.It is suggested theoret-ically by Vanderbilt and Wickham and supported by our experiments that the interface between the quan-tum dots and the wetting layer plays a pivotal role in the competition between the lattice distortion and the formation of dislocation.Vanderbilt and Wickham’s theory is proven by our results and also conﬁrms and enforces our previous conclusion that the pure Ge dots and an abrupt inter-face between the dots and wetting layer are availablewhich is attributed to no bulk atoms diﬀusion under ELA.In conclusion,we have studied the diﬀerent relax-ation mechanisms of the Ge and SiGe quantum dots on Ge and Si 0.77Ge 0.23ﬁlms,respectively,under ELA.We recover the pivotal role of the interface between the dots and the wetting layer.The relaxation of Ge dots by dislocation is attributed to no interface between Ge dots and the Ge layer,and that of SiGe dots by lattice tetragonal distortion results from the obvious interface between SiGe dots and the Si 0.77Ge 0.23ﬁlm.This is sustained by Vanderbilt and Wickham’s theory.References[1]Baribeau J M,Wu X,Rowell N L and Lockwood D J 2006J.Phys.:Condens.Matter 18R139[2]TersoﬀJ and LeGoues F K 1994Phys.Rev.Lett.723570[3]Sutter P,Schick I,Ernst W and Sutter E 2003Phys.Rev.Lett.91176102[4]Rastelli A,Stoﬀel M,TersoﬀJ,Kar G S and Schimidt O G2005Phys.Rev.Lett.95026103[5]Montalenti F,Raiteri P,Migas D B,von K¨a nel H,RastelliA,Manzano C,Costantini G,Denker U,Schimidt O G,Kern K and Miglio L 2004Phys.Rev.Lett.93216102[6]Kamins T I,Medeiros-Ribeiro G,Ohlberg D A A andWilliams R S 1999J.Appl.Phys.851159[7]Han G Q,Zeng Y G,Yu J Z,Cheng B W and Yang H T2007J.Cryst.Growth (submitted)[8]Misra N,Xu L,Pan Y L,Cheung N and Grigoropoulos CP 2007Appl.Phys.Lett.90111111[9]Vanderbilt D and Wickham L K 1991Mater.Res.Soc.Symp.Proc.202555[10]Rastelli A,Stoﬀel M,TersoﬀJ,Kar G S and Schmidt O G2005Phys.Rev.Lett.95026103[11]Huang L,Liu F,Lu G-H and Gong X G 2000Phys.Rev.Lett.96016103。

Smooth Projective Hashing and Two-Message Oblivious Transfer

Smooth Projective Hashing and Two-MessageOblivious TransferYael Tauman KalaiMassachusetts Institute of Technologytauman@,/∼taumanAbstract.We present a general framework for constructing two-messageoblivious transfer protocols using a modiﬁcation of Cramer and Shoup’snotion of smooth projective hashing(2002).Our framework is actuallyan abstraction of the two-message oblivious transfer protocols of Naorand Pinkas(2001)and Aiello et.al.(2001),whose security is based onthe Decisional Diﬃe Hellman Assumption.In particular,this frameworkgives rise to two new oblivious transfer protocols.The security of oneis based on the N’th-Residuosity Assumption,and the security of theother is based on both the Quadratic Residuosity Assumption and theExtended Riemann Hypothesis.When using smooth projective hashing in this context,we must dealwith maliciously chosen smooth projective hash families.This raises newtechnical diﬃculties that did not arise in previous applications,and inparticular it is here that the Extended Riemann Hypothesis comes intoplay.Similar to the previous two-message protocols for oblivious transfer,ourconstructions give a security guarantee which is weaker than the tradi-tional,simulation based,deﬁnition of security.Nevertheless,the securitynotion that we consider is nontrivial and seems to be meaningful forsome applications in which oblivious transfer is used in the presence ofmalicious adversaries.1IntroductionIn[CS98],Cramer and Shoup introduced theﬁrst CCA2secure encryption scheme,whose security is based on the Decisional Diﬃe Hellman(DDH)As-sumption.They later presented an abstraction of this scheme based on a new notion which they called“smooth projective hashing”[CS02].This abstrac-tion yielded new CCA2secure encryption schemes whose security is based on the Quadratic Residuosity Assumption or on the N’th Residuosity Assumption [Pa99].1This notion of smooth projective hashing was then used by Genarro Supported in part by NSF CyberTrust grant CNS-04304501The N’th Residuosity Assumption is also referred to in the literature as the Deci-sional Composite Residuosity Assumption and as Paillier’s Assumption.and Lindell[GL03]in the context of key generation from humanly memoriz-able passwords.Analogously,their work generalizes an earlier protocol for this problem[KOY01],whose security is also based on the DDH Assumption.In this paper,we use smooth projective hashing to construct eﬃcient two-message oblivious transfer protocols.Our work follows the above pattern,in that it generalizes earlier protocols for this problem[NP01,AIR01]whose security is based on the DDH assumption.Interestingly,using smooth projective hashing in this context raises a new issue.Speciﬁcally,we must deal with maliciously chosen smooth projective hash families.This issue did not arise in the previous two applications because these were either in the public key model or in the common reference string model.1.1Oblivious TransferOblivious transfer is a protocol between a sender,holding two stringsγ0and γ1,and a receiver holding a choice bit b.At the end of the protocol the receiver should learn the string of his choice(i.e.,γb)but learn nothing about the other string.The sender,on the other hand,should learn nothing about the receiver’s choice b.Oblivious transfer,ﬁrst introduced by Rabin[Rab81],is a central primitive in modern cryptography.It serves as the basis of a wide range of cryptographic tasks.Most notably,any secure multi-party computation can be based on a secure oblivious transfer protocol[Y86,GMW87,Kil88].Oblivious transfer has been studied in several variants,all of which have been shown to be equivalent. The variant considered in this paper is the one by Even,Goldreich and Lempel [EGL85](a.k.a.1-out-of-2oblivious transfer),shown to be equivalent to Rabin’s original deﬁnition by Cr´e peau[Cre87].The study of oblivious transfer has been motivated by both theoretical and practical considerations.On the theoretical side,much work has been devoted to the understanding of the hardness assumptions required to guarantee obliv-ious transfer.In this context,it is important to note that known construc-tions for oblivious transfer are based on relatively strong computational as-sumptions–either speciﬁc assumptions such as factoring or Diﬃe Hellman (cf.[Rab81,BM89,NP01,AIR01])or generic assumption such as the existence of enhanced trapdoor permutations(cf.[EGL85,Gol04,Hai04]).Unfortunately, oblivious transfer cannot be reduced in a black box manner to presumably weaker primitives such as one-way functions[IR89].On the practical side,research has been motivated by the fact oblivious transfer is considered to be the main bottle-neck with respect to the amount of computation required by secure multiparty protocols.This makes the construction of eﬃcient protocols for oblivious transfer a well-motivated task.In particular,constructing round-eﬃcient oblivious transfer protocols is an important task.Indeed,[NP01](in Protocol4.1)and[AIR01]independently constructed a two-message(1-round)oblivious transfer protocol based on the DDH Assumption(with weaker security guarantees than the simulation based security).Their work was the starting point of our work.1.2Smooth Projective HashingSmooth projective hashing is a beautiful notion introduced by Cramer and Shoup [CS02].To deﬁne this notion they rely on the existence of a set X(actually a distribution on sets),and an underlying N P-language L⊆X(with an associ-ated N P-relation R).The basic hardness assumption is that it is infeasible to distinguish between a random element in L and a random element in X\L.This is called a hard subset membership problem.A smooth projective hash family is a family of hash functions that operate on the set X.Each function in the family has two keys associated with it:a hash key k,and a projection keyα(k).Theﬁrst requirement(which is the standard requirement of a hash family)is that given a hash key k and an element x in the domain X,one can compute H k(x).There are two additional requirements: the“projection requirement”and the“smoothness requirement.”The“projection requirement”is that given a projection keyα(k)and an element in x∈L,the value of H k(x)is uniquely determined.Moreover,com-puting H k(x)can be done eﬃciently,given the projection keyα(k)and a pair (x,w)∈R.The“smoothness requirement,”on the other hand,is that given a random projection key s=α(k)and any element in x∈X\L,the value H k(x) is statistically indistinguishable from random.1.3Our resultsWe present a methodology for constructing a two-message oblivious transfer pro-tocol from any(modiﬁcation of a)smooth projective hash family.In particular, we show how the previously known(DDH based)protocols of[NP01,AIR01]can be viewed as a special case of this methodology.Moreover,we show that this methodology gives rise to two new oblivious transfer protocols;one based on the N’th Residuosity Assumption,and the other based on the Quadratic Residuosity Assumption along with the Extended Riemann Hypothesis.Our protocols,similarly to the protocols of[NP01,AIR01],are not known to be secure according to the traditional simulation based deﬁnition.Yet,they have the advantage of providing a certain level of security even against malicious adversaries without having to compromise on eﬃciency(see Section3for further discussion on the guaranteed level of security).The basic idea.Given a smooth projective hash family for a hard subset mem-bership problem(which generates pairs X,L according to some distribution), consider the following two-message protocol for semi-honest oblivious transfer. Recall that the sender’s input is a pair of stringsγ0,γ1and the receiver’s input is a choice bit b.R→S:Choose a pair X,L(with an associated NP-relation R L)according to the speciﬁed distribution.Randomly generate a triplet(x0,x1,w b)where x b∈R L,(x b,w b)∈R L,and x1−b∈R X\L.Send(X,x0,x1).S→R:Choose independently two random keys k0,k1for H and sendα(k0)andα(k1)along with y0=γ0⊕H k0(x0)and y1=γ1⊕H k1(x1).R:Retrieveγb by computing y b⊕H kb (x b),using the witness w b and the pro-jection keyα(k b).The security of the receiver is implied by the hardness of the subset mem-bership problem on X.Speciﬁcally,guessing the value of b is equivalent to dis-tinguishing between a random element in L and a random element in X\L. The security of the sender is implied by the smoothness property of the hash family H.Speciﬁcally,given a random projection keyα(k)and any element in x∈X\L,the value H k(x)is statistically indistinguishable from random.Thus, the message y1−b gives no information aboutγ1−b(since x1−b∈X\L).Note that the functionality of the protocol is implied by the projection property. Technical diﬃculty.Notice that when considering malicious receivers,the security of the sender is no longer guaranteed.The reason is that there is no guarantee that the receiver will choose x1−b∈X\L.A malicious receiver might choose x0,x1∈L and learn both values.To overcome this problem,we extend the notion of a hard subset membership problem so that it is possible to verify that at least one of x0,x1belongs to X\L.This should work even if the set X is maliciously chosen by the receiver.It turns out that implementing this extended notion in the context of the DDH assumption is straightforward[NP01,AIR01].Loosely speaking,in this case X is generated by choosing a random prime p,and choosing two random elements g0,g1in Z∗p of some prime order q.The resulting set X is deﬁned by X {(g r00,g r11):r0,r1∈Z q},the corresponding language L is deﬁned by L {(g r0,g r1):r∈Z q},and the witness of each element(g r0,g r1)∈L is its discrete logarithm r.In order to enable the sender to verify that two elements x0,x1are not both in L,we instruct the receiver to generate x0,x1by choosing at random two distinct elements r0,r1∈Z q,setting x b=(g r00,g r01),w b=r0,and x1−b=(g r00,g r11).Notice that x b is uniformly distributed in L,x1−b is uniformly distributed in X\L,and the sender can easily check that it is not the case that both x0and x1are in L by merely checking that they agree on theirﬁrst coordinate and diﬀer on their second coordinate.Implementing this veriﬁability property in the context of the N’th Residuos-ity Assumption and the Quadratic Residuosity Assumption is not as easy.This part contains the bulk of technical diﬃculties of this work.In particular,this is where the Extended Riemann Hypothesis comes into play in the context of Quadratic Residuosity.2Smooth Projective Hash FunctionsOur deﬁnition of smooth projective hashing diﬀers from its original deﬁnition in [CS02].The main diﬀerence(from both[CS02]and[GL03])is in the deﬁnition of the smoothness requirement,which we relax to Y-smoothness,and in the deﬁnition of a subset membership problem,where we incorporate an additional requirement called Y-veriﬁability.Notation.The security parameter is denoted by n .For a distribution D ,x ←D denotes the action of choosing x according to D ,and x ∈support (D )means that the distribution D samples the value x with positive probability.We denote by x ∈R S the action of uniformly choosing an element from the set S .For any two random variables X,Y ,we say that X and Y are -close if Dist (X,Y )≤ ,where Dist (X,Y )denotes the statistical diﬀerence between X and Y .2We say that the ensembles {X n }n ∈N and {Y n }n ∈N are statistically indistinguishable if there exists a negligible function (·)such that for every n ∈N ,the random variables X n and Y n are (n )-close.3Recall that a function ν:N →N is said to be negligible if for every polynomial p (·)and for every large enough n ,ν(n )<1/p (n ).Hard subset membership problems.A subset membership problem M spec-iﬁes a collection {I n }n ∈N of distributions,where for every n ,I n is a probability distribution over instance descriptions .Each instance description Λspeciﬁes two ﬁnite non-empty sets X,W ⊆{0,1}poly (n ),and an NP-relation R ⊂X ×W ,such that the corresponding language L {x :∃w s.t.(x,w )∈R }is non-empty.For every x ∈X and w ∈W ,if (x,w )∈R ,we say that w is a witness for x .We use the following notation throughout the paper:for any instance description Λwe let X (Λ),W (Λ),R (Λ)and L (Λ)denote the sets speciﬁed by Λ.Loosely speaking,subset membership problem M ={I n }n ∈N is said to be hard if for a random instance description Λ←I n ,it is hard to distinguish random members of L (Λ)from random non-members.Deﬁnition 1(Hard subset membership problem).Let M ={I n }n ∈N be a subset membership problem as above.We say that M is hard if the ensembles{Λn ,x 0n }n ∈N and {Λn ,x 1n }n ∈N are computationally indistinguishable,where Λn ←I n ,x 0n ∈R L (Λn ),and x 1n ∈R X (Λn )\L (Λn ).4Projective hash family.We next present the notion of a projective hash family with respect to a hard subset membership problem M ={I n }n ∈N .Let H ={H k }k ∈K be a collection of hash functions.K ,referred to as the key space,consists of a set of keys such that for each instance description Λ∈M ,5there is a subset of keys K (Λ)⊆K corresponding to Λ.For every Λand for every k ∈K (Λ),H k is a hash function from X (Λ)to G (Λ),where G (Λ)is some ﬁnite non-empty set.We denote by G = Λ∈M G (Λ).We deﬁne a projection key function α:K →S ,where S is the space of projection rmally,2Recall that Dist (X,Y ) 1 s ∈S |P r [X =s ]−P r [Y =s ]|,or equivalently,Dist (X,Y ) max S ⊂S |P r [X ∈S ]−P r [Y ∈S ]|,where S is any set that con-tains the support of both X and Y .3For simplicity,throughout this paper we say that two random variables X n and Y n are statistically indistinguishable,meaning that the corresponding distribution ensembles {X n }n ∈N and {Y n }n ∈N are statistically indistinguishable.4Note that this hardness requirement also implies that it is hard to distinguish be-tween a random element x ∈R L (Λ)and a random element x ∈R X (Λ).We will use this fact in the proof of Theorem 1.5We abuse notation and let Λ∈M denote the fact that Λ∈support (I n )for some n .a family(H,K,S,α,G)is a projective hash family for M if for every instance descriptionΛ∈M and for every x∈L(Λ),the projection key s=α(k)uniquely determines H k(x).(We stress that the projection key s=α(k)is only guaranteed to determine H k(x)for x∈L(Λ),and nothing is guaranteed for x∈X(Λ)\L(Λ).) Deﬁnition2(Projective hash family).(H,K,S,α,G)is a projective hash family for a subset membership problem M if for every instance description Λ∈M there is a well deﬁned(not necessarily eﬃcient)function f such that for every x∈L(Λ)and every k∈K(Λ),f(x,α(k))=H k(x).Eﬃcient projective hash family.We say that a projective hash family is eﬃcient if there exist polynomial time algorithms for:(1)Sampling a key k∈R K(Λ)givenΛ;(2)Computing a projectionα(k)fromΛand k∈K(Λ);(3) Computing H k(x)fromΛ,k∈K(Λ)and x∈X(Λ);and(4)Computing H k(x) fromΛ,(x,w)∈R(Λ)andα(k),where k∈K(Λ).Notice that this gives two ways to compute H k(x):either by knowing the hash key k,or by knowing the projection keyα(k)and a witness w for x.Y-smooth projective hash family.Let Y be any function from instance de-scriptionsΛ∈M to subsets Y(Λ)⊆X(Λ)\L(Λ).Loosely speaking,a projective hash family for M is Y-smooth if for every instance descriptionΛ=(X,W,R), for every x∈Y(Λ),and for a random k∈R K(Λ),the projection keyα(k) reveals(almost)nothing about H k(x).Deﬁnition3(Y-smooth projective hash family).A projective hash family (H,K,S,α,G)for a subset membership problem M is said to be Y-smooth if for every(even maliciously chosen)instance descriptionΛ=(X,W,R)and every x∈Y(Λ),the random variables(α(k),H k(x))and(α(k),g)are statistically indistinguishable,where k∈R K(Λ)and g∈R G(Λ).6A Y-smooth projective hash family thus has the property that a projection of a (random)key enables the computation of H k(x)for x∈L,but gives almost no information about the value of H k(x)for x∈Y(Λ).Remark.This deﬁnition of Y-smooth projective hash family diﬀers from the original deﬁnition proposed in[CS02]in two ways.First,it requires the smooth-ness property to hold against maliciously chosen instance descriptionsΛ,whereas in[CS02]the smoothness is only with respect toΛ∈M.Second,it requires the smoothness property to hold with respect to every x∈Y,whereas in[CS02]the smoothness condition is required to hold for randomly chosen x∈R X\L.The main reason for our divergence from the original deﬁnition in[CS02] is that we need to cope with maliciously chosenΛ.We would like to set Y= X\L(as in[CS02]),and construct a(X\L)-smooth projective hash fam-ily.However,we do not know how to construct such a family,for which the 6We assume throughout this paper,without loss of generality,that a(maliciously chosen)Λhas the same structure as an honestly chosenΛ.smoothness condition holds for every(even maliciously chosen)Λ.7Therefore, we relax our smoothness requirement and require only Y-smoothness,for some Y⊆X\L.In both our constructions of Y-smooth projective hash families, Y(Λ)⊂X(Λ)\L(Λ)for maliciously chosenΛ∈M,and Y(Λ)=X(Λ)\L(Λ)for every honestly chosenΛ∈M.Jumping ahead,the latter will enable the(honest) receiver to choose x b∈R L(Λ),x1−b∈R X(Λ)\L(Λ)such that x1−b is also in Y(Λ).This will enable the(honest)sender to be convinced of its security by checking that either x0or x1is in Y(Λ),and it will enable the(honest)receiver to be convinced that a(dishonest)sender cannot guess the bit b,assuming the underlying subset membership problem is hard.(From now on the reader should think of Y(Λ)as equal to X(Λ)\L(Λ)for everyΛ∈M.)Thus,we need a subset membership problem M such that for every honestly chosenΛ∈M it is easy to sample uniformly from both L(Λ)and X(Λ)\L(Λ). On the other hand,for every(even maliciously chosen)(Λ,x0,x1)it is easy to verify that either x0∈Y(Λ)or x1∈Y(Λ).To this end we deﬁne the notion of a“Y-veriﬁably samplable”subset membership problem.Deﬁnition4(Y-veriﬁably samplable subset membership problem).A subset membership problem M={I n}n∈N is said to be Y-veriﬁably samplable if the following conditions hold.1.Problem samplability:There exists a probabilistic polynomial-time algorithmthat on input1n,samples an instanceΛ=(X,W,R)according to I n.2.Member samplability:There exists a probabilistic polynomial-time algorithmthat on input an instance descriptionΛ=(X,W,R)∈M,outputs an ele-ment x∈L together with its witness w∈W,such that the distribution of x is statistically close to uniform on L.3.Non-member samplability:There exists a probabilistic polynomial-time al-gorithm A that given an instance descriptionΛ=(X,W,R)∈M and an element x0∈X,outputs an element x1=A(Λ,x0),such that if x0∈R L then the distribution of x1is statistically close to uniform on X\L,and if x0∈R X then the distribution of x1is statistically close to uniform on X.4.Y-Veriﬁability:There exists a probabilistic polynomial-time algorithm B,thatgiven any triplet(Λ,x0,x1),veriﬁes that there exists a bit b such that x b∈Y(Λ).This should hold even ifΛis maliciously chosen.Speciﬁcally:–For everyΛand every x0,x1,if both x0∈Y(Λ)and x1∈Y(Λ)then B(Λ,x0,x1)=0.–For every honestly chosenΛ∈M and every x0,x1,if there exists b such that x b∈L(Λ)and x1−b∈support(A(Λ,x b)),then B(Λ,x0,x1)=1.For simplicity,throughout the paper we do not distinguish between uniform and statistically close to uniform distributions.This is inconsequential.7We note that[CS02,GL03]did not deal with maliciously chosenΛ’s,and indeed the smoothness property of their constructions does not hold for maliciously chosenΛ’s.3Security of Oblivious TransferOur deﬁnition of oblivious transfer is similar to the ones considered in previous works on oblivious transfer in the Bounded Storage Model[DHRS04,CCM98].A similar(somewhat weaker)deﬁnition was also used in[NP01]in the context of their DDH based two message oblivious transfer protocol.In what follows we let viewˆS (ˆS(z),R(b))denote the view of a cheating senderˆS(z)after interacting with R(b).This view consists of its input z,its random coin tosses,and the messages that it received from R(b)during the interaction.Similarly,we let viewˆR (S(γ0,γ1),ˆR(z))denote the view of a cheating ReceiverˆR(z)after interacting with S(γ,γ1).Deﬁnition5(Secure implementation of Oblivious Transfer).A two party protocol(S,R)is said to securely implement oblivious transfer if it is a protocol in which both the sender and the receiver are probabilistic polynomial time machines that get as input a security parameter n in unary representation.Moreover,the sender gets as input two stringsγ0,γ1∈{0,1} (n),the receiver gets as input a choice bit b∈{0,1},and the following conditions are satisﬁed:–Functionality:If the sender and the receiver follow the protocol then for any security parameter n,any two input stringsγ0,γ1∈{0,1} (n),and any bit b,the receiver outputsγb whereas the sender outputs nothing.8–Receiver’s security:For any probabilistic polynomial-time adversaryˆS,exe-cuting the sender’s part,for any security parameter n,and for any auxiliary input z of size polynomial in n,the view thatˆS(z)sees when the receiver tries to obtain theﬁrst message is computationally indistinguishable from the view it sees when the receiver tries to obtain the second message.That is,{viewˆS (ˆS(z),R(1n,0))}n,z c≡{viewˆS(ˆS(z),R(1n,1))}n,z–Sender’s security:For any deterministic(not necessarily polynomial-time) adversaryˆR,executing the receiver’s part,for any security parameter n,for any auxiliary input z of size polynomial in n,and for anyγ0,γ1∈{0,1} (n), there exists a bit b such that for everyψ∈{0,1} (n),the view ofˆR(z)when interacting with S(1n,γb,ψ),and the view ofˆR(z)when interacting with S(1n,γ0,γ1),are statistically indistinguishable.9That is,{viewˆR (S(1n,γ0,γ1),ˆR(z))}n,γ,γ1,zs≡{viewˆR(S(1n,γb,ψ),ˆR(z))}n,γb,ψ,zNote that Deﬁnition5(similarly to the deﬁnitions in[DHRS04,NP01])de-parts from the traditional,simulation based,deﬁnition in that it handles the security of the sender and of the receiver separately.This results in a some-what weaker security guarantee,with the main drawback being that neither the 8This condition is also referred to as the completeness condition.9We abuse notation by letting S(1n,γb,ψ)denote S(1n,γ0,ψ)if b=0,and letting it denote S(1n,ψ,γ1)if b=1.sender nor the receiver are actually guaranteed to“know”their own input.(This is unavoidable in two message protocols using“standard”techniques).It is easy to show that Deﬁnition5implies simulatability for semi honest adversaries(the proof is omitted due to lack of space).More importantly,Deﬁni-tion5also gives meaningful security guarantees in face of malicious participants. In the case of a malicious sender,the guarantee is that the damage incurred by malicious participation is limited to“replacing”the input stringsγ0,γ1with a pair of strings that are somewhat“related”to the receiver’sﬁrst message(with-out actually learning anything about the receiver’s choice).In the case of a mali-cious receiver,Deﬁnition5can be shown to provide exponential time simulation of the receiver’s view of the interaction(similarly to the deﬁnition of[NP01]).In particular,the interaction gives no information to an unbounded receiver beyond the value ofγb.(Again,the proof is omitted due to lack of space.)4Constructing2-Round OT ProtocolsLet M={I n}n∈N be a hard subset membership problem which is Y-veriﬁably samplable,and let(H,K,S,α,G)be a an eﬃcient Y-smooth projective hash family for M.Recall that the Y-veriﬁably samplable condition of M implies the existence of algorithms A and B as described in Section2.We assume for simplicity that for any n and for anyΛ∈I n,G(Λ)={0,1} (n), and that the two messagesγ0,γ1,to be transferred in the OT protocol,are binary strings of length at most (n).Let n be the security parameter.Let(γ0,γ1)be the input of the sender and let b∈{0,1}be the input of the receiver.R→S:The receiver chooses a random instance descriptionΛ=(X,W,R)←I n.It then samples a random element x b∈R L together with its corre-sponding witness w b,using the member samplability algorithm,and invokes Algorithm A on input(Λ,x b)to obtain a random element x1−b∈X\L.It sends(Λ,x0,x1).S→R:The sender invokes algorithm B on input(Λ,x0,x1)to verify that there exists a bit b such that x1−b∈Y(Λ).If B outputs0then it aborts,and ifB outputs1then it chooses independently at random k0,k1∈R K(Λ),andsendsα(k0)andα(k1)along with y0=γ0⊕H k0(x0)and y1=γ1⊕H k1(x1).R:The receiver retrievesγb by computing y b⊕H kb (x b)using the projectionkeyα(k b)and the pair(x b,w b).We next prove that the above protocol is secure according to Deﬁnition5. Intuitively,the receiver’s security follows from the fact that x b is uniformly distributed in L,x1−b is uniformly distributed in X\L,and from the assumption that it is hard to distinguish random L elements from random X\L elements. The sender’s security follows from the assumption that(H,K,S,α,G)is a Y-smooth projective hash family for M,and from the assumption that one of x0 or x1is in Y(Λ)(otherwise,it will be detected by B and the sender will abort).Theorem1.The above2-round OT protocol is secure according Deﬁnition5,assuming M is a Y-veriﬁably samplable hard subset membership problem,and assuming(H,K,S,α,G)is a Y-smooth projective hash family for M.Proof.we start by proving the receiver’s security.Assume for the sake of con-tradiction that there exists a(malicious)probabilistic polynomial-time senderˆS such that for inﬁnitely many n’s there exists a polynomial size auxiliary input z n such thatˆS(z n)can predict(with non-negligible advantage)the choice bit b when interacting with R(1n,b).In what follows,we useˆS(z n)to break the hard-ness of M,by distinguishing between x∈R L and x∈R X.Given an instance descriptionΛ=(X,W,R)←(I n)and an element x∈X:1.Choose at random a bit b and let x b=x2.Apply algorithm A on input(Λ,x b)to obtain an element x1−b.3.FeedˆS(z n)the message(Λ,x0,x1),and obtain its prediction bit b .4.If b =b then predict“x∈R L”and if b =b then predict“x∈R L.”Notice that if x b∈R L thenˆS(z n)will predict the bit b with non-negligible advantage(follows from our contradiction assumption).On the other hand,if x b∈R X then x1−b is also uniformly distributed in X.In this case it is impossible (information theoretically)to predict b.We now turn to prove the sender’s security.LetˆR be any(not necessarily polynomial time)malicious receiver,and for any n∈N,let z n be any polynomial size auxiliary information given toˆR.Let(Λn,x0,x1)be theﬁrst message sent by ˆR(zn).Our goal is to show that for every n∈N and for everyγ0,γ1∈{0,1} (n),there exists b∈{0,1}such that the random variables viewˆR(S(1n,γ0,γ1),ˆR(z n))and viewˆR (S(1n,γb,ψ),ˆR(z n))are statistically indistinguishable.We assume without loss of generality that either x0∈Y(Λn)or x1∈Y(Λn). If this is not the case,the sender aborts the execution and b can be set to either0 or1.Let b be the bit satisfying x1−b∈Y(Λn).By the Y-smoothness property of the hash family,the random variables(α(k),H k(x1−b))and(α(k),g)are statis-tically indistinguishable,for a random k∈R K(Λn)and a random g∈R G(Λn). This implies that the random variables(α(k),γ1−b⊕H k(x1−b))and(α(k),g) are statistically indistinguishable,which implies that viewˆR(S(1n,γ0,γ1),ˆR(z))and viewˆR(S(1n,γb,ψ),ˆR(z))are statistically indistinguishable.5Constructing Smooth Projective Hash FamiliesWe next present two constructions of Y-smooth projective hash families for hard subset membership problems which are Y-veriﬁably samplable.One based on the N’th Residuosity Assumption,and the other based on the Quadratic-Residuosity Assumption together with the Extended Reimann Hypothesis.A key vehicle in both constructions is the notion of an( ,Y)-universal projective hash family. Deﬁnition6(Universal projective hash families).Let M={I n}n∈N be any hard subset membership problem.A projective hash family(H,K,S,α,G)。

标准模型的CP破坏

标准模型的CP破坏在现代粒子物理中，标准模型是一种成功描述了基本粒子相互作用的理论框架。

其中一个重要的破坏因素是CP破坏，指的是在物理过程中，粒子与反粒子的性质（如荷电性和宇称）不对称的现象。

本文将介绍标准模型中CP破坏的原因和影响，并讨论相关的实验验证和理论发展。

一、CP破坏的原因标准模型认为，CP破坏可能是由以下几个因素导致的：1. 强相互作用的CP破坏：标准模型中的强相互作用由夸克之间的胶子交换引起。

然而，实验观测到夸克和反夸克之间的差异，这表明了强相互作用的CP破坏。

2. 弱相互作用的CP破坏：标准模型中的弱相互作用由W和Z玻色子传递。

然而，实验观测到弱力相互作用中的一些现象不符合CP对称，如K介子的弱衰变。

3. 电弱相互作用的CP破坏：标准模型将电磁力和弱力看作是统一的电弱力。

但是，由于电磁和弱力相互作用的差异，电弱相互作用中的CP破坏也不可避免。

二、CP破坏的实验验证为了验证标准模型中的CP破坏，科学家们进行了一系列的实验研究。

以下是其中几个重要的实验结果：1. 希格斯粒子的CP性质：2013年，欧洲核子研究组织（CERN）的大型强子对撞机（LHC）实验室发现了希格斯粒子。

通过进一步的实验研究，科学家们确定了希格斯粒子的CP性质。

2. B介子的CP破坏：研究人员通过对B介子的精确测量，观测到了B介子的弱衰变中的CP破坏现象。

这一结果对于验证标准模型中弱相互作用的CP破坏提供了重要证据。

3. 中性介子的CP破坏：中性介子的混合和CP破坏被广泛研究。

实验观测到了中性介子的弱衰变中的CP破坏现象，并与理论计算结果相吻合。

三、CP破坏的理论发展标准模型虽然成功地描述了基本粒子相互作用，但它无法解释CP 破坏的原因和程度。

为了解决这个问题，科学家们提出了一些超出标准模型的理论，并进行了相关的研究：1. 超对称理论：超对称理论是一种扩展标准模型的理论框架，其引入了超对称粒子。

这些粒子可以解释CP破坏现象，并解决一些标准模型中的问题。

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arXiv:hep-ph/9507445v3 3 Aug 1995HEPHY-PUB624/95UWThPh-1995-9June1995

CP–violatingasymmetriesintop–quarkproductionanddecayine+e−annihilationwithintheMSSM

AlfredBartlInstitutf¨urTheoretischePhysik,Universit¨atWienA–1090Vienna,Austria

EkaterinaChristovaInstituteofNuclearResearchandNuclearEnergyBoul.TzarigradskoChaussee72,Soﬁa1784,Bulgaria.

WalterMajerottoInstitutf¨urHochenergiephysik,¨OsterreichischeAkademiederWissenschaftenA–1050Vienna,Austria

AbstractWeobtainanalyticformulaeforthecrosssectionofthesequentialprocessesofe+e−→t¯tandt→bl+ν/¯t→¯bl−¯νinthelaboratoryframe,wherethedependenceontripleproductcorrelationsofthetype(ˆq1×ˆq2·ˆq3),inducedbyCPviolationbothintheproductionandthedecayareexplicitelyshown.DiﬀerentobservablessensitivetoCPviolationaredeﬁnedandcalculatedintheMinimalSupersymmetricStandardModel(MSSM).TheobservablessensitivetoCPviolationareoftheorderof10−3.Thedependenceonthemassesofthesupersymmetricparticlesisalsoshown.1.IntroductionPrecisionmeasurementsofvariousproductionanddecaymodesofthetopquarkareexpectedtoprovidealsoinformationaboutphysicsbeyondtheStandardModel(SM).TestingnewphysicsinobservableswhicharesensitivetoCPviolationseemsespeciallypromising.Asthetopquarkdoesnotmixwithothergenerations,theGIMmechanismofunitarityconstraintsleadstonegligiblysmalleﬀectsofCPviolationintheSM.Thus,observationofCPnoninvarianceintop–quarkphysicswoulddeﬁnitelybeasignalforphysicsbeyondtheSM[1,2,3,4,5].HereweshallconsiderCPviolationinducedbysupersymmetry(SUSY).IntheMinimalSupersymmetricStandardModel(MSSM)[6],therearemorepossibilitiestointroducecomplexcouplingsthanintheSM.Evenwithoutgenerationmixing,nonzerocomplexphasescanoccurintheLagrangianthatcannotberotatedawaybyasuitablerediﬁnitionoftheﬁelds.TheygiverisetoCPviolationwithinasinglegeneration,freeoftheunitaritysupressionoftheGIMmechanism.Intop–quarkproductionanddecayCPviolationisduetoradiativecorrections.ThemagnitudeisdeterminedbytheratioofthemassesofthetopquarkandtheSUSYparticlesintheloop.Havinginmindthelargetop–quarkmass,mt=175GeV[7],wemayexpectthattheCP–violatingeﬀectsareonlymoderatelysuppressed.Thus,testingSUSYthroughCP–violatingobservablesintop–quarkphysicsisapromisingtaskforfuturecolliders.Here,aspossibleevidenceofCPviolationweconsiderT–oddtripleproductcorrelationsofthetype

(q1q2q3)≡(q1×q2·q3)(1)whereq1,2,3canbeanyoneofthe3–momentaine+e−→t¯torofthet(¯t)–decayproductst→bl+ν(¯t→¯bl−¯ν).Thismethodhasbeenproposedin[1,2]forageneralstudyofCPviolationint¯tproductionine+e−annihilationandinppcollisions.Thecorrelations(1)arecalledT–oddastheychangesignunderaﬂipofthe3–momentainvolved.However,thisdoesneitherimplytime–reversalnoninvariancenorCPviolationifCPTisassumed.Whenloopcorrectionsareincluded,T–oddcorrelationscanariseeitherfromabsorptivepartsintheamplitude(so-calledﬁnalstateinteractions[8]),orfromCPviolation.TheformereﬀectisaconsequenceoftheunitarityoftheS–matrix,anditcanbeeliminatedeitherbytakingthediﬀerencebetweentheprocessweareinterestedinanditsCPconjugate[9]or

1bydirectestimates.T–oddcorrelationsintheSMduetogluonorHiggsbosonexchangeintheﬁnalstateshaverecentlybeenconsideredin[10].Notethatincolliderexperimentstop–antitopquarkpairswillbecopiouslypro-ducedandthedecaymodest→bl+νand¯t→¯bl−¯νwilloccursimultaneously.Therefore,itwillbepossibletoformthediﬀerencebetweenthetwoconjugateprocessesinthesameexperiment.Theappearanceoftripleproductcorrelationsofthetype(1)canalsobeex-plainedbythefactthatthetop–quarkpolarizationhasnon–vanishingtransversecomponentsbothintheproductionplaneandperpendiculartoit.Becauseofthelargemassofthetopquarktheproducedtand¯tcanberegardedasfreequarkswithdeﬁnitemomentaandpolarizationsthatarenotaﬀectedbyhadronization.Thustheirpolarizationstatecanbeinferedfromthedistributionoftheirdecayproducts.Inthet¯tproductionprocess

e+(q¯l)+e−(ql)→t(pt)+¯t(p¯t),(2)aT–oddcorrelationinthec.m.systemis(ξqlpt)[3],whereξisthetop–quarkpolarizationvector.Evidently,thiscorrelationisdiﬀerentfromzeroonlyifξhasacomponentnormaltotheproductionplane.Inthesemileptonictand¯tdecays:

t→b(pb)l+(pl+)ν(pν)(3)¯t→¯b(p¯b)l−(pl−)¯ν(p¯ν)(4)

atripleproductcorrelationintherestframeofthetopquarkis(ξpbpl+)[4].Hereitisthepolarizationofthetopquarknormaltothedecayplanethatcontributes.IntheproductionaswellasinthedecayweshallonlyconsidercorrelationsduetoCPviolation.Asthepolarizationofthetopquarkisnotadirectlyobservablequantity,weobtaininformationabouttheabovespin–momentacorrelationsbytripleproductcorrelationsoftype(1)amongthe3-momentaoftheparticlesinthesequentialprocesses: