When q theory meets large losses risks and agency conflicts

a r X i v :h e p -p h /9409446v 2 1 O c t 1994ITP–SB–94–42hep-ph/9409446September,1994High energy scattering in QCD and cross singularities of Wilson loops I.A.Korchemskaya ∗Dipartimento di Fisica,Universit`a di Parma and INFN,Gruppo Collegato di Parma,I–43100Parma,Italy and G.P.Korchemsky †Institute for Theoretical Physics,State University of New York at Stony Brook,Stony Brook,New York 11794–3840,U.S.A.AbstractWe consider elastic quark-quark scattering at high energy and fixed transferred mo-mentum.Performing factorization of soft gluon exchanges into Wilson line expectation value we find that there is one-to-one correspondence between high energy asymptotics in QCD and renormalization properties of the so called cross singularities of Wilson ing this relation we show that the asymptotic behavior of the quark-quark scattering amplitude is controlled by a 2×2matrix of the cross anomalous dimensions.We evaluate the matrix of cross anomalous dimension to two-loop order and study the properties of the obtained expressions to higher loop order.1.IntroductionRecent experimental data from Tevatron and HERA renewed our interest to theoretical in-terpretation of the well known phenomena in the physics of strong interactions like growth of the total hadronic cross section at high energy and increasing of the structure function of deep inelastic scattering at small values of the Bjorken variable x.In both cases we deal with the asymptotic behavior of hadronic scattering amplitudes at high energy s andfixed trans-ferred momenta t the so called Regge behavior in high-energy QCD[1].This problem is one of the longstanding in QCD and previous attempts to solve it have led to the discovery of the BFKL pomeron[2].However,found in the leading logarithmic approximation,αs≪1and αs log s∼1,the BFKL pomeron leads to the expressions for the scattering amplitudes which violate the unitarity Froissart bound.To preserve the unitarity of the S−matrix,one has to go beyond the leading logarithmic approximation calculating the scattering amplitudes.The problem turns out to be very complicated and the following approaches have been proposed:•Generalized leading logarithmic approximation[3,4],in which we start with the lead-ing logarithmic result and add“minimal”number of nonleading corrections in order to unitarize the result;•Two-dimensional reggeonfield theory[5],in which the high-energy scattering of gluons is described by the S−matrix of the effective two-dimensionalfield theory corresponding to dynamics of transverse gluonic degrees of freedom;•Quasielastic unitarity approximation[6],in which one takes into account only contribu-tions of soft gluons with transverse momenta much smaller hadronic scale.These schemes are approximate and they were developed to resum special class of corrections which are expected to determine the high-energy asymptotics of the scattering amplitudes.In each case,QCD is replaced by simplified effective theory which inherits a rich structure of the original theory.Recently[7,8],a progress has been made using the generalized leading logarithmic approxi-mation.It was found that in this approximation high energy QCD turns out to be a completely integrable model equivalent to the one-dimensional Heisenberg magnet of spin s=0.This opens the possibility to apply powefull quantum inverse scattering method and calculate the hadronic scattering amplitudes by means of the Generalized Bethe Ansatz[8].There were different proposals for the effective two-dimensional reggeonfield theory[5,9] and the hope is that the model can be solved exactly.Although to the lowest order of PT the effective reggeon theory reproduces the QCD expressions for the scattering amplitudes,the all order perturbative solution is not available yet.The present paper is devoted to the calculation of the hadronic scattering amplitudes in the quasielastic unitarity approximation[6].In this approximation,we use the parton model and approximate the hadron-hadron interaction as the scattering of partons.Partons interact with each other by exchanging soft gluons with energy which is much smaller than parton energy,s, but much bigger than the QCD scaleΛQCD in order for the perturbative QCD to be applicable. Being calculated to the lowest orders of PT,the parton-parton scattering amplitudes get large perturbative corrections(αs log s log t)n due to soft gluon exchanges[6]and these Sudakov logarithms need to be resummed to all orders of PT.The resummation of leading logarithmic corrections can be performed using the“evolution equation”technique[6,10]but we don’thave a regular way to resum and control nonleading logarithmic corrections to the scattering amplitude.A new approach which enables us to take into account systematically both leading and nonleading logarithmic corrections to the parton-parton scattering amplitudes has been proposed in [11].In this approach,the partonic scattering in QCD is described by the dynamics of the gauge invariant collective variables defined asW =W (C 1,C 2,...,C n )≡ 0|T tr R 1P e ig C 1dx ·A (x )···tr R n P e ig C n dx ·A (x )|0 ,(1.1)the so called Wilson loop functions .Here,the path-ordered exponentials are evaluated along the closed paths C 1...C n in Minkowski space-time and the gauge fields are defined in the irreducible representations R 1...R n of the SU (N )gauge group.One should stress that it is not for the first time when one dealt with this object.There were attempts [12]in 80’s to study the nonperturbative dynamics of QCD in terms of Wilson loops.The interest to the Wilson loops was renewed after it was recognized [13]that the same loop functions enter into consideration in perturbative QCD when we study the effects of soft gluons in hardonic processes.Interacting with soft gluons described by gauge field A µ(x ),partons behave as relativistic charged classical particles and the path-ordered exponentials appear as eikonal phases of partons.The integration paths C 1...C n have a meaning of semi-classical trajectories of partons and the choice of the representations R 1...R n is fixed by their charges.In particular,R is fundamental and adjoint representation of the SU (N )group for quarks and gluons,respectively.The paper is organized as follows.In sect.2we consider the amplitude of near forward elastic quark-quark scattering and show its relation with the renormalization properties of the so called cross singularities of Wilson loops.In sects.3and 4we analyze the cross singularities of Wilson loops to the lowest orders of PT and find two-loop expression for the matrix of cross anomalous dimensions.The properties of the obtained expressions which can be generalized to all orders of PT are studied in sect.5.The details of the calculations of the two-loop Feynman diagrams contributing to the Wilson lines are given in Appendices A and rge N limit of the Wilson line is analysed in Appendix C.2.High energy scattering in QCDLet us briefly summarize the results of the paper [11]concerning the relation between high energy behavior of the scattering amplitudes in QCD and the renormalization properties of the Wilson loops.We consider the near forward elastic quark-quark scattering in the following kinematics:s,m 2≫−t ≫λ2≫Λ2QCD.Here,s =(p 1+p 2)2is the invariant energy of quarks with mass m ,t =(p 1−p ′1)2is the transferred momentum and λ2is the IR cutoff(characteristic hadronic scale)which is introduced to regularize infrared divergences.Notice that we don’t need to fix the relation between s and m and quarks may be heavy.The scattering amplitude T i ′j ′ij contains the color indices of the incoming and outgoing quarks.The quarks interact with each other by exchanging soft gluons with the total momentum q =p 1−p ′1.In the center of mass frame of incoming quarks,for s ≫−t ,the transferred momentum has the light-cone components q =(q +,q −, q )with q ±=12(q 0±q 3)=0and q 2=− q 2=t .Since the transferred momentum is much smaller than the energies of incoming quarks,the only effect of their interaction with soft gluons isthe appearance of additional phase in the wave functions of the incoming quarks.This phase, the so called eikonal phase,is equal to a Wilson line P e i C dx·A(x)defined in the fundamental representation of the SU(N)group and evaluated along the classical trajectory C of the quark. We combine the eikonal phases of both quarks and obtain the representation for the quark-quark scattering amplitude as[11]T i′j′ij sλ2 =sinhγ d2z e−i z· q W i′j′ij(γ, z2λ2),t=− q2,(2.2)where the line function W i′j′ijis given byW i′j′ij(γ, z2λ2)= 0|T P e ig ∞−∞dαv1·A(v1α) i′i P e ig ∞−∞dβv2·A(v2β+z) j′j|0 .(2.3)Here,two Wilson lines are evaluated along infinite lines in the direction of the quark velocities v1=p1/m and v2=p2/m and the integration paths are separated by the impact vector z=(0+,0−, z)in the transverse direction,v1·z=v2·z=0.Being expanded in powers of the gaugefield,expression(2.2)reproduces the quark-quark scattering amplitude in the eikonal approximation.Integration over two-dimensional impact vector z was introduced in(2.2)to ensure the total transferred momentum in the t−channel to be q=(0+,0−, q).Indeed,it follows from(2.2)that the total momentum of gluons k tot. propagating in the t−channel is restricted by the followingδ−functions:δ(k tot.·v1)δ(k tot.·v2)δ( k tot.− q)=1sinhγδ(4)(k tot.−q),where thefirstδ−function comes from integration overαin(2.3),the second one from inte-gration overβand the last one from integration over z in(2.2).To compensate the additional factor,sinhγ,in the r.h.s.of this relation,the same factor was introduced in the expression (2.2).The scattering amplitude(2.2)depends on the quark velocities v1and v2,the transferred momentum q and IR cutoffλ.These variables give rise to only two scalar dimensionless invariants:(v1v2)=s/m2and t/λ2as explicitly indicated in(2.2).The s−dependence of the amplitude comes through the dependence on the angleγbetween quark4−velocities v1and v2 defined in Minkowski space-time as(v1·v2)=coshγ.(2.4) For arbitrary velocities v1and v2,the angleγmay take real and complex values and in the limit of high energy quark-quark scattering(s≫m2)we haveγ=logs2.1.High-energy scattering in QEDOne may use the expression (2.2)for the scattering amplitude in this case,butthe calculation of the Wilson line (2.3)is simplified because for abelian gauge group a path-ordered exponent coincides with an ordinary exponent.Moreover,since photons don’t interact with each other,the calculation of Wilson lines in QED is reduced to the integration of a free photon propagator D µν(x )along the path and the result of calculation isW QED (γ,z 2λ2)=exp (ie )24πcoth γ,(2.6)where λis a fictitious photon mass.After substitution of this relation into (2.2)and integration over impact vector we get the expression for the scattering amplitude in QED [14]T QED s λ2 =ie 2cosh γλ2 −i e 24πcoth γ)4πcoth γ).(2.7)In the limit s/m 2→∞or,equivalently γ→∞,the expectation value (2.6)does not depend on s and,as a consequence,the scattering amplitude has the asymptotics T/T Born ∼s 0with T Born =ie2m 2the amplitude in the Born approximation.This implies that photon is notreggeized in QED [14].2.2.Wilson lines in perturbative QCDThe evaluation of the Wilson line in perturbative QCD is much more complicated than in QED.To explain the approach [11]for the evaluation of the Wilson line (2.3),let us consider as an example the one-loop calculation of W in the Feynman ing the definition (2.3),we getW 1−loop =I ⊗I +(t a ⊗t a )g 2[−(v 1α−v 2β)2+ z 2+i 0]D/2−1,(2.8)where a direct product of the gauge generators defined in the fundamental representation takes care of the color indices of the quarks.In this expression,gluon is attached to both Wilson lines at points v 1αand v 2β+z and we integrate the gluon propagator v µ1v ν2D µν(v 1α−v 2β−z )over positions of these points.To regularize IR divergences we introduced the dimensional regularization with D =4−2ε,(ε<0)and λbeing the IR renormalization parameter.There is another contribution to W 1−loop corresponding to the case when gluon is attached by both ends to one of the Wilson lines.A careful treatment shows that this contribution vanishes.Performing integration over parameters αand βin (2.8)we getW 1−loop (γ,λ2 z 2)=I ⊗I +(t a ⊗t a )αs MS −scheme,this result coincides up to color factor with the lowest term in the expansion of the analogous expression (2.6)in QED in powers of e 2.The evaluation of the Wilson line(2.3)in QCD is based on the following observation.Theone-loop expression(2.9)for the line function is divergent for z=0andε<0.This divergencehas an ultraviolet origin because it comes from integration over smallαandβin(2.8),that is from gluons propagating at short distances(v1α−v2β)between quark trajectories asα,β→0.One should notice that the ultraviolet(UV)divergences of Wilson lines at z=0have nothing to do with the“conventional”ultraviolet singularities in QCD.For z=0,the integrationpaths of Wilson lines in(2.3)cross each other at point0and UV divergences,the so calledcross divergences,appear when one integrates gluon propagators along integration path at the vicinity of the cross point[15].We note that the cross divergences do not appear in W1−loop fornonzero z because,as it enters into the integral(2.8),nonzero z2regularizes gluon propagator at short distances asα,β→0.Thus, z2has a meaning of an UV cutofffor the one-loop line function W and the depen-dence of the original line function W(γ,λ2 z2)on z2is in one-to-one correspondence with the dependence of the same Wilson line but with z=0on the UV cutoffwhich we have to introduceto regularize the cross singularities.This property suggests the following way for calculation ofthe z−dependence of the Wilson lines(2.3).First,we put z=0in the definition(2.3)of the line function and introduce the regularization of cross singularities of W.Then,we renormalizecross singularities and identify UV cutoffwith impact vector asµ2=1/ z2.We conclude that the z−dependence of the line function W and,as consequence,the t−asymptotics of the scat-tering amplitude(2.2)are controlled by the renormalization properties of the cross singularitiesof Wilson loops.2.3.Renormalization properties of Wilson linesThe renormalization properties of the loop functions in QCD have been studied in detail[15]and can be summarized as follows.Being expanded in powers of gauge potential,W(C1,...,C n) can be expressed as multiple integrals of the Green functions along the paths C1...C n.Theloop function is not a well defined object because it contains different kinds of divergences.First of all,it has the conventional ultraviolet(UV)divergences of the Green functions in perturbative QCD.Moreover,as it wasfirst found in[16],the Wilson loops have very specificUV divergences which depend on the properties of the integration paths C in the definition (2.3).For instance,the expansion of the loop function to the lowest order of PT involvesthe contour integral C dxµ C dyνDµν(x−y)which is potentially divergent at x=y due to singular behavior of the gluon propagator at short distances.The divergences come either when y approaches x along the path C or when the path crosses itself and both x and yapproach the cross point.In both cases divergences have an UV origin because they comefrom integration at short distances.In thefirst case,UV divergences can be absorbed into renormalization of the coupling constant and gaugefields provided that the integration path is smooth everywhere.Otherwise,if the path is smooth everywhere except of a one point where it has a cusp,additional UV divergences,the so-called“cusp”singularities,appear which can be renormalized multiplicatively[17].The corresponding anomalous dimension,Γcusp(γ,g),the cusp anomalous dimension is a gauge invariant function of the coupling constant and the cusp angle.If the integration path crosses itself(or the paths C1...C n cross each other),additional “crossed”singularities appear in the loop function[15].It was found[13]that these renormalization properties of the Wilson loops which look liketheir undesired features are of the most importance in perturbative QCD.The same function,the cusp anomalous dimension of a Wilson line,appears when one studies the infrared(IR) singularities of on-shell form factors or the velocity-dependent anomalous dimension in the effective heavy quarkfield theory.The anomalous dimensions of the Wilson lines govern the IR logarithms in the same manner as the anomalous dimensions of the local composite twist-2 operators control the collinear singularities one encounters studying the structure functions of deep inelastic scattering.Moreover,there is a remarkable relation[11]between the high-energy behavior of the scattering amplitudes in the quasielastic unitarity approximation and the renormalization properties of the“cross”divergences of the loop function W.2.4.Cross anomalous dimensionThe renormalization properties of the cross divergences were studied in[15].It was shown that the loop function(1.1)with all Wilson loops defined in the fundamental representation of the SU(N)group(R1=···=R n=F)and paths having a cross point,is mixed under renormalization with loop functions evaluated along the integration paths which are different from original paths at the vicinity of the cross point.As an important example we consider the Wilson lines(W1)i′j′ij and(W2)i′j′ij defined infig.1.Although the integration paths infig.1 have an infinite length and they are open we could get two Wilson loops by projecting the line functions(W1)i′j′ij and(W2)i′j′ij onto the color structureδi′jδj′i.We choose the Wilson lines infig.1(a)and1(b)to be defined in the fundamental represen-tation of the SU(N)gauge group.According to the general analysis[15],the line function of fig.1(a)has cross singularities and under their renormalization it is mixed with the Wilson line offig.1(b).As a consequence,the renormalized line functions W1and W2satisfy the following renormalization group(RG)equation[15]µ∂∂g W a=−Γab cross(γ,g)W b,a,b=1,2,(2.10)where W a≡(W a)i′j′ij andµis renormalization point.Here,Γcross(γ,g)is the cross anomalousdimension which is a gauge invariant2×2matrix depending only on the coupling constant and the angleγbetween lines at the cross point.It is important to notice that the RG equation (2.10)is valid only in the fundamental representation of the gauge group and its generalization to another representations is uknown.2.5.Evaluation of the scattering amplitudeWe recall that the evaluation of the scattering amplitude(2.2)is based on the following property of the line function ing the definition(2.3)of W we introduce into consideration the Wilson line W1infig.1(a).The only difference between them is that the integration paths in (2.3)do not cross each other for nonzero z.For z=0the Wilson line W(γ, z2λ2)is UVfinite but for z=0it coincides with W1and has cross divergences.The distance between quark trajectories, z2,in the definition(2.3)of W plays a role of UV cutofffor cross singularities and the z−dependence of W is the same as the dependence of the Wilson line W1(γ,µ2/λ2)on the renormalization parameterµ.Solving the RG equation(2.10)for W1(γ,µ2/λ2)with the boundary conditions,W1(γ,1)=δi′iδj′j and W2(γ,1)=δi′jδj′i,we substituteµ2=1/ z2andfind the following expression for the scattering amplitude[11]Ti ′j′ij s λ2 =sinh γ d 2 z e −i z q A 11(γ, z 2λ2)δii ′δjj ′+A 12(γ, z 2λ2)δij ′δji ′ ,(2.11)where A 11and A 12are elements of the 2×2matrixA qq γ,z 2λ2 =T exp − 1/zλdττΓcross (iπ−γ,g (τ)),where γis the angle between velocities of incoming quark and antiquark.The expression (2.11)takes into account all log t and log s corrections to the scattering amplitude.We conclude from (2.12)that it is the matrix of the cross anomalous dimensions which governs the high energy behavior of the scattering amplitude.As it follows from (2.11),the s −dependence of the amplitude comes from the γ−dependence of Γcross (γ,g )while the t −dependence originates from the evolution of the coupling constant.To find the asymptotic behavior of the scattering amplitude (2.11)we need to know the large γ−behavior of Γcross (γ,g )to all orders of perturbation theory.To this end,we perform the one-loop calculation of Γcross (γ,g )in the next section and try to find the properties of this matrix which can be generalized to higher loop orders.3.One-loop calculation of the cross anomalous dimen-sionTo find the cross anomalous dimension we evaluate the line functions of fig.1(a)and 1(b)to the lowest order of PT and substitute them into (2.10).In the Born approximation the line functions have trivial expressionsW (0)1=δi ′i δj ′j ≡|1 ,W (0)2=δi ′j δj ′i ≡|2 ,(3.13)where |1 and |2 denote two states in color space.To one-loop order the line functions are given by path integrals similar to that in (2.8).To evaluate the integrals we introduce the following parameterization of the integration paths of fig.1,C I =v 1α,C II =v 2β,C III =v 1β,C IV =v 2α,(3.14)where 0<α<∞and −∞<β<0and where v 1and v 2are quark velocities.The integration paths in fig.1(a)and 1(b)cross each other at point 0and go to infinity along the vectors v 1and v 2.As a consequence,the line functions W 1and W 2have UV divergences due to the cross point and IR divergences due to the infinite length of the paths.To regularize the cross singularities we use the dimensional regularization with D =4−2εand in order to regularize IR divergences we introduce a fictitious gluon mass λ.We fix the Feynman gauge and define the gluon propagator in the coordinate representation as D µν(x )=g µνD (x )withD (x )=−i d D kk 2−λ2+i 0=−14α .(3.15)After the decomposition of the integration path of fig.1(a)as C =C I +C II +C III +C IV we get the set of Feynman diagrams of fig.2which contribute to one-loop corrections to the line function W 1.Then,the contribution of the diagram of fig.2(1)to W 1is given by(ig )2t a i ′i t a j ′j C I dx µ C II dy νD µν(x −y )≡−g 2(v 1v 2)t a ⊗t a ∞0dα 0−∞dβD (v 1α−v 2β),where integration is performed over positions of gluons on the paths C I and C II and the direct product of the gauge group generators takes care of color indices of the line function.Substi-tuting the gluon propagator(3.15)and integrating over αand βwe get the expression for the “Feynman integral”F 1=(ig )2C I dx µ C II dy νD µν(x −y )=−αs λ2 εΓ(1+ε)π 4πµ22ε(iπ−γ)coth γ,F 3=−2F 4=−αsλ2 εΓ(1+ε)MS −scheme.Finally,the renormalized one-loop expression for the line function W 1is given byW (1)1=−αsλ2(t a ii ′t a jj ′)iπcoth γ.(3.18)The calculation of the line function W 2involves the integration over the path of fig.1(b)which is different from the path of fig.1(a)only at the cross point.The contribution of the individualFeynman diagram of fig.2to the line function W 1has the form of the product,W =F ·C ·w ,of the corresponding Feynman integral (F ),the color factor (C )and the combinatorial weight of the diagram (w ).The difference between the paths of fig.1(a)and 1(b)at the cross point is not important when one calculates the Feynman integral F and the combinatorial weight w but it does affect the color factors of the corresponding diagrams.This means,that to any order of perturbation theory the same Feynman integrals contribute to both line functions and the only difference between W 1and W 2isthatintegralsenterwithdifferentcolor factors.In particular,using the expressions (3.16)and (3.17)we get the one-loop expression for the line function W 2as W (1)2=C F δi ′j δj ′i (2F 1+4F 4)+t a i ′j t a j ′i (2F 2+2F 3).After substitution of the Feynman integrals (3.16)and (3.17)into this expression we subtract a pole in theπlog µ22N δij δkl +1πΓ(γ),(3.21)Γ(γ)= −iπN coth γ .Here,γis the angle between quark velocities v 1and v 2in Minkowski space-time defined in (2.4).3.1.Properties of the one-loop ΓcrossThe obtained expression (3.21)for one-loop Γcross obeys the following interesting properties.All elements of the matrix Γcross have nontrivial imaginary parts which change their sign under the replacement γ→iπ−γ:Im Γcross (iπ−γ,g )=−Im Γcross (γ,g ).As was shown in sect.2.5,this transformation of the angle allows us to relate quark-quark and quark-antiquark scattering amplitudes.Calculating the determinant of the matrix(3.21)we obtain the expressiondetΓcross(γ,g)= αs N2 ,(3.22) which,first,has zero imaginary part and,second,is invariant underγ→iπ−γ.This property implies that the elements of the matrix(3.21)are“fine tunned”.An additional argument in favour of this observation comes from the consideration of the largeγbehavior ofΓcross.In the limit of largeγdifferent elements of the matrix have the following behaviorΓ11cross∼Γ12cross∼O(γ0),Γ12cross∼Γ22cross∼O(γ),which leads to the asymptotics detΓcross∼O(γ)in general.However,the one-loop result (3.22)implies that the leading term O(γ)vanishes and the determinant has the asymptotics detΓcross∼O(γ0)while trΓcross∼O(γ).The eigenvalues of the matrixΓ(γ)satisfy the characteristic equationΓ2±−Γ± Nγcothγ−N−2iπN −π2N2−1N3γ−1+O γ−2 ,(3.24) withγ=log(s/m2)in the limit s≫m2.3.2.Asymptotic behavior of the scattering amplitudesLet us substitute the one-loop expression(3.21)for the matrixΓcross into(2.11)and(2.12). One-loop matricesΓcross(γ,g(τ))commute with each other for differentτand we can omit T−ordering in the definition(2.12)of the matrix A.After diagonalization of the one-loop matrixΓ(γ)by a proper unitary transformation we getA qq γ,λ2z2 =Γ+−Γ(γ)ταs(τ)Γ−−Γ+exp −Γ+ 1/zλdτπ ,where the eigenvaluesΓ±were defined in(3.23).Finally,wefind the following expression for the scattering amplitude(2.11)T i′j′ij=δi′iδj′j T(0)+t a i′i t a j′j T(8),(3.25) where two invariant amplitudes correspond to the exchange in the t−channel by states with the quantum numbers of vacuum and gluon and are given byT(0)=−sinhγΓ+−Γ−(T+−T−),T(8)=2iπcoshγΓ+−Γ−.(3.26)Here the notation was introduced for the Fourier transformsT ±=tταs (τ)Γ± d 2z e −i z · q log 1/z 2Λ2QCD2πΓ± sλ2 Γ 1+αsΓ 1−αstsm 2 α(t ),(3.30)with the Regge trajectory α(t )=−αsλ2.We can improve the leading logarithm approxi-mation(3.30)by taking into account nonleading corrections to (3.29)in the limit αs log s/m 2∼αs log t/λ2∼ing the large energy behavior of the eigenvalues (3.24)we find the following expressions for the amplitudes of singlet and octet exchangesT (0)=−T 0Γ−(T +−T −),T (8)=2iπT 0 T +−Γ−2m 2t and Γ±defined in (3.24).The functions T +and T −have a Regge like behavior (3.29)and for Γ+≫Γ−we have T +≪T −.For Γ−=0the expression (3.31)coincides withthe leading log result(3.30).We stress that the amplitude T(0)of the singlet exchange is unvanishing only due to nonleading logarithmic corrections.Moreover,as follows from(3.31), the amplitude T(0)gets dominant contribution from T−and not from T+.The same is true for the amplitude T(8)of the octet exchange in which exponential fall of T+can not compete with the factorΓ−/Γ+in front of T−.Thus,the high-energy asymptotic behavior of the scattering amplitude(3.31)is dominated by the contribution of T−and as a consequence the amplitude of the octet exchange is suppressed by the factor1/Γ+=O(log−1s/m2)as compared to that to the amplitude of the singlet paring this behavior with(3.30)we concludethat nonleading logarithmic corrections drastically change the leading log asymptotics of the scattering amplitude.Expression(3.29)was found under condition that we neglect theτ−dependence of the coupling constantαs(τ)in(3.27).We notice,however,that(3.29)becomes divergent for the special value of the coupling constantαs=2π/Γ±.To understand the origin of this divergence we deduce from(3.27)that it is the distance between quark trajectories,z2,whichfixes the scale of the coupling constant.Then,for the perturbative expansion to be meaninfull this distance should be much bigger than the QCD scale1/Λ2QCD.On the other hand,to get the scattering amplitude in(3.27)we have to integrate in(3.27)over all possible z2including large distances. For the z−integral in(3.27)to get dominant contribution in PT one has to impose additional conditions onΓ±and q2,or equivalently on s and t.Otherwise,the perturbative expression (3.27)become divergent at large distances.The analysis of PT applicability conditions for (3.27)can be performed similar to the analysis given in[19]for the Drell-Yan process.The properties of the scattering amplitude are closely related to the particular form of the one-loop cross anomalous dimension(3.21).Natural question arises whether the asymptotic behavior of the scattering amplitudes will be changed after we take into account higher order corrections to the cross anomalous dimension.In the next section we answer this question by performing the calculation of the matrix of cross anomalous dimension to two-loop order in the Feynman gauge.4.Two-loop calculation of the cross anomalous dimen-sionTofind two-loop expression for the cross anomalous dimension we have to calculate the line functions W1and W2to the second order of PT by taking into account the next terms in the expansion of Wilson lines in powers of the coupling constant and effects of gluon self-interaction. The resulting Feynman diagrams contributing to W1are shown infigs.3–5and we divide them into three different groups1.QED-like diagrams offig.3in which gluons don’t interact with each other;2.Self-energy diagrams offig.4containing self-energy corrections to the gluon propagator;3.Three-gluon diagrams offig.5having three-gluon vertex of self-interaction.Evaluating the diagrams offig.5containing three gluon vertex,we notice that the Lorentz indices of the three gluon vertexΓµνρare saturated by the vectors v1or v2depending to which line the gluons are attached.As a consequence,the diagrams with all three gluons attached to the same line vanish asΓµνρvµ1vν1vρ1=0.We didn’t include these diagrams infig.5.。

高三英语学术文章单选题50题1. In the scientific research paper, the term "hypothesis" is closest in meaning to _.A. theoryB. experimentC. conclusionD. assumption答案：D。

解析：“hypothesis”的意思是假设，假定。

“assumption”也表示假定，假设，在学术语境中，当提出一个假设来进行研究时，这两个词意思相近。

“theory”指理论，是经过大量研究和论证后的成果；“experiment”是实验，是验证假设或理论的手段；“conclusion”是结论，是研究之后得出的结果，所以选D。

2. The historical article mentioned "feudal system", which refers to _.A. democratic systemB. hierarchical social systemC. capitalist systemD. modern political system答案：B。

解析：“feudal system”是封建制度，它是一种等级森严的社会制度。

“democratic system”是民主制度；“capitalist system”是资本主义制度；“modern political system”是现代政治制度，与封建制度完全不同概念，所以选B。

3. In a literary review, "metaphor" is a figure of speech that _.A. gives human qualities to non - human thingsB. compares two different things without using "like" or "as"C. uses exaggeration to emphasize a pointD. repeats the same sound at the beginning of words答案：B。

Self-Regulatory Focus Theory (SRFT) is a psychologicalSelf-Regulatory Focus Theory (SRFT) is a psychological theory that explains how individuals approach goals and make decisions. It suggests that people have two different mindsets when it comes to achieving their goals: promotion focus and prevention focus.Promotion focus is characterized by a desire to achieve positive outcomes and gain advantages. People with a promotion focus are motivated by the possibility of success and tend to engage in actions that will help them achieve their goals. They are more likely to take risks and seek out new opportunities.Prevention focus, on the other hand, is characterized by a desire to avoid negative outcomes and losses. People with a prevention focus are motivated by the possibility of failure and tend to engage in actions that will help them avoid mistakes or problems. They are more likely to play it safe and stick to familiar routines.In terms of leadership, SRFT suggests that leaders who have a strong promotion focus may be more effective at inspiring and motivating their team members to achieve ambitious goals. They may be more willing to take risks and embrace change, which can help their team members grow and develop.However, leaders who have a strong prevention focus may be more effective at avoiding problems and minimizing risks. They may be more cautious and detail-oriented, which can help ensure that their team members are following best practices and avoiding costly mistakes.Ultimately, the most effective leaders are those who are able to balance promotion and prevention focus, depending on the situation and the needs of their team. By understanding the strengths and weaknesses of each mindset, leaders can make better decisions and guide their team members towards success.。

UNIT1PEOPLE OF ACHIEVEMENT一、阅读词汇——在词块中明义1．physical properties物理特征personal property私人财产2．from liquid to vapour从液体到蒸气3．illegal/banned substances非法/禁用物品without substance毫无事实根据4．a top politician大牌政客5．numerous people许多人6．extraordinary genius非凡的天才7．an educational institute教育机构a distribution institution分配制度8．mourn the dead哀悼逝者9．a water-saving device节水装置10．draft a speech起草发言稿二、表达词汇——在语境中活用(一)在括号内写出蓝体词汇在语境中的汉语意思1.2021·全国乙卷书面表达Almost all kinds of information can be obtained through the Internet.(vt.获得)2．She defeated all her opponents and won the gold medal in shooting.(vt.击败)3．Surprisingly,students of the senior schools are mostly girls.(adv.主要地) 4．Citizens in this area were forced to flee the city.(vt.迅速离开)5．The competition had to be put off under the special circumstance.(n.状况) 6．The theory is not yet scientifically established.(n.理论)7．I first encountered him when studying at Cambridge.(vt.偶然碰到)8．Large sums of money have been donated to the disaster area.(n.金额)(二)写出蓝体词汇的语境之义及拓展形式1．Understanding history is vital to understanding ourselves as a people andas a nation.(adj.极其重要的)拓展：vitally adv.极其；极大地2．Tsinghua University was founded in1911.(vt.建立)拓展：foundation n．基础；(机构或组织的)创建；创办→foundational adj.基础的；基本的3．From your smile I infer that you are pleased.(vt.推断)拓展：inference n．推断；推理；推论4.2019·江苏高考Music was his true passion,though he had never performed outside the family.(n.酷爱)拓展：passionate adj.热情的；充满激情的5．Mr Smith works as a professor at Oxford University.(n.教授)拓展：profession n．职业；专业→professional adj.职业的；专业的6.2021·浙江6月高考He showed us that even a single desire...can make fora remarkable life.(adj.非凡的)拓展：remarkably adv.引人注目地，明显地；显著地7．He has committed himself to supporting his brother's children.(vt.承诺)拓展：commitment n．承诺，保证；奉献，投入→committed adj.尽心尽力的；坚定的；坚信的8．The country has acknowledged having taken every means to fight against any possible infection.(vt.承认)拓展：acknowledgement n．承认；感谢9．You should sit down and analyse your strengths and weaknesses.(vt.分析)拓展：analysis n．分析；分析结果10．Two independent research bodies reached the same conclusion.(n.结论)拓展：conclude vt.推断11．This led to an unexpected consequence.(n.结果)拓展：consequent adj.随之发生的→consequently adv.因此；所以三、词块短语——在语境中辨义活用写出或选出加蓝部分在语境中的汉语意思1.2021·全国乙卷书面表达Smart online habits can also lead to high efficiency for your study.促使2.2021·新高考Ⅰ卷You have to make sure you don't turn two pages at once and...确保3.2020·全国卷ⅢBut she insists on us eating healthy food.坚决要求4．It is our duty to make contributions to our motherland.对……做出贡献5.2021年1月新高考8省联考卷Would you like to recommend some English poems based on school experience？以……为依据6．The plan put forward by a local farmer has been got through at the meeting.提出7．Unfortunately,the great scientist passed away last year.去世8．The poor boy,not dry behind the ears,had to make a living by himself.谋生9．A good student usually knows how to sum up knowledge in good time.总结10．It's important to draw out a child's potential capacities.DA．做出B．拟订C．鼓励D．发掘11.2021·全国乙卷书面表达Surfing the Internet and playing games take up much time when we should work on our lessons.CA．担任B．开始从事C．占用D．拿起四、经典句式——在佳句背诵中品悟规则用法1.教材原句Upon hearing that she had been awarded the Nobel Prize,she said,“The honour is not just mine.There is a team behind me,and all the people of my country...”(“on/upon＋名词/动名词”作状语)当听到自己被授予诺贝尔奖时，她说：“这份荣誉不仅仅属于我。

Unit 6 Anger could be controlledScore: Time: 40’Part I. Listening ComprehensionDirection: This part is to test your listening ability. It consists of 4 sections.Section A (4 points)Directions: This section is to test your ability to give proper responses. There are 4 recorded questions in it. After each question, there is a pause. The questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A, B, C and D.1. A. He is fine. B. I can’t stand him any more!.C. I don’t know.D. I’m fine.2. A. Nothing. I’d rather not talk about it. B. I’m sorry.C. I don’t understand.D. I see.3. A. I’m happy. B. I think so.C. See you then.D. Chances are slim!4. A. I’m tired. B. I’m fine.C. Yeah. In fact, I have an interview next Monday.D. I have to work.Section B(4 points)Directions: This section is to test your ability to understand short dialogues. There are 2 dialogues in it. After each dialogue, there is a recorded question. The dialogues and questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A, B, C and D.5. A. The man. B. The woman.C. Both of them.D. None of them.6. A. He is busy today. B. He doesn’t like the woman.C. He is angry.D. He is sad.Section C (4 points)Directions: In this section, you will hear a conversation. After the conversation, there are 2 recorded questions. Both the conversation and questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A, B, C and D.7. A. She bought a beautiful bag.B. She just got a job at a consulting firm.C. She fell in love.D. She will have a vocation.8. A. He lost his money.B. He failed in the exam.C. He’s having a hard time finding a job right now.D. He lost his coat.Section D (8 points)Directions:In this section you will hear a recorded short passage. Listen to the passage and fill in each blank IN NO MORE THAN THREE WORDS. The passage will be read three times.Because anger can be powerful, managing it is sometimes challenging. It takes plenty of self-awareness and self-control to manage angry feelings. Self-awareness is the (9) __________ to notice what you’re feeling and thinking, and why. When you get angry, take a (10) __________ to notice what you’re feeling and thinking. Self-control is all about thinking before you act. It puts some precious seconds or minutes between feeling (11) __________ and taking an action you’ll regret. Together, self-awareness and self-control allow you to (12) __________about how to act when you’re feeling an intense emotion like anger.Part II. Vocabulary & StructureDirections: This part is to test your ability to construct correct and meaningfulsentences. It consists of 2 sections.Section A (10 points)Directions: In this section, there are 5 incomplete statements. You are required to complete each one by deciding on the most appropriate word or words from the 4 choices marked A, B, C and D.13. Writing is a powerful tool for a teenager trying to________ emotionsA. controlsB. controlC. controlledD. controlling14. A teen who suffers from anger problems should be ________ to write.A. to encourageB. encouragingC. encouragesD. encouraged15. Artistic projects such as painting, acting and music are all effective ways to __________ anger.A. expressB. expressionC. expressingD. expresses16. Each feeling is__________ on a process of internal reasoning.A. baseB. basisC. basedD. basing17. In a moment of anger, you may feel ________ against the violent emotions that you experience.A. powerB. powerfulC. powersD. powerlessSection B (15 points)Directions:There are 5 incomplete statements here. Fill in each blank with the proper form of the words given in the brackets.18.Everyone has certain __________(challenge) stresses, but how we deal with them is what’s important.19. Peter Stearns played an important part in __________ (research) the differences in anger between genders.20. He stated that anger is an __________(emotion) response to situations.21. After discovering the anger there should be discussion and self-examination in order to __________(relieve) the anger.22. One motivation for ________(seek) anger management can be career related.Part III. Reading ComprehensionDirections: This part is to test your reading ability. You will find 2 tasks for you to fulfill. You should read the reading materials carefully and do the tasks as you are instructed.Task 1 （10 points）Directions: After reading the following passage, you will find 5 questions or unfinished statements. For each question or statement there are 4 choices marked A, B, C and D. You should make the correct choice.Conflict is a normal part of any healthy relationship. After all, two people can’t be expected to agree on everything, all the time. Learning how to deal with conflict—rather than avoiding it—is crucial. When conflict is mismanaged, it can cause great harm to a relationship, but when handled in a respectful, positive way, conflict provides an opportunity to strengthen the bond between two people. By learning these skills for conflict resolution, you can keep your personal and professional relationships strong and growing.Conflict arises from differences, both large and small. It occurs whenever people disagree over their values, motivations, perceptions, ideas, or desires. Sometimes these differences appear trivial, but when a conflict triggers strong feelings, a deep personal need is often at the core of the problem. These needs can be a need to feel safe and secure, a need to feel respected and valued, or a need for greater closeness and intimacy.Everyone needs to feel understood, nurtured, and supported, but the ways in which these needs are met vary widely. Differing needs for feeling comfortable and safe create some of the most severe challenges in our personal and professional relationships.Think about the conflicting need for safety and continuity versus the need to explore and take risks. You frequently see this conflict between toddlers and theirparents. The chil d’s need is to explore, so the street or the cliff meets a need. But the parents’ need is to protect the child’s safety, so limiting exploration becomes a bone of contention between them.The needs of both parties play important roles in the long-term success of most relationships, and each deserves respect and consideration. In personal relationships, a lack of understanding about differing needs can result in distance, arguments, and break-ups. In workplace conflicts, differing needs are often at the heart of bitter disputes, sometimes resulting in broken deals, fewer profits and lost jobs. When you can recognize the legitimacy of conflicting needs and become willing to examine them in an environment of compassionate understanding, it opens pathways to creative problem solving, team building, and improved relationships.23. What is crucial when there is a conflict?A. Learning how to deal with conflictB. Avoid conflictC. Forget conflictD. Find the reason of conflict24. According to the writer, in what situation can conflict provide an opportunity to strengthen the bond between two people?A. When conflict is mismanagedB. when conflict is handled in a respectful, positive wayC. When conflict arisesD. When conflict disappears25. What causes conflict?A. strong feelingsB. strong desiresC. a deep personal needD. differences, both large and small26. In personal relationships, a lack of understanding about differing needs can result in__________.A. harmonyB. break-upsC. affectionD. close relationship27. Which of the following is not mentioned in the passage among the results caused by differing needs in workplace conflicts?A. broken dealsB. fewer profitsC. lost jobsD. less investmentTask 2 (10 points)Directions: The following are tips for managing and resolving conflict. After reading them, you are required to answer the questions.Managing and resolving conflict requires the ability to quickly reduce stress and bring your emotions into balance. You can ensure that the process is as positive as possible by sticking to the following guidelines:•Listen for what is felt as well as said. When we listen we connect more deeply to our own needs and emotions, and to those of other people. Listening also strengthens us, informs us, and makes it easier for others to hear us whenit’s our turn to speak.•Make conflict resolution the priority rather than winning or “being right.”Maintaining and strengthening the relationship, r ather than “winning”the argument, should always be your first priority. Be respectful of the otherperson and his or her viewpoint.•Focus on the present.If you’re holding on to grudges based on past resentments, your ability to see the reality of the current situation will beimpaired. Rather than looking to the past and assigning blame, focus on whatyou can do in the here-and-now to solve the problem.•Pick your battles.Conflicts can be draining, so it’s important to consider whether the issue is really worthy of your time and energy. Maybe you don’twant to surrender a parking space if you’ve been circling for 15 minutes, but if there are dozens of empty spots, arguing over a single space isn’t worth it.•Be willing to forgive. Resolving conflict is i mpossible if you’re unwilling or unable to forgive. Resolution lies in releasing the urge to punish, which cannever compensate for our losses and only adds to our injury by furtherdepleting and draining our lives.•Know when to let something go. If you ca n’t come to an agreement, agree to disagree. It takes two people to keep an argument going. If a conflict is goingnowhere, you can choose to disengage and move on.28. What will happen if you listen to others in resolving conflicts?_________________________________________________________________29. What should be your first priority?_________________________________________________________________30. What if you hold on to grudges based on past resentments?_________________________________________________________________31. I f you’re unwilling or unable to forgive, is it possible to resolve conflict?_________________________________________________________________32. How do you understand the sentence “If you can’t come to an agreement, agree to disagree.”?_________________________________________________________________ Part IV. Translation (15 points)Directions: This part is to test your ability to translate English into Chinese. Each of the two sentences is followed by three choices of suggested translation marked A, B and C. Make the best choice. For the paragraph numbered 35, write your translation in the corresponding space.33.A significant number of teenagers seeking professional help, because they are unable to cope with increased pressures.A. 有些很重要的孩子寻求专业的帮助，因为他们无法应对越来越大的压力。

行为金融学理论（Behavioral finance theory）The modern financial theory classic that people's decisions are based on rational expectations (Rational Expectation), risk avoidance (Risk Aversion), the utility maximization and constantly update their knowledge and decision making assumptions, but a lot of psychological research shows that people's actual investment decision is not so. Secondly, the modern financial theory and the efficient market hypothesis is established on the basis of effective competition in the market, and a large number of studies show that non rational investors often can obtain higher returns than investors. Behavioral finance is based on this kind of market vision, and develops a new financial study using the psychological study of people's actual decision-making process.Behavioral finance studies the mispricing of investment in the investment market due to its own investment behavior, and the resulting behavioral anomaly is the place where Alfa (beyond the market rate of return) is generated. Experts on behavioral finance more, managers have more chances to find Alfa, but also the financial behavior so the seed and buried self destruction, Alfa in the market is less, the market will become more effective, and behavioral anomalies in the market less, then study the financial financial will have no need to there. Second, the more managers who want to beat the market, the harder they work, the more effective the market will become and the less likely it will be to beat the market.The emergence of 4.3.1. behavioral financeAs early as 1950s, people began to study behavioral economics,but earlier studies were rather scattered. It was not until 1970s that Kahneman (Daniel Kahneman) and Tversky (Amos Tversky) conducted extensive and systematic research on this field. Behavioral economics emphasizes that people's behavior is not only driven by interest, but also influenced by many psychological factors. The prospect theory combines psychological research and economic research effectively, reveals the decision-making mechanism under uncertainty, and opens up a completely new research field.4.3.2. is a leading representative of behavioral financeKahneman, the founder of Behavioral Finance (Daniel Kahneman) in 1934 was born in Israel in 1954, graduated from the Hebrew University, and in 1961 obtained a doctorate in psychology at the University of California, after the turn at the Hebrew University faculty. Another creator Tversky (Amos Tversky) was born on 1937 in Israel, has been at the University of Michigan studied philosophy and psychology at the Hebrew University, after graduation, here met his best partner Kahneman, which opened their lifelong friendship and excellence in academic research, and in 1979 jointly issued the basic theory of "behavioral finance prospect theory" (Prospect Theory). Later, he went to the University of California at Berkeley in the United States, and he went to Standford in the United states.Kahneman because of the prospect theory of behavioral finance contribution in 2002 received the Nobel Prize in economics, but it is a pity but Tversky in 6 years ago (1996 years) died, only 59 years old, can not wait for the arrival of honor.4.3.3. behavioral finance, major perspectivesBehavioral finance mainly puts forward two theories:A. BSV (Barberis, Shlefer, and, Vishny, 1998),B. DHS (Daniel, Hirsheifer, and, Subramanyam, 1998).First, the BSV theory holds that returns are stochastic, but the general investor erroneously believes that there are two paradigms for income change:Paradigm A: investors think that earnings change is mean reversion, and stock volatility is only a temporary phenomenon, and does not need to adjust its behavior according to changes in income. This behavior will cause investors to respond to the expected lack of earnings, and when the actual earnings do not match the expectations, they will be adjusted, so that changes in the stock price reaction to changes in earnings lags behind.Paradigm B: investors think that changes in earnings tend to be trend, and share prices have the same direction and continuous effects on earnings. Such investors tend to tend to expand the trend by mistake and overreact to changes in earnings.Second, DHS theory divides investors into two categories: one is the information one, the other is the non information. Without information, its investment behavior will not be affected by the judgment bias, and the information can be easily affected by the judgment bias.The DHS model divides the judgment bias of the information into two categories: one is overconfidence, and the other is biased self attribution (self-contribution). Overconfidence leads investors to exaggerate the accuracy of their stock valuation; biased self attribution leads investors to underestimate the impact of public information on stock value. That is to say, when the investor pursues this model, it will lead to the deviation between the personal information and the public information,This divergence leads to short-term continuity and long-term support for share prices.4.3.4. main behavioral finance modelUnder the framework of the two kinds of BSV and DHS, put forward the prospect theory of Behavioral Finance (Prospect Theory), behavioral portfolio theory (Behavioral Portfolio Theory) and the behavior asset pricing model (Behavioral BAPM Asset Pricing Model) on behavioral finance model.A. prospect theoryTheory (Prospect) combines psychological research and economic research effectively, reveals the decision-making mechanism under uncertainty, and opens up a whole new research field. In this sense, Kahneman's award may change the direction of future economics.In general, the prospect theory has the following three basicprinciple: (a) the majority of people in the face of the time are risk averse; (b) the majority of people in the face of loss when the risk preference; (c) are more sensitive to losses than get.Law of prospect theory: people are often cautious and unwilling to take risks when they are faced with them, while everyone is an adventurer in the face of losses. In the face of the time to avoid risks, and in the face of preference for the risk of loss, and the loss and the gain is relative to the reference point for the change, people use things in the evaluation point of view, can change people's attitude toward risk.The law of prospect theory two: People's sensitivity to loss and gain is different, and the pain of loss is far greater than that of happiness. In the 1992 study, Tversky and Kahneman found that people usually needed two times the loss of earnings to make up for the pain caused by the loss.B. behavioral portfolio theoryThe combination theory of BPT (Behavioral Portfolio Theory) behavior of assets, in 1985 by Shefrin and Statman put forward the theory that Pyramid investors have layered structure of the portfolio, each layer corresponds to the specific investment objectives and risk investors. Some of the money is invested at the bottom of the safest, and some funds are invested in more risky higher ups, with correlations between layers.Relatively speaking, the traditional portfolio theory to portfolio as a whole, and it is assumed that only the covariancebetween different securities account in building the portfolio, and are risk averse investors, and this behavior in real life is not entirely consistent.C. behavioral asset pricing modelBehavioral Model BAPM (Behavioral Asset Pricing asset pricing) investors are divided into information traders and noise traders. Information traders are rational investors who support the CAPM model of modern financial theory, avoid cognitive errors, and have variance preferences. Noise traders are apt to make conscious errors and have no strict variance preferences.When the information traders occupy the main body of the market, the market is efficient; when the noise traders occupy the market main body, the market is inefficient. In BAPM, the returns on securities are determined by the "Behavioral Beta", where the market portfolio is more representative. For example, noise traders tend to overestimate the price of growth stocks, and the proportion of growth stocks in the corresponding market is higher, because the behavioral portfolio is proportional to the market mix and the proportion of mature stocks should be raised.Statman further pointed out that the decision to supply and demand is people's utilitarian considerations (product costs, alternatives, prices, etc.) and value expression considerations (personal tastes, special preferences, etc.). CAPM includes only utilitarian considerations, while BAPM includes both. Due to the characteristics of BAPM value, andthe utilitarian characteristics, therefore, it is effective to accept a market from can't beat the market, on the other hand, from the meaning of rationalism of refuse market efficiency, the future development of finance has a profound revelation.In short, the behavioral finance through questioning on modern financial core hypothesis "theory of rational people", put forward the prospect theory, utility function of investors is concave function, and face the loss of utility function is a convex function. In financial transactions, investors psychological factors will make the actual decision-making process of optimal decision process is described from the classical finance theory, and system of rational deviation, and not because of the statistical average and eliminate.The investment strategies based on behavioral finance include average capital strategy, time diversification strategy, contrarian investment strategy and inertial investment strategy.4.3.5. behavioral finance explains the main behavioral anomalies in the marketA. overreactionPeople are too sensitive to asset prices, information conferences make people overreact, resulting in excessive or falling securities prices.B. disposition effectDue to the cognitive bias of investors,For the performance of the investment profit and loss of certainty ". The" loss aversion of the heart ", reflected in the behavior for selling profitable stocks to sell, easy to be a losing stock phenomenon, resulting in the relatively long time firmly.C. noise tradingShort - term investors and noise traders in the market have their own information. In his collection of information, by which investors more specific information, the more likely he is to profit, and such information may be associated with the basic value of information, also may be unrelated with the basic value of noise, which is called the information aggregation positive spillover effect. This effect may make the traders who obtain new information can not get the corresponding return, which is not conducive to the collection of information and the allocation of resources.D. herd effectInvestors are affected and imitated by other investors under the influence of uncertain information. That is, "all investors run in the same direction, and no one struggles with the overwhelming majority of people."."There are two main herding effects in the stock market:The first is the information based herd effectComplete information is a premise hypothesis of neo classical finance theory, but in fact, even in the modern society where information is highly disseminated, information is inadequate. In the case of insufficient information, investors do not make decisions entirely on the basis of their own information decisions, but on the basis of other people's investment behavior. The herding performance is "follow suit" or "the village" phenomenon.The second is the reputation based and reward based herd effectThis effect is most common in the fund manager, because employers do not understand the fund managers, fund managers do not understand their own investment capacity, in order to avoid investment mistakes and reputation risks and their remuneration, fund managers have motivation to mimic other fund managers' investment behavior. If many fund managers take the same action, the herd effect will emerge.。

CHAPTER 1 /RISK IN OUR SOCIETYKEY CONCEPTS AND TERMSFundamental risk: A fundamental risk is a risk that affects the entire economy or large numbers of persons or groups within the economy.Hazard: A hazard is a condition that creates or increase the chance of loss.Law of large number: As the number of exposure units increase, the more closely the actual loss experience will approach the expected loss experience.Liability risks: you can be held legally liable if you do something that results in bodily injury or property damage to someone else.Moral hazard: Moral hazard is dishonesty or character defects in an individual that increase the frequency or severity of loss.Morale hazard: Morale hazard is carelessness or indifference to a loss because of the existence of insurance.Physical hazard: A physical hazard is a physical condition that increase the chance of loss. Premature death: Premature death is defined as the death of a household head with unfulfilled financial obligations.Pure risk: Pure risk is defined as a situation in which there are only the possibilities of loss or no loss.Speculative risk: Speculative risk is defined as a situation in which either profit or loss is possible.REVIEW QUESTIONS1. How does objective risk differ from subjective risk?Objective risk is defined as the relative variation of actual loss from expected loss. Objective risk declines as the number of exposures increases. Objective risk can be measured.Subjective risk is defined as uncertainty based on a person’s mental condition or state of mind. The impact of subjective risk varies depending on the individual. High subjective risk often results in conservative and prudent behavior, while low subjective risk may result in less conservative behavior.2. Define peril, hazard, physical hazard, moral hazard, morale hazard, and legal hazard.Peril: peril is defined as the cause of loss.Physical hazard: A physical hazard is a physical condition that increase the chance of loss.Moral hazard: Moral hazard is dishonesty or character defects in an individual that increase the frequency or severity of loss.Morale hazard: Morale hazard is carelessness or indifference to a loss because of the existence of insurance.Legal hazard: Legal hazard refers to characteristics of the legal system or regulatory environment that increase the frequency or severity of losses.3. Explain the difference between pure and speculative risk and between fundamental and particular risk.pure and speculative risk:First, private insurers generally insure only pure risk. Second, the law of large numbers can be applied more easily to pure risk than to speculative risk. Finally, society may benefit from a speculative risk even though a loss occurs, but it is harmed if a pure risk is present and a loss occurs.fundamental and particular risk:Government assistance may be necessary to insure a fundamental risk.4. Identify the major types of pure risk that are associated with great financial insecurity. (P 5) The major types of pure risk that can create great financial insecurity include Personal risks, property risks, and liability risks.Personal risks are risks that directly affect an individual.5. Describe briefly the five major methods of handling risk. Give example of each method.(P 9)APPLICATION QUESTIONSSeveral methods are available for handling risk. However, certain techniques are more appropriate than others in a given situation.a.(1) Should retention be used in those situations where both loss frequency and loss severityare high? Explain your answer. (P 11)(2) Explain why loss control is a highly desirable method for handling risk.(P 10)b. Explain why chance of loss and risk are not the same thing.(P 3)CHAPTER 2 / INSURANCE AND RISKKEY CONCEPTS AND TERMSAdverse selection: Adverse selection is the tendency of persons with a higher-than-average chance of loss to seek insurance at standard (average) rates, which if not controlled by underwriting, results in higher-than-expected loss levels.Fortuitous loss: A fortuitous loss is one that is unforeseen and unexpected and occurs as a result of chance.Indemnification：Indemnification means that the insured is restored to his or her approximate financial position prior to the occurrence of the loss.Insurance: Insurance is the pooling of fortuitous losses by transfer of such risks to insurers, who agree to indemnify insureds for such losses, to provide other pecuniary benefits on their occurrence, or to render services connected with the risk.Law of large numbers: the law of large numbers states that the greater the number of exposures, the more closely will the actual results approach the probable results that are expected from an infinite number of exposures.Underwriting: Underwriting refers to the process of selecting and classifying applicants for insurance.REVIEW QUESTIONS1. Explain the major characteristics of a typical insurance plan.(P 16)2. Explain the law of large numbers and show how the law of large numbers can be used by aninsurer to estimate future losses. (P 17)3. Explain the major requirements of an insurable risk.（P 18）APPLICATION QUESTIONS1.Although no risk completely meets all of the ideal requirements of an insurable risk, somerisks come much closer to meeting them than others.a.Identify the ideal requirements of an insurable risk.(P 18)pare and contrast automobile collisions and war in terms of how well they meet therequirements of an insurable risk.( p 18)2.One author states that “The law of large numbers forms the basis of insurance.” Do you agreeor disagree with this statement? Explain your answer.CHAPTER 5 / FUDAMENTAL LEGAL PRINCIPLESKEY CONCEPTS AND TERMSActual cash value（实际现金价值）: Actual cash value is defined as replacement cost less depreciation.(重置成本—折旧)Aleatory contract(射幸合同): Aleatory contract is a contract where the values exchanged may not be equal but depend on an uncertain event.Commutative contract(等价交易合同) : A commutative contract is one in which the values exchange by both parties are theoretically equal.Conditional contract（条件合同）: Conditions are provisions inserted in the policy that qualify or place limitations on the insurer’s promise to perform.Consideration(对价): the value that each party gives to the other. The insured’s consideration is payment of the first premium (or a promise to pay the first premium) plus an agreement to abide by the conditions specified in the policy. The insurer’s consideration is the promise to do certain things as specified in the policy.Contract of adhesion（符合性合同）: A contract of adhesion means the insured must accept the entire contract, with all of its terms and conditions.Material fact(重要事实)：Material means that if the insurer knew the true facts, the policy would not have been issued, or it would have been issued on different terms.Offer and acceptance(要约和承诺): The first requirement of a binding insurance contract is that there must be an offer and acceptance of its item. In most case, the applicant for insurance makes the offer, and the company accepts or rejects the offer.Principle of indemnity: The principle of indemnity states that the actual amount of the loss; stated differently, the insured should mot profit from a loss.Principle of utmost good faith（最大诚信原则）: A higher degree of honesty is imposed on both parties to an insurance contract than is imposed on parties to other contracts.Subrogation(代位追偿): Subrogation means substitution of the insurer in place of the insured for the purpose of claiming indemnity from a third person for a loss covered by insurance. Unilateral contract(单务合同)：A unilateral contract means that only one party makes a legally enforceable promise.Valued policy(定值保险单)：A valued policy is a policy that pays the face amount of insurance ifa total loss occurs.Waiver(弃权)：Waiver is defined as the voluntary relinquishment of a known legal right.REVIEW QUESTIONS1. Explain the principle of indemnity. How does the concept of actual cash value support theprinciple of indemnity? (P 30)2. What is an insurable interest? Why is an insurable interest required in every insurancecontract? (P 32)3. Explain the principle of subrogation. Why is subrogation used? (P34-P35)4. Explain the principle of utmost good faith. How do the legal doctrines of representations,concealment, and warranty support the principle of utmost good faith? (P36-P37)5. Identify the four requirements that must be met to have a valid insurance contract. (P37-P39)CHAPTER 6 / ANALYSIS OF INSURANCE CONTRACTSKEY CONCEPTS AND TERMSAggregate deductible(总额免赔): An aggregate deductible is sometimes used in commercial property insurance, by which all covered losses during the year are added together until they reach a certain level.“All risk”policy（一切险保险单）:All losses are covered except those losses specifically excluded.Coinsurance clause(共保条款): A coinsurance clause in a property insurance contract requires the insured to insure the property for a stated percentage of its insurable value. If the coinsurance requirement is not met at the time of loss, the insured must share in the loss as a coinsurer. Deductible(免赔额): A deductible is a provision by which a specified amount is subtracted from the total loss payment that otherwise would be payable.Elimination (waiting) period(剔除/等待期): An elimination period is a stated period of time at the beginning of a loss during which no insurance benefits are paid.Endorsements and riders: In property and liability insurance, an endorsement is a written provision that adds to, deletes from or modifies the provisions in the original contract. In life and health insurance, a rider is a document that amends or changes the original policy.Exclusions(除外责任): Exclusion are another basic part of any insurance contract. There are three major types of exclusion: excluded perils, excluded losses, and excluded property.Insuring agreement(承保协议): The insuring agreement summarizes the major promises of the insurer. The insurer, in other words, agree to do certain things, such as paying losses from insured perils , providing certain services ,or agreeing to defend the insured in a liability lawsuit.Large-loss principle(大损失原则): The concept of using insurance premiums to pay for large losses rather than for small losses is often called the large-loss principle.Named-perils policy(制定风险保单): The contract must indicate the person or person for whom the protection is provided.Pro rata liability(比例责任条款): Each insurer’s share of the loss is base on the proportion that its insurance bears to the total amount of insurance on the property.Straight deductible(绝对免赔额): With a straight deductible, the insured must pay a certain number of dollars of loss before the insurer is required to make a payment.REVIEW QUESTIONS1. Describe the basic of an insurance contract.(P 45)2. Identify the major types of exclusions typically found in insurance contract. Why areexclusions used by insurers?(P 46)3. Define the term conditions. What is the significance of the conditions section to theinsured?(P47-P48)4. What is an endorsement or rider? If an endorsement conflicts with a policy provision, how isthe problem resolved? (P48)5. Why do deductibles appear in insurance contracts? Indentify some common deductibles thatare found in insurance contracts. (P49-P50)CHAPTER 7 / THE LIABILITY RISKKEY CONCEPTS AND TERMSAbsolute (strict) liability(绝对责任): Absolute liability means that liability is imposed regardless of negligence or fault.Comparative negligence law(比较过失法则): Under a comparative negligence law, if both the plaintiff (injured person) and the defendant contribute to the plaintiff’s injury, the financial burden of the injury is shared by both parties according to their respective degrees of fault. Contributory negligence law(共有过失): Contributory negligence means that if the injured person’s conduct falls below the standard of care required for his or her protection, and such conduct contributed to the injury, the injured person cannot collect damages.Imputed negligence (疏忽归咎): Imputed negligence means that under certain conditions, the negligence of one person can be attributed to another.Last clear chance rule (最后机会原则): The last clear chance rule states that a plaintiff who is endangered by his or her own negligence can still recover damages from the defendant if the defendant has a last clear chance to avoid the accident but fails to do so.Negligence (疏忽): Negligence typically is defined as the failure to exercise the standard of care required by law to protect others from an unreasonable risk of harm.Proximate cause(近因原因): A proximate cause is a cause unbroken by any new and independent cause, which produces an event that otherwise would not have occurred.Punitive damages (惩罚赔偿金): Punitive damages are paid to punish people and organizations so that others are deterred form committing the same wrongful act.Tort(侵权): Tort is a legal wrong for which the law allows a remedy in the form of money damages.REVIEW QUESTIONS1. Define the meaning of a tort and list the three broad classes of torts.(P57)2. Define negligence. What are the essential elements of a negligent act.(P57-P58)3. Describe some legal defenses that can be used if person is sued. (P59)4. Explain the meaning of imputed negligence.(P59)CHAPTER 8 / HOMEOWNERS INSURANCEKEY CONCEPTS AND TERMSAppraisal clause(估价条款): The appraisal clause is used when the insured and insurer agree that the loss is covered, but the amount lf the loss is in dispute.Fair rental value(公平的租用价值): Fair rental value means the rental value of that part of the residence premises rented to others or held for rental less any expense that do not continue while the premises are not fit to live in.Mortgage clause(抵押条款): The mortgage clause is designed to protect the mortgagee’s insurable interest.REVIEW QUESTIONS1. List the basic coverages that are provided in Section I of the homeowners policy? (P75-P81)2. What duties are imposed on the insured after a property loss occurs?(P87左)3. Explain briefly how the mortgage clause protects the insurable interest of the mortgagee.（P90）CHAPTER 16 / FUNDAMENTALS OF LIFE INSURANCEKEY CONCEPTS AND TERMSLegal reserve(法定准备金): Because the method of investing and accumulating the fund is regulated by state law, it is referred to as a legal reserve.Level-premium method(均衡保费方法): Under the level-premium method, premiums do not increase from year to year but remain level throughout the premium paying period, and the insured has lifetime protection to age 100.Met amount at risk(净风险额): The difference between the face amount of the policy and the legal reserve is called the met amount at risk.Premature death(过早死亡): Premature death can be defined as the death of a family head with outstanding unfulfilled financial obligations, such as dependents to support, children to educate, and a mortgage to pay off.Yearly renewable term Insurance(按年续保的定期寿险): Yearly renewable term insurance provide life insurance protection for only one year.REVIEW QUESTIONS1. Explain the meaning of premature death and identify the costs associated with it.(P114)2. Explain the yearly renewable term method for providing life insurance to individuals.(P125)3. Explain the level-premium method for providing life insurance to individuals.(P127)CHAPTER 17 / TYPES OF LIFE INSURANCEKEY CONCEPTS AND TERMSCash surrender value(解约退还金): Ordinary life insurance also has an investment or saving element called a cash surrender value. The cash values are due to the overpayment of insurance premiums during the early year.Endowment insurance(两全险): Endowment insurance is another traditional form of life insurance. An endowment policy pays the face amount of insurance if the insured dies within a specified period; if the insured survives to the end of the endowment period, the face amount is paid to the policyowner at that time.Limited-payment policy(限期缴费终身寿险): A limited-payment policy is another type of traditional whole life insurance. The insurance is permanent, and the insured has lifetime protection. The premiums are level, but they are paid only for a certain period.Ordinary life insurance(普通终身寿险): Also called straight life and continuous premium whole life, provides lifetime protection to age 100, and the death claim is a certainty.Preferred risks(优良标准体保单): Many life insurers sell policies at lower rates to individuals known as preferred risks. These people are individuals whose mortality experience is expected to be lower than average.Term insurance(定期寿险): Provides a death benefit if the insured dies during a specified period. Universal life insurance(万能寿险): Universal life insurance can be defined as a flexible premium policy that provides protection under a contract that unbundles the protection and saving components.Variable life insurance(变额寿险): Variable life insurance can be defined as a fixed-premium policy in which the death benefit and cash surrender values vary according to the investment experience of a separate account maintained by the insurer.Whole life insurance(终身寿险): Whole life insurance is a cash-value policy that provide lifetime protection.REVIEW QUESTIONS1.2. Describe the basic characteristics of term insurance.3. When is the use of term insurance appropriate?4.5. Describe the basic characteristics of ordinary life insurance.6.7. Under what situations can an ordinary life policy be used?8. Describe the basic features of a variable life insurance policy.9.10. Explain the major characteristics of universal life insurance.APPLICATION QUESTION1.Mark, age 32, wants to purchase a five-year term insurance policy in the amount of $100,000.The policy is both renewable and convertible,a.b.Describe the situations under which term insurance can be used,c.d.What rights does Mark have because the policy is renewable and convertible? Explainyour answer.e.f.If Mark wishes to save money for retirement purposes, do you recommend purchase ofthis contract?g.Explain to Mark the advantages and disadvantages of a reentry term policy.。