The Study Of QCD Chiral Phase Transition And The Hybrid Stars Within Effective Models

The Nambu-Jona-Lasinio(NJL)model is one of the effective theories,proposed by Nambu and Jona-Lasinio in 1961.With the simplified gluon propagator,the four-fermion and the six-fermion interaction,this model is convenient to be applied in nu-merical calculations,and many successes have been achieved in the study of hadron physics.In this work,we will employ the(2+1)-flavor NJL model to study the chiral phase transition in the quantum chromodynamics(QCD)and the structure of the hy-brid star.Firstly,we employ the proper time regularization(PTR)to study the QCD phase transition and the equation of state(EOS)at zero temperature.Then we modi-fy the original(2+1)-flavor NJL model and use a new algorithm to study the solution of the quark gap equation to overcome two shortages coming from the model and the iteration method,respectively.As a result,we get the new EOS and part of the QCD phase diagram.Finally,the EOSs obtained above are applied to calculate the mass-radius relation of the hybrid star.Combined with five constraints coming from theoretical predictions and astro observations,we constrain the hybrid EOS with the smooth hadron-quark phase transition,and get the constrained parameter space.In the first chapter,we give a brief introduction to the QCD,the NJL model as well as the hybrid star.In the second chapter,the chiral phase transition and the EOS in the(2+1)-flavor strong interacted matter for zero temperature and finite chemical potential are studied with the PTR.We find that the chiral phase transition is second-order in the chiral limit,but a crossover in non-chiral limit.For comparison,we choose three parameter sets in the calculation,but no significant difference is found between the corresponding EOSs.Furthermore,the(2+1)-flavor QCD system is demonstrated to be more stable than that of two flavors by a comparison of their binding energies.Therefore,the EOS of(2+1)-flavor quark is more favored in the study of the hybrid star.In the third chapter,some new approaches to study the(2+1)-flavor quark EOS and the chiral phase transition are introduced.Inspired by the operator product expansion(OPE)method,we consider the dependence of the four-fermion coupling strength G onthe quark condensate,which can be simplified in the form of G?G1+G2(?u+?d+?s).Then the quark EOS can be derived in this case.Same with the parameter fixing process in the second chapter,most of the parameters are fixed to fit five experimental data at zero temperature and chemical potential.In addition,to determine the ratio of G1 to G2,we fit the critical temperature Tc to the result of lattice QCD(LQCD).If we compare the light quark condensate for zero chemical potential in this approach with that in the original NJL model,we will find that our result is more consistent with that of LQCD.Apart from the work above,we also study the solution of the quark gap equation in the non-chiral limit with a new algorithm,especially the pseudo-Wigner solution in the non-chiral limit where the chiral symmetry is partially restored.With this method,the evolution of the solution of the quark gap equation with an increasing current quark mass can be shown directly from the chiral limit to non-chiral limit.For a low chemical potential(?<?TCP=272.5 MeV)where no chiral phase transition but a crossover happens,our result of the Nambu and positive pseudo-Wigner solution is consistent with the strict physical solution obtained by the iterative method.The most important is,this algorithm can give a criterion where the pseudo-Wigner solution emerges in this case.But for large chemical potentials(?>?TCP the Nambu and pseudo-Wigner solution diverge and the algorithm is invalid.In the fourth chapter,we study the hybrid EOS as well as the structure of the hybrid star with some constraints from astro observations.The APR model as well as the relativistic mean field(RMF)model are employed to describe the nucleons in the hadronic EOS.With the three-window interpolating approach,the quark EOS can be connected to the hadronic EOS smoothly to generate the hybrid EOS.Then we substitute it into the Tolman-Oppenheimer-Volkoff(TOV)equation to get the mass-radius relation of the hybrid star.As a result,the mass of the heaviest hybrid star in our model is in consistent with the astro observation PSR J0348+0432,PSR J1614-2230,and PSR J1946+3417.In addition,we study the constraint on the hybrid EOS with a smooth hadron-quark phase transition in the light of the recent gravitational wave observation GW170817.Specifically,with the tidal deformability(TD)during the binary neutron star(BNS)merger and other four constraints coming from theoretical predictions and astro-observations,we can get the suitable parameter space.The result shows that the core of the hybrid star is not a pure quark core,but a mixed phase of hadrons and quarks.Furthermore,although the NL3?? model is already excluded by the constraint of TD from GW 170817,this model is still useful for characterizing the hadronic matter in the hybrid star.