Relations For Low-Energy Constants In Chiral Lagrangians Of Meson-Baryon Interactions

Hadron physics involves the non-perturbative problem of strong interactions,which makes it difficult to understand hadron properties from first principles.In some specific approximations,we can use the effective field theory of quantum chromodynamics(QCD)to deal with problems in hadron physics,such as using the chiral perturbation theory(χPT)to study the interactions involving of pseudoscalar mesons,using the heavy quark effective theory to study the properties of hadrons containing heavy quarks,and so on.Chiral perturbation theory is a powerful tool in describing low-energy strong interactions.In the theory,the Lagrangian and matrix elements axe organized in terms of a consistent power of small momentum for chiral particles,that is,they are expanded by chiral order.The calculation of matrix elements needs the most general effective Lagrangian,while each independent term of the Lagrangian is accompanied by a priori unknown low-energy coupling constant(LEC).In principle,these LECs are determined by the underlying fundamental theory,QCD.However,as long as one cannot solve QCD in the non-perturbative regime,other methods to determine the values of these LECs are required.Determing the unknow LECs is a major task in the application of χPT.It is related to some studies in hadron physics.The study of LEC related problems is important in understanding the laws of low energy strong interactions.In this thesis,we derive the constraint relations between LECs by combing the hadron-level and quarklevel physics with the chiral quark model(χQM).These relations are helpful in studying physical problems with χPT.In this thesis,the Lagrangian in χQM is regarded as an equivalent description of the hadron Lagrangian at the quark level.Through the comparison for the same matrix element calculated at both hadron level and quark level,one can find LEC relations between hadron-level and quark-level Lagrangians.Then the LEC relations between different hadron-level Lagrangians can be obtained by appling the same quark-level Lagrangian to different baryon systems.This is a model method that can be used systematically to study the LEC problem before one can solve the non-perturbative problem from the first principles.This method requires a complete chiral Lagrangian with independent terms and can be generalized to any order in principle.The corrections to the LEC relations can also be systematically considered in this method.As a preliminary study,the baryons mainly involved in this thesis are the nucleons in the SU(2)case,the octet baryons in the SU(3)case,and the Δ(1232)baryons in the SU(2)case.The baryons in the first two cases have a spin of 1/2 while the baryons in the latter case have a spin of 3/2.·In the LEC studies for the meson-baryon Lagrangians,the relations between the LECs in the baryon chiral perturbation theory(BχPT)and the coupling constants in χQM are established by assuming that the baryon-baryon-meson coupling can be equivalently described by the quark-quark-meson coupling.Then,through the correspondence for the same coupling vertex between SU(2)χQM and SU(3)χQM,one finally gets the LEC relations between SU(2)BχPT and SU(3)BχPT for the first three chiral orders.In addition,some LEC relations at the same order in SU(3)chiral Lagrangians are also obtained.Since LECs in the SU(2)case can be determined by a large number of experimental data while the experimental data in the SU(3)case are less,the values of LECs in SU(3)Lagrangians can be constrained by the obtained LEC relations.The numerical analysis roughly supports these relations.In the situation that the available experimental data are not enough,one may employ such constraints to reduce the number of undetermined parameters in theoretical applications.·In the LEC studies for chiral Lagrangians containing Δ(1232),we also try to relate relevant LECs to those in the 7r-N case.For brevity,we mainly focus on LEC relations between hadron-and quark-level Lagrangians.Considering that the description for spin-3/2 field differs from that for spin-1/2 field,we introduce an additional multiplication factor when establishing correspondences between the hadron Lagrangian structure and the quark Lagrangian structure.The existence of such factors was not noticed in the literature.From the phenomenological perspective,the necessity of these factors is discussed and the values of several factors are determined.Although the obtained LEC relations depend on these multiplication factors whose values are not fully determined,such relations will still be useful in studying the related properties of the Δ(1232).From the obtained hadron-level LEC relations,it can be found that not all the LECs at the hadron-level in the SU(3)case can be constrained by those in the SU(2)case.The reason is that the inclusion of strange quark definitely introduces independent degree of freedom and thus new LECs.Under the assumption that two quarks in the baryon are spectators and do not participate in the interaction,all the obtained LEC relations are simple linear relations.In the general case that mesons may couple with different quarks in the baryon,the LEC relations obtained in this thesis will be corrected to some extent,which needs further studies in subsequent works.