Modified Breit-Wigner formula for mesonic resonances describing OZI decays of confined $qba
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。
非线性动力学入门-西安交通大学教师个人主页
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另一方面梁的轴向应变的表达式也会因变形大小的不同而采用不同的表达式比如小变形时应变而当考虑大变形时可能采用的应变表达式就是进而得到的梁的振动方程将会是一个含有高度非线性项的偏微分方程组
非线性动力学入门
张新华
西安交通大学 工程力学系 2011 年 07 月
前 言
─1687 年，牛顿(Isaac Newton, 1643 ～ 1727)发表了《自然哲学之数学原 理》(Mathematical Principles of Natural Philosophy)，标志着经典力学(亦即牛 顿力学)的正式诞生。牛顿力学主要研究自由质点系的宏观运动规律。 ─1788 年，拉格朗日(Joseph Louis Lagrange, 1736 ～ 1813)发表了分析力 学教程(Analytical Mechanics)，标志着拉格朗日力学的诞生。Lagrange 力学属 于分析力学的主要内容之一，在位形空间中研究带有约束的质点系动力学。 ─1833 年，哈密尔顿(William Rowen Hamilton, 1805 ～ 1865)对 Lagrange 力学进行了改造，引进了相空间(2n 维空间)，对系统内在的对称性(辛对称， Symplectic)进行了刻画。狭义上的哈密尔顿力学只适用于保守系统，而广义 的哈密尔顿力学在适用于非保守系统。哈密尔顿力学也属于分析力学的主要 组成部分。在此后发展起来的量子力学中 Hamilton 力学发挥着巨大的作用。 目前在天体力学、计算 Hamilton 力学，量子力学，甚至弹性力学(即所谓的 辛弹性力学)中哈密尔顿力学依然发挥着重要作用。 ─1927 年，Birkhoff(George David Birkhoff, 1844 ～ 1944)发表了“动力系 统”(Dynamical Systems)，标志着 Birkhoff 动力学的正式问世。Birkhoff 动力 学建立了研究非完整力学的框架。 ─1892 ～ 1899， 彭加莱(Henri Poincaré, 1854 ～ 1912)发表了三卷本的“天 体力学中的新方法”(New Methods of Celestial Mechanics)，系统性地提出了 研究动力学系统的定性方法，即几何方法。经典力学的目标之一就是设法求 得系统的解析解，而 Poincaré意识到对于大多数非线性系统而言，求其解析 解是不可能的，而必须发展新的研究方法。他超越了他的时代，极富远见地 预测到了非线性系统混沌现象(系统的解对初始条件具有极端敏感依赖性)的 存在。更为重要的是，Poincaré开创了研究非线性动力系统的几何方法，当之 无愧地被誉为非线性科学之父，其影响是划时代的。 ─1892 年，李亚普诺夫(Aleksandr Mikhailovich Lyapunov, 1857 ～ 1918)在 他的博士论文“运动稳定性的一般问题”(General problem of the stability of motion )中，系统地探讨了非线性动力学系统的稳定性问题。他提出了两种研 究稳定性的方法：李亚普诺夫第一方法(间接方法)和李亚普诺夫第二方法(直 接方法)。他从代数角度出发，对动力学系统的研究开创了一个崭新的领域。 彭加莱与李亚普诺夫，前者从几何角度，后者从代数角度，开拓了非线 性科学的研究疆域和研究手段。 ─1963 年，Lorenz(Edward Norton Lorenz, 1917 ～ 2008)发表了“确定性 非周期流”(Deterministic Nonperiodic Flow)的论文，认为大气系统的性态对 初值极为敏感，从而导致准确的长期天气预报是不可能的。该文标志着人类 首次借助于计算机发现了混沌(Chaos)现象的存在。 ─1757 年，欧拉(Leonhard Euler, 1707 ～ 1783)发表了压杆稳定性的论 文，首次探讨了力学系统的分岔现象。作为分岔理论重要分支的突变理 论(Catastrophe Theory)则主要由法国数学家托姆(René Thom, 1923 ～ 2002)于 上个世纪 60 年代创立，由齐曼(Christopher Zeeman，1925 ～)在 70 年代大力 推广普及。 ─1834 年，英国的罗素(John Scott Russell, 1808 ～ 1882)骑着马在 Union 运河上散步时，发现了现在称之为孤立波(又称作孤波，Solitary wave)的 i
原子核β衰变寿命经验公式
原子核β衰变寿命经验公式
夏金戈;李伟峰;方基宇;牛中明
【期刊名称】《物理学报》
【年(卷),期】2024(73)6
【摘要】基于β衰变的费米理论,提出一个计算原子核β衰变寿命且不含自由参数的经验公式.通过引入奇偶效应、壳效应以及同位旋依赖,新提出的经验公式显著改进了对原子核β衰变寿命的预言精度.对于寿命小于1 s的原子核,新经验公式的预言结果与实验寿命常用对数的均方根偏差降至0.220,这比不含自由参数的经验公式提高约54%,甚至优于目前已有的其他经验公式和微观的准粒子无规相位近似方法.在未知核区,新经验公式预言的轻核区原子核的β衰变寿命一般短于各微观模型的预言结果,而其预言的重核区原子核的β衰变寿命与各微观模型预言结果基本一致.进一步采用新经验公式预言了核素图上丰中子原子核的β衰变寿命,为r-过程的模拟提供了寿命输入.
【总页数】8页(P176-183)
【作者】夏金戈;李伟峰;方基宇;牛中明
【作者单位】安徽大学物理与光电工程学院;安徽理工大学力学与光电物理学院【正文语种】中文
【中图分类】O57
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Geant4模拟质子入射InP产生的位移损伤
第19卷 第1期 太赫兹科学与电子信息学报Vo1.19，No.1 2021年2月 Journal of Terahertz Science and Electronic Information Technology Feb.，2021 文章编号：2095-4980(2021)01-0176-05Geant4模拟质子入射InP产生的位移损伤白雨蓉，贺朝会，谢 飞，李永宏，臧 航(西安交通大学核科学与技术学院，陕西西安 710049)摘 要：磷化铟(InP)作为重要的第二代半导体材料，禁带宽度大，电子漂移速度快，抗辐照性能比Si,GaAs好，可作为制备空间飞行器上电学器件的备选材料。
随着半导体器件的尺寸纳米化，空间环境中低能质子辐照元件所导致的位移损伤成为影响元件电学性能的主要因素之一。
本文使用Geant4模拟得到低能质子入射InP产生的初级撞出原子(PKA)种类及占比和不同能量质子的非电离能量损失(NIEL)的深度分布。
结果表明：质子俘获和核反应的概率随质子能量的增加而增加，进而使弹性碰撞产生的反冲原子In,P的占比减少，其他反冲原子占比增加；NIEL峰值随质子能量的增加而降低，且NIEL峰有向前移动的趋势，即随着质子能量增加，位移损伤严重区域逐渐由材料末端移至材料表面。
关键词：非电离能量损失模型；Geant4；空间质子辐射；磷化铟中图分类号：TN304.2＋3文献标志码：A doi：10.11805/TKYDA2019383Geant4 simulation of displacement damage induced by proton irradiation in InPBAI Yurong，HE Chaohui，XIE Fei，LI Yonghong，ZANG Hang(School of Nuclear Science and Technology，Xi’an Jiaotong University，Xi’an Shaanxi 710049，China)Abstract：As an important second-generation semiconductor material, indium phosphide has wide bandgap, fast electron drift and better radiation resistance than Si and GaAs. It can be used as analternative material for the preparation of electrical devices on space vehicles. With the nano-size ofsemiconductor devices, the displacement damage caused by low-energy proton irradiation in spaceenvironment is one of the main factors affecting the electrical properties of components. In this paper, thetypes and proportions of Primary Knock-on Atom(PKA) produced by low energy protons irradiation and thedepth distribution of Non-Ionizing Energy Loss(NIEL) of protons with different energies are obtained byGeant4 simulation. The results show that the probability of proton capture and nuclear reaction increaseswith the increase of proton energy, which decreases the proportion of recoil atoms In and P and enhancesother recoil atoms in elastic collision. The NIEL peak tends to move forward in depth of the bulk materialwith the increase of proton energy, which means the area of serious displacement damage gradually shiftsfrom the end of the material to the surface of the material.Keywords：Non-Ionizing Energy Loss；Geant4；space proton irradiation damage；InP对半导体器件的位移损伤研究始于20世纪70年代，主要以地面辐照试验为主，M Yamaguchi, R J Walters 等[1-4]对InP,GaAs,GaN等III-V族化合物半导体材料做了一系列的粒子束辐照实验，得到位移损伤对III-V族半导体器件电学性能的影响规律。
梁伟红(广西师范大学)
16
f0(500) production is clearly dominant.
f0(980) shows up as a small peak.
17
Exp.
Conclusion: Our results agree with the experimental results. This gives a strong support to the idea of the low lying scalar mesons as being formed from the interaction of pairs of pseudoscalar mEexspo.ns.
(2)
1 12 f2
Tr[(
)2
M4 ],
( f 93 MeV) ——the pion decay constant
There are 5 coupled channels:
(1), 0 0(2), K K (3), K 0K 0(4), (5)
The V matrix elements are taken from
VP ApJ / cos , ( A 1, for an arbitrary normalizat ion)
invariant mass (Minv ) distributi on :
~t t BJ /
B J /
( pJ / cos ),
(in the B rest frame )
• Formalism
• Results and discussions • Summary
2n
• The nature of the light scalar mesons is a topic of longstanding debate.
B→VV中的因子化和新物理
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π介子衰变
π介子衰变
π介子衰变是粒子物理学中一个重要的研究课题。
它可以从原子核中产生其他粒子，并有助于我们理解原子核结构，宇宙及宇宙射线的形成过程。
π介子衰变是指一种核反应过程，它被认为是原子核的基本过程之一，它可以从一种原子核产生另一种原子核，它可以解释无穷多的宇宙现象。
它利用一种叫做π-介子的粒子，它是一种有质量的弱中子，它可以在原子核中运行，能够与原子核发生相互作用。
π-介子的大小小于原子核的大小，它可以将原子核拆分成更小的部分，也就是所谓的原子核裂变。
当π-介子在原子核内运动时，可以将原子核拆分成一个称为“质子”的带正电荷的粒子，和另一种叫做“中子”的带负电荷的粒子。
当两个原子核的质子和中子组合在一起时，即可形成另一个原子核结构。
π-介子衰变被认为是宇宙中发射宇宙射线的主要原因之一。
当π-介子衰变发生时，发出的放射性产物可以用来制造宇宙射线，这些宇宙射线会穿越星系或是宇宙，最终来到地球上。
这就是为什么我们可以看到宇宙射线在太空中漂浮的原因。
π-介子衰变还可以被用来证明狭义相对论的有效性。
它可以帮助科学家定量计算出原子核和宇宙结构的一些重要特性，例如原子核质量，宇宙中物质的构成和它们的能量。
总而言之，π-介子衰变是一种重要的核反应过程，它为我们理解原子核结构、宇宙及宇宙射线的形成提供了重要的线索，也帮助科
学家证明了狭义相对论的正确性。
因此，π-介子衰变仍然是研究者继续探索的重要方向。
hidebrend-benesi方程
hidebrend-benesi方程是描述流体动力学的一种数学模型，它由二战期间的物理学家hidebrend和benesi在1943年提出。
hidebrend-benesi方程是描述非线性波动现象的方程，适用于许多领域，如气象学、海洋学、地质学和生物学等。
hidebrend-benesi方程具有许多有趣的数学性质和实际应用价值，因此受到了广泛的关注和研究。
hidebrend-benesi方程的数学表达式具有一定的复杂性，它可以描述波动的传播和相互作用。
hidebrend-benesi方程的一般形式为：\[ u_{tt} - c^2u_{xx} + au^2 + bu^3 = 0 \]其中，\(u\)是波动的幅度，\(x,t\)分别是空间和时间变量，\(c,a,b\)是常数。
hidebrend-benesi方程的特点在于它具有非线性项\(u^2\)和\(u^3\)，这使得它的数学性质和解的性质都非常丰富。
hidebrend-benesi方程的研究可以追溯到上世纪50年代，当时hidebrend-benesi方程首次出现时，其非线性性质给数学家和物理学家们带来了很多困惑。
hidebrend-benesi方程的解析解通常很难得到，只有在特定情况下才能使用传统的数学方法求解。
然而，随着计算机技术的发展，数值方法成为了研究hidebrend-benesi方程的主要手段之一。
通过数值模拟和计算，人们可以研究hidebrend-benesi方程的解的性质，如稳定性、非线性波动现象和模式形成等。
hidebrend-benesi方程的非线性性质使得它在实际应用中具有广泛的价值。
在气象学中，hidebrend-benesi方程可以用来描述大气中的非线性波动现象，如风暴、台风和涡旋等。
在海洋学中，hidebrend-benesi方程也可以用来研究海浪的非线性传播和交互。
hidebrend-benesi方程在地质学和生物学领域中也有着重要的应用，例如描述地震波的传播和生物体内的非线性波动现象。
Weak Interactions of Light Flavours
LSM = LH (φ) + LG (W, Z, G) + Higgs Gauge ¯ / ψ+ ψiD
ψ=fermions ψ,ψ′ =fermions
The Standard Model Lagrangian has four parts: ¯ ′ gψψ′ ψφψ Yukawa
QCD and QED conserve C,P,T separately. Local Field theory by itself implies CPT. The fermion and Higgs2 part of the SM-lagrangian conserves CP and T as well. The only part that violates CP and as a consequence also T is the Yukawa part. The Higgs part is responsible for two parameters, the gauge part for three and the HiggsFermion part contains in principle 27 complex parameters, neglecting Yukawa couplings to neutrinos. Luckily most of the 54 real parameters in the Yukawa sector are unobservable. After diagonalizing the lepton sector there only the three charged lepton masses remain. The quark sector can be similarly diagonalized leading to 6 quark masses, but some parts remain in the difference between weak interaction eigenstates and mass-eigenstates. The latter is conventionally put in the couplings of the charged W -boson, which is given by Vud Vus Vub dα g α − uα cα t γ µ (1 − γ5 ) Vcd Vcs Vcb sα − √ Wµ 2 2 V V V b
超统一场论
物理学是研究物质的基本结构和物质运动最一般规律的科学。
迄今为止，人类认识的宇宙间的力有四种，那就是强力、弱力、电磁力、万有引力。
虽然这四种力无论从强度上，还是从作用距离上都有着巨大的差异。
但是理论物理学家却认为自然界是和谐的，统一的，四种力之间不仅具有内在联系，而且是统一的。
长期以来，世界上有不少物理学家，一直在试图找到一个统一、简洁、和谐的数学公式，来概括这四种自然力。
1、统一理论的进展从本世纪20年代开始，爱因斯坦花费了半生的精力，力图把电磁力与万有引力统一起来。
海森堡也作了种种尝试，但都没有成功。
直到1967年，温伯格、萨拉姆、格拉肖等人提出了弱力与电磁力的统一模型，统一理论才取得了一点进展。
G·S·W理论所预言的四个规范波色子有三个得到了证实，但仍有一个希格斯粒子没有找到。
因此，承认该理论还为时过早。
在G·S·W理论得到了部分证实之后，近年来一些物理学家提出各种“大统一”理论（GUTS），试图证明除引力外的其他三种自然力同源。
被称为“SU （5）型”的乔治·格拉肖的大统一理论认为：（1）质子的寿命为1031年，主要衰变为正电子和π介子；（2）存在着名为“磁单极子”的很重的基本粒子。
然而，“大统一”理论未得到任何证实。
2、爱因斯坦广义相对论难以解释的问题爱因斯坦于本世纪初，在牛顿引力理论的基础上，建立了广义相对论，即引力理论的相对论。
虽然广义相对论能够解释水星的近日点的进动，预言了光线在恒星附近的偏折，但它仍然难以解释天体物理学中几个最基本的问题，即2.1 宇宙遗失97%质量问题；2.2 星系的外缘恒星比内缘恒星公转速度快的问题；2.3 星系的形状问题。
3、超统一场论的基本思想超统一场论所要解决的是支配天体运动的力、弱力、强力及电磁力四种力的统一。
面对差异如此之大的四种力，它摈弃了“弱电统一理论”中相互作用是交换虚光子或中间波色子的过程，代之以能量和能量守恒为核心的场论。