Chiral-scale Effective Theory And Its Applications

There are four interactions including electromagnetic interaction,gravitational interaction,strong interaction and weak interaction in nature.Different interactions have different symmetries and we can study some aspects ofinteraction theory through symmetry.Quan-tum Chromo Dynamics(QCD)with quarks and gluons as fundamental degrees of freedom is now believed to be the fundamental theory describing strong interactions.In QCD,there are global(approximate)chiral symmetry,local norm symmetry,(approximate)isospin symmetry,scale symmetry and discrete C,P and T symmetry.In the low energy region,due to the non-perturbation effect of QCD,the chiral symmetry will break spontaneously,and the basic degree of freedom of strong interaction will become hadrons.In this paper we are concerned with the various possible physical effects of this spontaneous breaking of symmetry.One of the most important techniques is Eeffective Field Theories(Short name is EFTs)in which the low energy expansion of the system,such as Chiral Perturbation The-ory(ChPT).At present,some theoretical models such as chiral effective theory and the heavy baryon chiral effective theory can describe the pseudoscalar mesons,vector mesons and baryons,but because of the large decay width of the scalar meson,it can not describe the structure of scalar meson,especially the lightest scalar meson fo(500).Therefore,it is meaningful to construct a chiral-scale effective theory with dilatonic meson.There-fore,in this paper,we use the C-T method with an assumption that is an infrared fixed point(IRFP)of the running coupling constant ?s in non-perturbative QCD exists,so that? is 0 at this point.The mass of dilatonic meson fo(500)is close to the mass of K me-son,then it is used as a pseudo-Nambu Goldstone boson to explain the origin of the scalar meson-dilaton.It comes from two aspects,one is the spontaneously broken of the scale in-variant,and the other is the explicitly broken of the scale invariant arising from two parts:the ?s is departure from the infrared fixed point and the flow quark mass.Based on the standard chiral perturbation theory with chiral symmetry and scale symmetry,the scale-chiral effctive theory including a dilatonic meson which is the lightest scalar meson is established.One can systematically give:the leading-order chiral scale perturbation the-ory xPT,Lagrangian and the next-leading-order chiral scale perturbation theory XPT?Lagrangian containing dilaton and pseudoscalar mesons;the leading-order hidden local symmetry Lagrangian with scale invariant:LOHLSa and the next-leading-order hidden local symmetry Lagrangian with cale invariant:NLOHLSa involving dilaton and vector mesons;the leading-order Lagrangian:LObsHLS,with the hidden local symmetry and scale invariant including dilaton,low-lyling baryon octet and mesons.This is one of the innovations of this paper.The construction of a theory requires the detection and verification of experiments or other theoretical calculations.It should have certain meanings for the physical or natural interpretation and application.So we use the chiral-scale effective theory,considering the pseudoscalar mesons and The SU(3)taste symmetry of the baryon and the vector meson of SU(3)hidden local symmetry,to study the properties of the hadron in the medium in series and give the scaling behavior of the hadrons in the midium and more general definition of BR scaling,such as m?*/m?=?0,m?*/m?=??'/2+1,mB*/mB=m?*/m?=f?*/f?=?and so on.In LOSS(Leading Order Scale symmetry),some low energy constants in Lagrangian are also given prediction and discussion based on experimental measurements and physical processes.Some of these relation,when we allow ?'(?)2 as a high-temperature crystal simulation of nuclear matter,such asm?*/m?,mB*/mB based on LOSS is consistent with other theoretical results given.However,it may only be valid in the range of density?n1/2(?)2n0,and after n1/2,there will be a drastic change due to the topology.We need to be cautious.This is the second innovation of this paper.Based on the chiral effective field theory which is scale invariant and combined with the"chiral filter hypothesis",we take it as Fermi particles on the Fermi surface with the Fermi fluid fixed-point constant gAL to understand and answer the long-standing problem"quenching"gA simply in nuclear shell model,namely,the huge Gamow-Teller beta conversion and double beta decay of"quenchingA",gAeff?1 in the nuclear Gamow-Teller resonance.It provides a simpler way to answer the long-standing problem and is supported by the monte carlo calculation results of Pastore et al.By combining the hidden scale symmetry and part hidden symmetry in the nuclear effective field theory and combining the double soft-pion theorem,we predicted that the gamow-teller operator from the spatial component of the axial vector flow should not be affected by the QCD vacuum change caused by baryon density,while the first forbidden conversion operator from the time component should be greatly enhanced.namely gsA = gA,gAt=gA/?.We also discussed when the density is higher than the density of topology change n1/2,Landau-Migdal constant gAL? 1 will be converted to the"dilaton limit"value gAdilaton = 1 of high density.Although there is no rigorous evidence that there is an IR fixed point in the QCD of nuclear physics,the hidden scale symmetry in the half-skyrmion phase of the double parity appears,it exists in the finite nuclei and in dense matter which is "not buried".this is the third innovation of this article.In addition to the above three innovations,we also discuss other developments closely related to this paper,such as the equation of state related to compact stars,the mass-radius relationship of neutron stars,tidal deformation and so on.These developments further i1-lustrate the value of our chiral-scale theory.