Supersymmetric left-right model and scalar potential

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Can the Supersymmetric $mu$ parameter be generated dynamically without a light Singlet

a r X i v :h e p -p h /9404257v 1 12 A p r 1994DESY 94-061ISSN 0418-9833April 1994hep-ph/9404257Can the Supersymmetric µparameter be generated dynamically without a light Singlet?Ralf Hempfling Deutsches Elektronen-Synchrotron,Notkestraße 85,D-22603Hamburg,Germany ABSTRACTIt is generally assumed that the dynamical generation of the Higgs mass param-eter of the superpotential,µ,implies the existence of a light singlet at or below the supersymmetry breaking scale,M SUSY .We present a counter-example in which the singlet ﬁeld can receive an arbitrarily heavy mass (e.g.,of the order of the Planck scale,M P ≈1019GeV).In this example,a non-zero value of µis generatedthrough soft supersymmetry breaking parameters and is thus naturally of the order of M SUSY .The cancellation of quadratic divergences in the unrenormalized Green func-tions is one of the main motivations of supersymmetry(SUSY).It stabilizes any mass scale under radiative corrections and thus allows the existence of diﬀerent mass scales such as the electroweak scale,given by the Z boson mass,m z,and the Planck scale,M P.The minimal supersymmetric standard model(MSSM)is the most popular model of this kind due to its minimal particle content[1].In this model,the SU(2)L⊗U(1)Y symmetry breaking is driven by soft SUSY break-ing parameters.Thus,the SUSY breaking scale,M SUSY,has to be at or slightly above m z.For this mechanism to work it is also necessary that the SUSY Higgs mass parameter,|µ|<∼M SUSY.This parameter also determines the chargino and neutralino mass spectrum.From here one can deduce a experimental lower bound from LEP experiments of|µ|>∼m z/4independent of tanβ[2].The fact that in the MSSM theµ-parameter,which is a priori arbitrary,has to lie within the narrow range1will be evaded[5].We will demonstrate in the following that it is also possible to make N1heavy [say m N1=O(M P)]while keeping N1 =O(M SUSY)withoutﬁne-tuning.In this limit we recover the predictive Higgs sector of the MSSM[6]with its well deﬁned upper limit of the lightest Higgs boson mass[eq.(2)].First we need to extend the symmetry group of our Lagrangian in order to forbid the explicit Higgs mass term of the superpotential,W H=µH8(ξ+2N∗1N1−2N∗2N2−N∗3N3)2.(4)Here the inclusion of a Fayet-Iliopoulos term[7],ξ,is the easiest way of breaking the U(1)Y′gauge symmetry but one can envisage other alternatives[8].The VEVs are denoted byn1= N1 =0,n2= N2 =1λ+ λ2+4ξ , n3= N3 = λ.(5)The CP-even and CP-odd components of the scalarﬁeld N1are mass-degenerate mass-eigenstates with m N1=(m2+λ2n23)1/2.The gauge boson,g′,acquires a massm g′=g′(n22+n23/4)1/2via the Higgs mechanism.The masses of the remaining CP-,m g′(m N1,0;the zero mass eigenvalue corresponds even(CP-odd)scalars are m N1to the Goldstone boson which is absorbed to give mass to the gauge boson).Theand±m g′as required if mass eigenvalues of the fermionic components are±m N1SUSY is unbroken.Note that in addition to the gauge and the SUSY transformations the La-grangian is invariant under the global U(1)R-symmetry[9]which does not com-mute with SUSY.This symmetry transformsΦ→exp(inΦα)Φ,where nΦ= 2,0,0,0for the bosons and n Φ=1,−1,−1,1for the fermions(Φ=N1,N2,N3,g′). We now break SUSY explicitly in the standard fashion by including soft SUSY breaking terms[10]V soft=BmN1N2−AλN1N23+h.c.,(6) where A,B=O(M SUSY)are the soft SUSY breaking parameters.With these terms the R-symmetry is broken down to a discrete Z2symmetry(α=±π).If we minimize the full potential,V=V SUSY+V soft,weﬁndN1 ≈(A−B)mn2ξ.However,the condition N1 =0is protected by R-symmetry to all orders in perturbation theory and is only broken by adding soft SUSY breaking terms[eq.(6)].We now include in our model the full particle content of the MSSM.The Z2symmetry is equivalent to the usual R-parity that prevents baryon and lepton number violating interactions. The full superpotential can then be written asW=W N+W H+W Y,(8) where W H=κN1Hof W in eq.(8)and by requiring the absence of anomalies.These constraints can be satisﬁed by introducing additional pairs of SUSY multiplets T∼(n c,n w,Y,Y′1) and T c∼(¯n c,n w,−Y,Y′2).These representations have been included in pairs such√that below the U(1)Y′breaking scale,Useful conversations with W.Buchm¨u ller are gratefully ac-knowledgedREFERENCES1.H.P.Nilles,Phys.Rep.110,1(1984);H.E.Haber and G.L.Kane,Phys.Rep.117,75(1985);R.Barbieri,Riv.Nuovo Cimento11,1(1988).2.J.-F.Grivaz,in Proceedings of the Workshop on e+e−Collisions at500GeV:The Physics Potential,Munich,Annecy,Hamburg,DESY report DESY92-123B(1992).3.G.F.Guidice and A.Masiero,Phys.Lett.B206,480(1988);J.E.Kimand H.P.Nilles,Phys.Lett.B263,79(1991);J.A.Casas and C.Mu˜n oz, Phys.Lett.B306,288(1993).4.E.Witten,Phys.Lett.B105,267(1981);L.Ib´a˜n ez and G.G.Ross,Phys.Lett.B110,215(1982);P.V.Nanopoulos and K.Tamvakis,Phys.Lett.B113,151(1982).5.see,e.g.,J.Ellis,J.F.Gunion,H.E.Haber,L.Roszkowski and F.Zwirner,Phys.Rev.D39,844(1989).6.see,e.g.,J.F.Gunion,H.E.Haber,G.L.Kane,and S.Dawson,The HiggsHunter’s Guide,(Addison-Wesley,Redwood City,CA,1990).7.P.Fayet and J.Iliopoulos,Phys.Lett.B51,461(1974).8.e.g.,L.O’Raifeartaigh,Nucl.Phys.B96,331(1975).9.P.Fayet,Nucl.Phys.B90,104(1975);A.Salam and J.Strathdee,Nucl.Phys.B87,85(1975).10.L.Girardello and M.T.Grisaru,Nucl.Phys.B194,65(1982).。

PACSnumbers1215Ff,1130Hv,1210Dm,1125Mj…

a r X i v :0803.2889v 2 [h e p -p h ] 14 J u l 2008Mapping Out SU (5)GUTs with Non-Abelian Discrete Flavor SymmetriesFlorian Plentinger ∗and Gerhart Seidl †Institut f¨u r Physik und Astrophysik,Universit¨a t W¨u rzburg,Am Hubland,D 97074W¨u rzburg,Germany(Dated:December 25,2013)We construct a class of supersymmetric SU (5)GUT models that produce nearly tribimaximal lepton mixing,the observed quark mixing matrix,and the quark and lepton masses,from discrete non-Abelian ﬂavor symmetries.The SU (5)GUTs are formulated on ﬁve-dimensional throats in the ﬂat limit and the neutrino masses become small due to the type-I seesaw mechanism.The discrete non-Abelian ﬂavor symmetries are given by semi-direct products of cyclic groups that are broken at the infrared branes at the tip of the throats.As a result,we obtain SU (5)GUTs that provide a combined description of non-Abelian ﬂavor symmetries and quark-lepton complementarity.PACS numbers:12.15.Ff,11.30.Hv,12.10.Dm,One possibility to explore the physics of grand uniﬁed theories (GUTs)[1,2]at low energies is to analyze the neutrino sector.This is due to the explanation of small neutrino masses via the seesaw mechanism [3,4],which is naturally incorporated in GUTs.In fact,from the perspective of quark-lepton uniﬁcation,it is interesting to study in GUTs the drastic diﬀerences between the masses and mixings of quarks and leptons as revealed by current neutrino oscillation data.In recent years,there have been many attempts to re-produce a tribimaximal mixing form [5]for the leptonic Pontecorvo-Maki-Nakagawa-Sakata (PMNS)[6]mixing matrix U PMNS using non-Abelian discrete ﬂavor symme-tries such as the tetrahedral [7]and double (or binary)tetrahedral [8]groupA 4≃Z 3⋉(Z 2×Z 2)and T ′≃Z 2⋉Q,(1)where Q is the quaternion group of order eight,or [9]∆(27)≃Z 3⋉(Z 3×Z 3),(2)which is a subgroup of SU (3)(for reviews see, e.g.,Ref.[10]).Existing models,however,have generally dif-ﬁculties to predict also the observed fermion mass hierar-chies as well as the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix V CKM [11],which applies especially to GUTs (for very recent examples,see Ref.[12]).An-other approach,on the other hand,is oﬀered by the idea of quark-lepton complementarity (QLC),where the so-lar neutrino angle is a combination of maximal mixing and the Cabibbo angle θC [13].Subsequently,this has,in an interpretation of QLC [14,15],led to a machine-aided survey of several thousand lepton ﬂavor models for nearly tribimaximal lepton mixing [16].Here,we investigate the embedding of the models found in Ref.[16]into ﬁve-dimensional (5D)supersym-metric (SUSY)SU (5)GUTs.The hierarchical pattern of quark and lepton masses,V CKM ,and nearly tribi-maximal lepton mixing,arise from the local breaking of non-Abelian discrete ﬂavor symmetries in the extra-dimensional geometry.This has the advantage that theFIG.1:SUSY SU (5)GUT on two 5D intervals or throats.The zero modes of the matter ﬁelds 10i ,5H,24H ,and the gauge supermul-tiplet,propagate freely in the two throats.scalar sector of these models is extremely simple without the need for a vacuum alignment mechanism,while of-fering an intuitive geometrical interpretation of the non-Abelian ﬂavor symmetries.As a consequence,we obtain,for the ﬁrst time,a realization of non-Abelian ﬂavor sym-metries and QLC in SU (5)GUTs.We will describe our models by considering a speciﬁc minimal realization as an example.The main features of this example model,however,should be viewed as generic and representative for a large class of possible realiza-tions.Our model is given by a SUSY SU (5)GUT in 5D ﬂat space,which is deﬁned on two 5D intervals that have been glued together at a common endpoint.The geom-etry and the location of the 5D hypermultiplets in the model is depicted in FIG.1.The two intervals consti-tute a simple example for a two-throat setup in the ﬂat limit (see,e.g.,Refs.[17,18]),where the two 5D inter-vals,or throats,have the lengths πR 1and πR 2,and the coordinates y 1∈[0,πR 1]and y 2∈[0,πR 2].The point at y 1=y 2=0is called ultraviolet (UV)brane,whereas the two endpoints at y 1=πR 1and y 2=πR 2will be referred to as infrared (IR)branes.The throats are supposed to be GUT-scale sized,i.e.1/R 1,2 M GUT ≃1016GeV,and the SU (5)gauge supermultiplet and the Higgs hy-permultiplets 5H and2neously broken to G SM by a 24H bulk Higgs hypermulti-plet propagating in the two throats that acquires a vac-uum expectation value pointing in the hypercharge direc-tion 24H ∝diag(−12,13,15i ,where i =1,2,3is the generation index.Toobtainsmall neutrino masses via the type-I seesaw mechanism [3],we introduce three right-handed SU (5)singlet neutrino superﬁelds 1i .The 5D Lagrangian for the Yukawa couplings of the zero mode fermions then readsL 5D =d 2θ δ(y 1−πR 1) ˜Y uij,R 110i 10j 5H +˜Y d ij,R 110i 5H +˜Y νij,R 15j5i 1j 5H +M R ˜Y R ij,R 21i 1j+h.c. ,(3)where ˜Y x ij,R 1and ˜Y x ij,R 2(x =u,d,ν,R )are Yukawa cou-pling matrices (with mass dimension −1/2)and M R ≃1014GeV is the B −L breaking scale.In the four-dimensional (4D)low energy eﬀective theory,L 5D gives rise to the 4D Yukawa couplingsL 4D =d 2θ Y u ij 10i 10j 5H +Y dij10i 5H +Y νij5i ∼(q i 1,q i 2,...,q i m ),(5)1i ∼(r i 1,r i 2,...,r im ),where the j th entry in each row vector denotes the Z n jcharge of the representation.In the 5D theory,we sup-pose that the group G A is spontaneously broken by singly charged ﬂavon ﬁelds located at the IR branes.The Yukawa coupling matrices of quarks and leptons are then generated by the Froggatt-Nielsen mechanism [21].Applying a straightforward generalization of the ﬂavor group space scan in Ref.[16]to the SU (5)×G A represen-tations in Eq.(5),we ﬁnd a large number of about 4×102ﬂavor models that produce the hierarchies of quark and lepton masses and yield the CKM and PMNS mixing angles in perfect agreement with current data.A distri-bution of these models as a function of the group G A for increasing group order is shown in FIG.2.The selection criteria for the ﬂavor models are as follows:First,all models have to be consistent with the quark and charged3 lepton mass ratiosm u:m c:m t=ǫ6:ǫ4:1,m d:m s:m b=ǫ4:ǫ2:1,(6)m e:mµ:mτ=ǫ4:ǫ2:1,and a normal hierarchical neutrino mass spectrumm1:m2:m3=ǫ2:ǫ:1,(7)whereǫ≃θC≃0.2is of the order of the Cabibbo angle.Second,each model has to reproduce the CKM anglesV us∼ǫ,V cb∼ǫ2,V ub∼ǫ3,(8)as well as nearly tribimaximal lepton mixing at3σCLwith an extremely small reactor angle 1◦.In perform-ing the group space scan,we have restricted ourselves togroups G A with orders roughly up to 102and FIG.2shows only groups admitting more than three valid mod-els.In FIG.2,we can observe the general trend thatwith increasing group order the number of valid modelsper group generally increases too.This rough observa-tion,however,is modiﬁed by a large“periodic”ﬂuctu-ation of the number of models,which possibly singlesout certain groups G A as particularly interesting.Thehighly populated groups would deserve further system-atic investigation,which is,however,beyond the scopeof this paper.From this large set of models,let us choose the groupG A=Z3×Z8×Z9and,in the notation of Eq.(5),thecharge assignment101∼(1,1,6),102∼(0,3,1),103∼(0,0,0),52∼(0,7,0),52↔4FIG.3:Eﬀect of the non-Abelian ﬂavor symmetry on θ23for a 10%variation of all Yukawa couplings.Shown is θ23as a function of ǫfor the ﬂavor group G A (left)and G A ⋉G B (right).The right plot illustrates the exact prediction of the zeroth order term π/4in the expansion θ23=π/4+ǫ/√2and the relation θ13≃ǫ2.The important point is that in the expression for θ23,the leading order term π/4is exactly predicted by thenon-Abelian ﬂavor symmetry G F =G A ⋉G B (see FIG.3),while θ13≃θ2C is extremely small due to a suppression by the square of the Cabibbo angle.We thus predict a devi-ation ∼ǫ/√2,which is the well-known QLC relation for the solar angle.There have been attempts in the literature to reproduce QLC in quark-lepton uniﬁed models [26],however,the model presented here is the ﬁrst realization of QLC in an SU (5)GUT.Although our analysis has been carried out for the CP conserving case,a simple numerical study shows that CP violating phases (cf.Ref.[27])relevant for neutri-noless double beta decay and leptogenesis can be easily included as well.Concerning proton decay,note that since SU (5)is bro-ken by a bulk Higgs ﬁeld,the broken gauge boson masses are ≃M GUT .Therefore,all fermion zero modes can be localized at the IR branes of the throats without intro-ducing rapid proton decay through d =6operators.To achieve doublet-triplet splitting and suppress d =5pro-ton decay,we may then,e.g.,resort to suitable extensions of the Higgs sector [28].Moreover,although the ﬂavor symmetry G F is global,quantum gravity eﬀects might require G F to be gauged [29].Anomalies can then be canceled by Chern-Simons terms in the 5D bulk.We emphasize that the above discussion is focussed on a speciﬁc minimal example realization of the model.Many SU (5)GUTs with non-Abelian ﬂavor symmetries,however,can be constructed along the same lines by varying the ﬂavor charge assignment,choosing diﬀerent groups G F ,or by modifying the throat geometry.A de-tailed analysis of these models and variations thereof will be presented in a future publication [30].To summarize,we have discussed the construction of 5D SUSY SU (5)GUTs that yield nearly tribimaximal lepton mixing,as well as the observed CKM mixing matrix,together with the hierarchy of quark and lepton masses.Small neutrino masses are generated only by the type-I seesaw mechanism.The fermion masses and mixings arise from the local breaking of non-Abelian ﬂavor symmetries at the IR branes of a ﬂat multi-throat geometry.For an example realization,we have shown that the non-Abelian ﬂavor symmetries can exactly predict the leading order term π/4in the sum rule for the atmospheric mixing angle,while strongly suppress-ing the reactor angle.This makes this class of models 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Supersymmetric Chern-Simons models in harmonic superspaces

a r X i v :0805.4481v 1 [h e p -t h ] 29 M a y 2008SUPERSYMMETRIC CHERN-SIMONS MODELS IN HARMONIC SU-PERSPACESB.M.ZupnikBogoliubov Laboratory of Theoretical Physics,JINR,Dubna,Moscow Region,141980,Russia;E-mail:zupnik@theor.jinr.ruAbstractWe review harmonic superspaces of the D =3,N =3and 4supersymmetries and gauge models in these superspaces.Superspaces of the D =3,N =5supersymmetry use harmonic coordinates of the SO (5)group.The superﬁeld N =5actions describe the oﬀ-shell inﬁnite-dimensional Chern-Simons supermultiplet.1IntroductionSupersymmetric extensions of the D =3Chern-Simons theory were discussed in [1]-[10].A superﬁeld action of the D =3,N =1Chern-Simons theory can be interpreted as the superspace integral of the diﬀerential Chern-Simons superform dA +2iwhere i andˆk are two-component indices of the automorphism groups SU L(2)and SU R(2), respectively,αis the two-component index of the SL(2,R)group and m=0,1,2is the 3D vector index.The N=4supersymmetry transformations areδx m=−i(γm)αβ(ǫαjˆk θβjˆk−iǫβjˆkθαjˆk),(2.2)whereγm are the3Dγmatrices.The SU L(2)/U(1)harmonics u±i[11]can be used to construct the left analytic super-space[15]with the LA coordinatesζL=(x m L,θ+ˆkα).(2.3)The L-analytic prepotential V++(ζL,u)describes the left N=4vector multiplet A m,φˆkˆl ,λαiˆk,D ik.The D=3,N=4SY M action can be constructed in terms of this prepotential by anal-ogy with the D=4,N=2SY M action[14].Let us introduce the new notation for the left harmonics u±i=u(±1,0)iand the analogousnotation v(0,±1)ˆk for the right SL R(2)/U(1)harmonics.The biharmonic N=4superspaceuses the Grassmann coordinates[15]θ(±1,±1)α=u(±1,0)i v(0,±1)ˆkθiˆkα.(2.4)In this representation,we haveζL=(x m L,θ(1,±1)α),V++≡V(2,0),(2.5)D(1,±1)αV(2,0)=0,D(0,2)vV(2,0)=0.(2.6)The right analytic N=4coordinates areζR=(x m R,θ(±1,1)α),x m R=x m L−2i(γm)αβθ(−1,1)αθ(1,1)β.(2.7) The mirror R analytic prepotentialˆV(0,2)D(±1,1)ˆV(0,2)=0,D(2,0)uˆV(0,2)=0(2.8)describes the right N=4vector multipletˆA m,ˆφij,ˆλαiˆk ,ˆD ik,whereˆA m is the mirror vectorgaugeﬁeld using the independent gauge group.The right N=4SY M action is similar to the analogous left action.These multiplets can be formally connected by the map SU L(2)↔SU R(2).The N=4superﬁeld Chern-Simons type(or BF-type)action for the gauge group U(1)×U(1)connects two mirror vector multipletsdud3x L dθ(−4,0)V(2,0)(ζL,u)D(1,1)αD(1,1)αˆV(0,−2),(2.9) where the right connection satisﬁes the equationD(0,2)v ˆV(0,−2)=D(0,−2)v˜V(0,2),D(2,0)uˆV(0,−2)=0.(2.10)The component form of this action was considered in[16,17].We can identify the left and right isospinor indices in the N=4spinor coordinatesθαjˆk→θαjk=θα(jk)+12D++αD++αV−−.(2.14)The action of the corresponding CS-theory can be constructed in the full or analytic N=3superspaces[8,9].3Harmonic superspaces for the group SO(5)The homogeneous space SO(5)/U(2)is parametrized by elements of the harmonic5×5 matrixU K a=(U+i a,U0a,U−ia)=(U+1a,U+2a,U0a,U−1a,U−2a),(3.1) where a=1,...5is the vector index of the group SO(5),i=1,2is the spinor index of the group SU(2),and U(1)-charges are denoted by symbols+,−,0.The basic relations for these harmonics areU+i a U+k a=U+i a U0a=0,U−ia U−ka =U−ia U0a=0,U+i a U−ka=δi k,U0a U0a=1,U+i a U−ib +U−ia U+ib+U0a U0b=δab.(3.2)We consider the SO(5)invariant harmonic derivatives with nonzero U(1)charges∂+i=U+i a ∂∂U−ia,∂+i U0a=U+i a,∂+i U−ka=−δi k U0a,∂++=U+ia∂∂U0a −U0a∂∂U+i a ,[∂−i,∂−k]=εki∂−−,∂−k∂−k=−∂−−,where some relations between these harmonic derivatives are deﬁned.The U(1)neutral harmonic derivatives form the Lie algebra U(2)∂i k=U+i a ∂∂U−ia,[∂+i,∂−k]=−∂i k,(3.4)∂0≡∂k k=U+k a ∂∂U−ka,[∂++,∂−−]=∂0,∂i k U+l a=δl k U+i a,∂i k U−la =−δi l U−ka.(3.5)The operators∂+k,∂++,∂−k ,∂−−and∂i k satisfy the commutation relations of the Lie al-gebra SO(5).One deﬁnes an ordinary complex conjugation on these harmonicsU0a=U0a,(3.6) however,it is convenient to use a special conjugation in the harmonic space(U+i a)∼=U+i a,(U−ia)∼=U−ia,(U0a)∼=U0a.(3.7) All harmonics are real with respect to this conjugation.The full superspace of the D=3,N=5supersymmetry has the spinor CB coordi-natesθαa,(α=1,2;a=1,2,3,4,5)in addition to the coordinates x m of the three-dimensional Minkowski space.The group SL(2,R)×SO(5)acts on the spinor coordinates. The superconformal transformations of these coordinates are considered in Appendix.The SO(5)/U(2)harmonics allow us to construct projections of the spinor coordinates and the partial spinor derivativesθ+iα=U+i aθαa,θ0α=U0aθαa,θ−αi=U−iaθαa,(3.8)∂−iα=∂/∂θ+iα,∂0α=∂/∂θ0α,∂+iα=∂/∂θ−αi.The analytic coordinates(AB-representation)in the full harmonic superspace use these projections of10spinor coordinatesθ+iα,θ0α,θ−αi and the following representation of the vector coordinate:x m A ≡y m=x m+i(θ+kγmθ−k)=x m+i(θaγmθb)U+k a U−kb.(3.9)The analytic coordinates are real with respect to the special conjugation. The harmonic derivatives have the following form in AB:D+k=∂+k−i(θ+kγmθ0)∂m+θ+kα∂0α−θ0α∂+kα,D++=∂+++i(θ+kγmθ+k )∂m+θ+αk∂+kα,(3.10)D k l=∂k l+θ+kα∂−lα−θ−αl∂−kα.We use the commutation relations[D+k,D+l]=−εkl D++,D+k D+k=D++.(3.11) The AB spinor derivatives areD+iα=∂+iα,D−iα=−∂−iα−2iθ−βi∂αβ,D0α=∂0α+iθ0β∂αβ.(3.12) The coordinates of the analytic superspaceζ=(y m,θ+iα,θ0α,U K a)have the Grass-mann dimension6and dimension of the even space3+6.The functionsΦ(ζ)satisfy the Grassmann analyticity condition in this superspaceD+kαΦ=0.(3.13)In addition to this condition,the analytic superﬁelds in the SO (5)/U (2)harmonic super-space possess also the U (2)-covariance.This subsidiary condition looks especially simple for the U (2)-scalar superﬁeldsD k l Λ(ζ)=0.(3.14)The integration measure in the analytic superspace dµ(−4)has dimension zerodµ(−4)=dUd 3x A (∂0α)2(∂−iα)4=dUd 3x A dθ(−4).(3.15)The SO (5)/U (1)×U (1)harmonics can be deﬁned via the components of the real orthogonal 5×5matrix [20,21]U Ka = U (1,1)a ,U (1,−1)a ,U (0,0)a ,U (−1,1)a ,U (−1,−1)a (3.16)where a is the SO(5)vector index and the index K =1,2,...5corresponds to givencombinations of the U(1)×U(1)charges.We use the following harmonic derivatives∂(2,0)=U (1,1)b∂/∂U (−1,1)b−U (1,−1)b∂/∂U (−1,−1)b,∂(1,1)=U (1,1)b∂/∂U (0,0)b −U (0,0)b∂/∂U (−1,−1)b,∂(1,−1)=U (1,−1)b ∂/∂U (0,0)b−U (0,0)b∂/∂U (−1,1)b,∂(0,2)=U (1,1)b∂/∂U (1,−1)b−U (−1,1)b∂/∂U (−1,−1)b,∂(0,−2)=U (1,−1)b∂/∂U (1,1)b−U (−1,−1)b∂/∂U (−1,1)b.(3.17)We deﬁne the harmonic projections of the N =5Grassmann coordinatesθK α=θaαU K a =(θ(1,1)α,θ(1,−1)α,θ(0,0)α,θ(−1,1)α,θ(−1,−1)α).(3.18)The SO (5)/U (1)×U (1)analytic superspace contains only spinor coordinatesζ=(x m A ,θ(1,1)α,θ(1,−1)α,θ(0,0)α),(3.19)x m A=x m +iθ(1,1)γm θ(−1,−1)+iθ(1,−1)γm θ(−1,1),δǫx m A =−iǫ(0,0)γm θ(0,0)−2iǫ(−1,1)γm θ(1,−1)−2iǫ(−1,−1)γm θ(1,1),(3.20)where ǫKα=ǫαa U Ka are the harmonic projections of the supersymmetry parameters.General superﬁelds in the analytic coordinates depend also on additional spinor coor-dinates θ(−1,1)αand θ(−1,−1)α.The harmonized partial spinor derivatives are∂(−1,−1)α=∂/∂θ(1,1)α,∂(−1,1)α=∂/∂θ(1,−1)α,∂(0,0)α=∂/∂θ(0,0)α,(3.21)∂(1,1)α=∂/∂θ(−1,−1)α,∂(1,−1)α=∂/∂θ(−1,1)α.We use the special conjugation ∼in the harmonic superspaceU (p,q )a =U (p,−q )a ,θ(p,q )α=θ(p,−q )α, x m A =x m A,(θ(p,q )αθ(s,r )β)∼=θ(s,−r )βθ(p,−q )α, f (x A )=¯f(x A ),(3.22)where ¯fis the ordinary complex conjugation.The analytic superspace is real with respect to the special conjugation.The analytic-superspace integral measure contains partial spinor derivatives(3.21)1dµ(−4,0)=−they are traceless and anti-HermitianΛ†=−Λ.We treat these prepotentials as connections in the covariant gauge derivatives∇+i=D+i+V+i,∇++=D+++V++,δΛV+i=D+iΛ+[Λ,V+i],δΛV++=D++Λ+[Λ,V++],(4.4) D+kαδΛV+k=D+kαδΛV++=0,D i jδΛV+k=δk jδΛV+i,D i jδΛV++=δi jδΛV++,where the inﬁnitesimal gauge transformations of the gauge superﬁelds are deﬁned.These covariant derivatives commute with the spinor derivatives D+kαand preserve the CR-structure in the harmonic superspace.We can construct three analytic superﬁeld strengths oﬀthe mass shellF++=112πdµ(−4)Tr{V+j D++V+j+2V++D+j V+j+(V++)2+V++[V+j,V+j]},(4.5)where k is the coupling constant,and a choice of the numerical multiplier guarantees the correct normalization of the vector-ﬁeld action.This action is invariant with respect to the inﬁnitesimal gauge transformations of the prepotentials(4.4).The idea of construction of the superﬁeld action in the harmonic SO(5)/U(2)was proposed in[18],although the detailed construction of the superﬁeld Chern-Simons theory was not discussed in this work.The equivalent superﬁeld action was considered in the framework of the alternative superﬁeld formalism[20].The superconformal N=5invariance of this action was proven in[19].The action S1yields superﬁeld equations of motion which mean triviality of the su-perﬁeld strengths of the theoryF(+3) k =D++V+k−D+kV+++[V++,V+k]=0,F++=V++−D+k V+k −V+k V+k=0.(4.6)These classical superﬁeld equations have pure gauge solutions for the prepotentials onlyV+k=e−ΛD+k eΛ,V++=e−ΛD++eΛ,(4.7) whereΛis an arbitrary analytic superﬁeld.The transformation of the sixth supersymmetry can be deﬁned on the analytic N=5 superﬁeldsδ6V++=ǫα6D0αV++,δ6V+k=ǫα6D0αV+k,(4.8)δ6D+k V+l=ǫα6D0αD+k V+l,δ6D++V+l=ǫα6D0αD++V+l,(4.9) whereǫα6are the corresponding odd parameters.This transformation preserves the Grass-mann analyticity and U(2)-covariance{D0α,D+kβ}=0,[D k l,D0α]=0,[D+k,D0α]=D+kα,[D++,D0α]=0.(4.10)The action S1is invariant with respect to this sixth supersymmetryδ6S1= dµ(−4)ǫα6D0αL(+4)=0.(4.11)In the SO(5)/U(1)×U(1)harmonic superspace,we can introduce the D=3,N=5 analytic matrix gauge prepotentials corresponding to theﬁve harmonic derivativesV(p,q)(ζ,U)=[V(1,1),V(1,−1),V(2,0),V(0,±2)],(V(1,1))†=−V(1,−1),(V(2,0))†=V(2,0),V(0,−2)=[V(0,2)]†,(4.12) where the Hermitian conjugation†includes∼conjugation of matrix elements and trans-position.We shall consider the restricted gauge supergroup using the supersymmetry-preserving harmonic(H)analyticity constraints on the gauge superﬁeld parametersH1:D(0,±2)Λ=0.(4.13) These constrains yield additional reality conditions for the component gauge parameters.We use the harmonic-analyticity constraints on the gauge prepotentialsH2:V(0,±2)=0,D(0,−2)V(1,1)=V(1,−1),D(0,2)V(1,1)=0(4.14) and the conjugated constraints combined with relations(4.12).The superﬁeld CS action can be constructed in terms of these H-constrained gauge superﬁelds[21]2ikS=−V(2,0)V(2,0)}.(4.15)2Note,that the similar harmonic superspace based on the USp(4)/U(1)×U(1)harmon-ics was used in[22]for the harmonic interpretation of the D=4,N=4super Yang-Mills constraints.This work was partially supported by the grants RFBR06-02-16684,DFG436RUS 113/669-3,INTAS05-10000008-7928and by the Heisenberg-Landau programme.References[1]W.Siegel,Nucl.Phys.B156(1979)135.[2]J.Schonfeld,Nucl.Phys.B185(1981)157.[3]B.M.Zupnik,D.G.Pak,Teor.Mat.Fiz.77(1988)97;Eng.transl.:Theor.Math.Phys.77(1988)1070.[4]B.M.Zupnik,D.G.Pak,Class.Quant.Grav.6(1989)723.[5]B.M.Zupnik,Teor.Mat.Fiz.89(1991)253,Eng.transl.:Theor.Math.Phys.89(1991)1191.[6]B.M.Zupnik,Phys.Lett.B254(1991)127.[7]H.Nishino,S.J.Gates,Int.J.Mod.Phys.8(1993)3371.[8]B.M.Zupnik,D.V.Khetselius,Yad.Fiz.47(1988)1147;Eng.transl.:Sov.J.Nucl.Phys.47(1988)730.[9]B.M.Zupnik,Springer Lect.Notes in Phys.524(1998)116;hep-th/9804167.[10]J.H.Schwarz,Jour.High.Ener.Phys.0411(2004)078,hep-th/0411077.[11]A.Galperin,E.Ivanov,S.Kalitzin,V.Ogievetsky,E.Sokatchev,Class.Quant.Grav.1(1984)469.[12]A.Galperin,E.Ivanov,S.Kalitzin,V.Ogievetsky,E.Sokatchev,Class.Quant.Grav.2(1985)155.[13]A.Galperin,E.Ivanov,V.Ogievetsky,E.Sokatchev,Harmonic superspace,Cam-bridge University Press,Cambridge,2001.[14]B.M.Zupnik,Phys.Lett.B183(1987)175.[15]B.M.Zupnik,Nucl.Phys.B554(1999)365,Erratum:Nucl.Phys.B644(2002)405E;hep-th/9902038.[16]R.Brooks,S.J.Gates,Nucl.Phys.B432(1994)205,hep-th/09407147.[17]A.Kapustin,M.Strassler,JHEP04(1999)021,hep-th/9902033.[18]P.S.Howe,M.I.Leeming,Clas.Quant.Grav.11(1994)2843,hep-th/9402038.[19]B.M.Zupnik,Chern-Simons theory in SO(5)/U(2)harmonic superspace,arXiv0802.0801(hep-th).[20]B.M.Zupnik,Phys.Lett.B660(2008)254,arXiv0711.4680(hep-th).[21]B.M.Zupnik,Gauge model in D=3,N=5harmonic superspace,arXiv0708.3951(hep-th).[22]I.L.Buchbinder,O.Lechtenfeld,I.B.Samsonov,N=4superparticle and super Yang-Mills theory in USp(4)harmonic superspace,arxiv:0804.3063(hep-th).。

政策分析的过程框架与程序

准实验方法。准实验方法(a quasi-experimental approach)以心理学和社会学特别是坎贝尔(Donald Campbell)的心理学理论、弗里曼(Howard Freeman)和罗西(Peter Rossi)的社会学理论为基础。它强调努力安排前试验(a pretest)和后试验(a posttest)，控制团体和非随机的、准实验的团体。
标准(criteria)
模式不是别的，不过是一系列关于世界及其过程的概括或假定，一个关于实在的简化了的图像；它可以用来研究一项行为的结果，而不必采取实际的行动。模式有各种表现形式，如公式、物理结构、计算机程序等，甚至不过是一个心灵的图像而已。模式不仅可以用来预测备选方案的结果，而且可以应用于问题的建构或界定，甚至可以应用于整个分析过程。
指明一个特殊的备选方案作为取得目标的手段意味着一系列的结果，我们称这些结果是与备选方案相联系的效果。有些效果是对实现目标的积极的贡献，即利益；另一些效果则是与备选方案相联系的消极的结果，即成本。与备选方案相联系还有另一种效果，我们称之为外在的结果，即经济学所讲的外部效应(Externalities)。
2. 政策分析的基本因素
一般而言，政策分析的基本任务及程序是:(1)帮助决策者确定政策目标；(2)找出达成目标的各种可能的办法；(3)分析每个备选方案的各种可能结果；(4)依一定的标准排列各种备选方案的顺序。这些基本任务决定了政策分析中的各种因素及分析过程。根据奎德等人的论述，可以将政策分析的基本因素概括为如下七个方面：问题、目标、备选方案、模式、效果、标准和政治可行性。一、问题(issues or problems) 问题是一般科学发现的逻辑起点，同样也是政策分析的逻辑起点。政策分析中的问题是指政策问题，即政策分析者所要分析、研究或处理的对象。政策分析所要处理的问题是公共问题，而非私人问题。关于什么是私人问题和公共问题，这是难以明确区分的。问题界定构成了政策分析的一个极为重要的组成部分，好的开端等于成功的一半，即成功地界定问题等于完成分析任务的一半。

逻辑斯蒂增长英语

逻辑斯蒂增长英语
逻辑斯蒂增长（Logistic Growth）的英文是：Logistic Growth。

逻辑斯蒂增长模型，又称自我限制增长模型，是一种描述种群增长速率先增加后减小，呈“S”型曲线的数学模型。

它是生物学、生态学和数学等学科中常用的一种模型。

这种模型在生态学和流行病学等领域中尤为重要，因为它能够描述资源有限的情况下种群或疾病的增长情况。

在逻辑斯蒂增长模型中，种群的增长率与种群大小成反比，当种群大小接近环境容纳量时，增长率逐渐减小，最终趋于零。

这个模型可以用微分方程来描述，也可以通过离散时间递推公式来模拟。

Supersymmetric Microscopic Theory of the Standard Model

arXiv:hep-ph/0009046v1 5 Sepnological standard model (SM) of high energy physics [4-22] with enormous success settles order in entangled experimental data. Although it has proven to be in spectacular agreement with experimental measurements and highly successful in a description and predicting a wide range of phenomena, however, it suﬀers from some vexing problems and many key questions of both the phenomenological and SUSY aspects have yet to be answered. • In phenomenological aspect the mechanism of the electroweak symmetry breaking is a complete mystery. The most problematic ingredient of such a breaking is the Higgs boson (in simplest version), which has not yet been discovered experimentally. If a weakly interacting Higgs boson exists, it will then appear below the TeV scale. Many possible

Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider

DESY-08-060, IZTECH-P-08-03, CUMQ-HEP-149, HIP-2008-15/TH
Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider
Durmu¸ s A. Demir1,2 , Mariana Frank3 , Katri Huitu4 , Santosh Kumar Rai4 , and Ismail Turan3
Department of Physics, Izmir Institute of Technology, IZTECH, TR35430 Izmir, Turkey. 2 Deutsches Elektronen - Synchrotron, DESY, D-22603 Hamburg, Germany. 3 Department of Physics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, CANADA H4B 1R6. and 4 Department of Physics, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Finland. Several supersymmetric models with extended gauge structures, motivated by either grand uniﬁcation or by neutrino mass generation, predict light doubly-charged Higgsinos. In this work we study productions and decays of doubly-charged Higgsinos present in left-right supersymmetric models, and show that they invariably lead to novel collider signals not found in the minimal supersymmetric model (MSSM) or in any of its extensions motivated by the µ problem or even in extra dimensional theories. We investigate their distinctive signatures at the Large Hadron Collider (LHC) in both pair– and single–production modes, and show that they are powerful tools in determining the underlying model via the measurements at the LHC experiments.

JWatcher软件用户手册说明书

analysis is best.The chapter then moves into detailed, step-by-step instructions on how to run each analysis. The coverage of these procedures is,necessarily,a bit more detailed than the other sections because most users will not be familiar with the specific features of each test.Finally,Chapter15includes four different out-standing laboratory exercises that use JWatcher to teach students:(1)how to develop their own ethogram and score behavior,(2)the differences between time sampling and continuous recordings, (3)how to conduct sequential analysis,and(4)how to use both sequential analysis and basic analysis to refine research questions from initial pilot data.These exercises use video clips downloadable from the JWatcher website free of charge and would be excellent teaching tools in the classroom.This manual is a vast improvement over the Version0.9Manual available on the JWatcher website, which only covers some basic guidelines for running the software,explains what the individual file types do,and indicates how to analyze results.The online manual has no coverage of the complex sequential analysis functions of JWatcher1.0.In summary,this book is a necessity for users at all experience levels who wish to quantify behavior using an event recorder.JWatcher software is free of charge and this manual is affordable enough that several copies could be purchased for use in one’s research laboratory.The money from the sale of the manual is used to support further development of the software so that the future versions of the program can be offered free of charge.Theodore StankowichOrganismic&Evolutionary BiologyUniversity of Massachusetts Amherst Morrill Science Center South,611N.Pleasant Street,Amherst,MA01003E-mail:Advance Access publication February14,2008doi:10.1093/icb/icn005An Introduction to Nervous Systems. Ralph J.Greenspan,editor.Woodbury,NY:Cold Spring Harbor Laboratory Press,2007. 172pp.ISBN978-0-87969-0(hardcover)$65.00,ISBN 978-0-87969-821-8(paper)$45.00.Over the past30years,there have been several iterations of books aimed at capturing in brief the essence of the organization and function of the nervous system.Not uncommonly,they extract general princi-ples that would be more fully explored in a compre-hensive text but do not otherwise deviate significantly from the traditional form and content of presentation. This one does.Ralph Greenspan is an established neuroscientist who has pioneered novel research to explore basic and cognitive aspects of nervous system function using the fruit fly as a model system.As he states in the Preface of this book,the Neurocience Institute,of which he is a staff scientist,aims to be a provocative academy,to“push the envelope.”That philosophy is clearly conveyed in the creative,non-traditional style of presentation in this special book. The title of the book,“An Introduction to Nervous Systems,”is a bit misleading.A more accurate title, although cumbersome,would be something like “An Introduction to Nervous Systems through Exam-ination of Some Invertebrate Models.”The book uses select examples from invertebrate nervous systems to convey some fundamental principles that apply in some respects to the organization and function of thenervous system in general.In the final,short chapter—“Are All Brains Alike?Are All Brains Different?”—theauthor writes“Perhaps all nervous systems make useof common general strategies.Anatomical disparitiesmay mask underlying functional similarities in thetasks performed by various circuits.”At first glance,it is surprising that nowhere in thetext are there descriptions of what has been learnedabout ion channels and membrane potentials from classical studies of squid giant axons;of neuralnetwork properties from studies of the crustacean stomatogastric ganglion;of nervous system develop-ment from experiments on fruit fly nerve cord or nematode worms;of sensory signaling and receptionfrom the moth or cricket;or of insect social structure,for example.The author’s enthusiasm for Drosophila,which represents his main research subject,is reflectedin a substantial fraction of the book.Moreover,thereis little or no discussion of how the principles described are employed in mammals.Surveying thebreadth of the neurobiology landscape seems not to bethe primary purpose of this book.Rather,it describesselect examples that highlight what studies of“simple”invertebrate nervous systems have taught us.The taleslink organization of the nervous system to the organism’s behavior,for which invertebrates haveproven to be especially valuable.In a modern, molecular,mammalian research universe,the rich439 Downloaded from https:///icb/article/48/3/439/627027 by Guangxi University of Nationalities user on 18 September 2023history of fundamental contributions of invertebrates to neuroscience may too often be overlooked.It is especially in this respect that the book is a welcome contribution to the neurobiological literature.In the introduction to Chapter4—“Modulation,The Spice of Neural Life”—the author writes:“The capabilities of invertebrates have traditionally been underesti-mated.Perhaps this is because they are not warm and fuzzy...For whatever reason,it has taken us an inordinately long time to realize that even the simplest animals have the capacity for modifying their behavior by adjusting the activities of their nervous systems. Perhaps this is a fundamental,inseparable property of nervous systems.”Despite the fact that the book deviates from a traditional style,in its own way it follows a rather traditional sequence,e.g.,membrane potentials,then chemical signaling and sensing,then neural circuits,then neuromodulation,then biological clocks,then higher,or cognitive,function.There is a lot to like in this book,not only in its fascinating content but in the style of presentation. Ralph Greenspan weaves a tapestry about the molecular,cellular and network origins of function and behavior,and the implications for speciation, using a variety of invertebrate models.The images he creates are expressed as interesting,often humorous, readable stories about what some nervous systems do, how they do it,and how that has evolved using some basic principles in novel ways.Each chapter begins with a relevant quote or poem from a literary or scientific giant that sets the stage and tone for the often poetic introduction and description that follows. The stories themselves—about swimming in Paramecium and jellyfish,light detection by barnacles, decision making by marine snails,circadian rhythms, flying,and mating—are fascinating because they are set in a context of understanding the generation and modulation of behavior and,in some cases,the impact on ecology and evolution.Although the author states in the Preface that the book is intended for the neurobiology novice posses-sing a basic introductory knowledge of biology,this reviewer believes that it would be more appropriate for an individual with an introductory neurobiological background.For example,in the very first chapter, one quickly discovers that understanding“simple”systems can be quite complex.In particular,students new to neurobiology often struggle with concepts underlying the generation of membrane potentials and the relationship of voltage and current,yet the text and figures require some understanding of these topics.In this respect,the Glossary at the end of the book seems uneven,defining some very basic biological terms yet not defining“receptor potential,”for example,which is named but not explained in the caption of Figure3.10.Not to quibble,but this reviewer and two other neuroscientists who scanned the book question some statements or generalizations proposed,particularly in the Introduction(“What are Brains For”?).For example,on page1it states“When it comes to brains,size unquestionably matters.”While that is no doubt true,it may be the organization of cells,i.e.the way they interact,that is more relevant.If it is size that is so important,then one should note that about three quarters of cells in mammalian brain are glial cells, not neurons,some potentially capable of modulating chemical signaling at up to100,000synapses,yet their contributions are not mentioned(see below). Furthermore,spinal cords also possess much of the organization and cellular interactions,e.g.,integrating sensory input and generating motor output,yet we view their capabilities as somewhat lacking in comparison with brain.What might be the funda-mental differences between invertebrate and verte-brate nervous systems and between brain and spinal cord that yield unique aspects of functional compe-tence?Or,are they as different as we imagine them to be,particularly in comparing function in invertebrates versus vertebrates?These are some interesting questions—not found in a typical comprehensive text—that might be explored a bit further in the Introduction and perhaps elsewhere in the book.In addition,on page2,the author writes“Chemical sensing is almost certainly the original sense...,”yet mechanically gated ion channels that could sense changes in flow or pressure in the ambient environ-ment are universal and also have been identified in prokaryotic organisms.Also,on page4,the author writes“And because none of us wants to submit to being experimented upon...we study animals.”Yet, there is a substantial and rapidly growing literature that provides insights on the organization and function of human brain from studies of living persons—for example from functional MRI or stimulation/recording of brain of awake epileptic patients—or of postmortem tissue samples.There are several other aspects of the book in its current form that would benefit from revision in a second edition.First,the emphasis is on how invertebrate nervous systems inform on nervous systems in general,but it is not clear in many cases to what extent the general organization of the behaviors is similar in invertebrates and vertebrates or whether similar molecules or mechanisms are used for different purposes.Does evolution mix and match bits and pieces of behavioral components that moves behavior in new directions?One also wonders whether440Book ReviewsDownloaded from https:///icb/article/48/3/439/627027 by Guangxi University of Nationalities user on 18 September 2023there are good examples of invertebrate nervous systems and behaviors that do not translate well to a mammalian equivalent.Second,the book has a traditional neurocentric focus—and some inverte-brates indeed have few glial cells—yet in the past couple of decades it has become abundantly clear from studies of mammalian systems that interactions of neurons with glia play vital roles in regulation of neural function,development and blood flow.Third, some of the figures could benefit from greater clarity or correction of the illustration or of the explanation in the caption,including citing the source link that is listed in the Bibliography at the end of the book.In addition,the Preface could note the location of the relevant Bibliography,currently organized by chapters but separate from them.It should be noted that the author also recently co-edited a much more compre-hensive(800pages),related book(“Invertebrate Neurobiology”)with Geoffrey North.In summary,this is an excellent book for gaining an appreciation for the links between form-function and behavior in the nervous system from invertebrate model systems and one that is interesting and enjoyable to read.It should be particularly valuable in inspiring budding or established life scientists to read more on the subject or even to become engaged in the pursuit of elucidating fundamental principles of neurobiology and behavior.It should stimulate broad questions about nervous systems and behavior. From a pedagogical perspective,I could imagine it being assigned as a short text in a general course on neurobiology and behavior or in a specialized neurobiology course that focuses on invertebrates or as a supplement to a more comprehensive text.Robert M.GrossfeldDepartment of Zoology NC State University,Raleigh,NC27695E-mail:*************************Advance Access publication February15,2008doi:10.1093/icb/icn004Rodent Societies–An Ecological and Evolutionary Perspective.Jerry O.Wolff and Paul W.Sherman,editors. Chicago,IL:University of Chicago Press,2007.610pp. ISBN0-226-90536-5(cloth),$125.00and ISBN0-226-90537-3(paper),$49.00.As the editors point out in the first sentence of the first chapter,“The Rodentia is the largest order of mammals consisting of more than2000species and comprising44%of all mammals.”This breadth makes the task of compiling a definitive and comprehensive anthology on rodent societies a nearly impossible task,but the result is undoubtedly the most exhaustive and progressive analysis of rodent social behavior to date.Deftly edited by Jerry Wolff and Paul Sherman,this well-organized book,consisting of41chapters from61contributors is,without doubt,a significant compendium of more than50years of research.That being said,only a true rodent lover is likely to love this book.Its creation was prompted by the success of the two volumes within this series that preceded it:Primate Societies and Cetacean Societies(published by University of Chicago Press).Thus,the scope and format of Rodent Societies is in many ways similar to that of the previous two volumes.The text is organized into nine sections,beginning with a succinct,but satisfying,overview of rodent evolutionary history and proceeding through sexual behavior,life histories and behavior,behavioral development,social behavior, antipredator behavior,comparative socioecology,con-servation and disease,and a final concluding sectionwritten by the editors on potential directions for future research.Each chapter concludes with a summary thatbriefly reviews the material,identifies caveats,and frequently suggests strategies for future research.The chapters are written by some of the most productiveand well-known scholars in the field but,as expected ina multi-authored work,the quality is uneven.Some chapters do a better job than others of achieving thestated goal to“synthesize and integrate the currentstate of knowledge about the social behavior of rodents”and to“provide ecological and evolutionary contexts for understanding rodent societies.”However,it generally succeeds in combining ideasand strategies from a wide range of disciplines to generate new theoretical and experimental paradigmsfor exploring rodent social behavior.Despite this,itfeels outdated in many places.Much of the work citedin the text is not new,with the majority of citationsdating before2000and a substantial number datingbefore1985.Even the photographs,all in black andwhite,are fairly old and some date back to the1950s.Some of the illustrations are even hand-drawn.Thismakes the book feel like historical retrospective rathera breakthrough collaborative of evolutionary and behavioral biology.441 Downloaded from https:///icb/article/48/3/439/627027 by Guangxi University of Nationalities user on 18 September 2023。

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a rXiv:h ep-ph/3263v33Aug2IUHET-423Supersymmetric left-right model and scalar potential Biswajoy Brahmachari Physics Department,Indiana University,Bloomington IN-47405,USA AbstractLeft-right symmetric model[1]is a natural extension of standard model.The symmetry breaking chain can be written asG LR[SU(2)L×SU(2)R×U(1)B−L] ∆R−→G[SU(2)L×U(1)Y]H1 H2−→G0[U(1)em].(1)Symmetry breaking mechanism is normally understood in the following way.One uses symmetries of G LR to write down allowed terms of a classical scalar potential.A stable breaking of symmetry is obtained whenﬁeld conﬁguration(values ofﬁelds)is such that the potential is at its minimum at all space-time points.We know that these values ofﬁelds are the VEVs and we also know that the VEVs obey residual symmetries.Hence electric charge and color symmetries remain.Mininum energy state of Higgs scalars need not have the symmetry properties of the gauge bosons.So the symmetry of the combined system of fermions,gauge bosons and Higgs scalars can be broken.In this paper we willﬁrst state a miminal Higgs scalar spectrum of left-right symmetric model.Then we will write them in the form of square matrices and apply Hamiltion-Cayley theorem to these matrices to see what happens.It will lead to polymonial equations(quadratic for this case)which are satisﬁed by these matrices.We will physically interpret these equations as minimization conditions.Minimal Higgs choice for a model based on G LR is∆R=(1,3,2)∆L=(3,1,−2)φ=(2,2,0).One can write these VEVs as matrices in a SU(2)L×SU(2)R basis where rows are SU(2)R multiplets and columns are SU(2)L multiplets.In writing so one can suppress abelian U(1)B−L as well as non-abelian color degrees of freedoms.Then one getsφ = κ100κ2 ∆L = 00v L0 ∆R = 0v R00 .(2) We can read-oﬀthat φ breaks both SU(2)L and SU(2)R symmetries.However, ∆R breaks only the SU(2)R symmetry.From experiments one knows that SU(2)R symmetry is broken at a higher scale.This is because gauge bosons corresponding to broken SU(2)R symmetries are yet to be observed.Even though mass splitting between fermions within a SU(2)L multiplet parametrize SU(2)L breaking,values of parametersκ1,κ2remain un-known up to magnitudes of Yukawa couplings of corresponding fermions.Similarly we can think of similar manifestations of SU(2)R and SU(2)L×SU(2)R symmetries in the masses2of extra fermions.Thus we mustﬁnd a way to study allowed values ofκ1,κ2,v L and v R from theory.This is a motivation to further study the scalar potential.A number of studies of minimizing scalar potential exist[2].Typically,one writes the most general potential using gauge symmetries and then it is minimized by taking deriva-tives of potential with respect to VEVs and equating them to zero.This set of equations constrain parameter space of VEVs.We consider a reverse situation.We ask whether given only matrix forms of VEVs is it possible to construct a minimal potential which leads to desired symmetry breaking for all possible values ofκ1,κ2,v L and v R?In other words, instead of writing the complete potential and study the ranges ofκ1,κ2,v L and v R,is it possible to obtain the unique subset of terms of the potential which allow all possible values ofκ1,κ2,v L and v R?This what we answer below.The Hamilton-Cayley theorem states:Every square matrix must satisfy its own char-acteristic equation.That is,ifdet(A−λI)=c nλn+c n−1λn−1+...+c2λ2+c1λ+c0(3) thenc n A n+c n−1A n−1+...+c2A2+c1A+c0=0.(4) Using equations(2)(3)and(4)we getφ 2−(κ1+κ2) φ +κ1κ2=0 ∆L 2=0 ∆R 2=0.(5) These equations are satisﬁed for any value ofκ1,κ2,v L and v R.Suppersymmtry allows only trilinear terms in the superpotential.Thus minimization conditions are at most quadratic.It is a nice coincidence that2×2matrices lead to quadratic characteristic equations.The termκ1κ2is present in the minimization condition. We must have a linear term in superpotential.However there is no singlet scalar in the model.So we must haveEither:κ1∼0or:κ2∼0(6) Then the superpotential reads as,W=W1+W2W1=12κ1φ2W2=M L∆2L+M R∆2R(7) W2vanishes identically,for all values of v L,v R,M L,M R.It does not contribute to energy if the VEVs are of the form of(2).W1however needs to be minimized and all possible values3ofκ1orκ2are not allowed.We had to chose eitherκ1orκ2to vanish.So we have got a negative answer to our question.This is our result.Thus we have constructed a superpotential of supersymmetric left-right model using Hamilton-Cayley theorem.We had to chose eitherκ1orκ2to vanish.We have chosen κ2=0.This means that down sector of fermions remains massless.This research was supported by U.S Department of Energy under the grant number DE-FG02-91ER40661.References[1]J.C.Pati and A.Salam,Phys.Rev D10,275(1974);R.N.Mohapatra and J.C.Pati,Phys.Rev.D11,566(1975)[2]R.N.Mohapatra and G.Senjanovic,Phys.Rev.D23,165(1981);B.Brahmachari,M.K.Samal and U.Sarkar,Ahmedabad,b Report No:PRL-TH-94-4, e-Print Archive:hep-ph/94023234。