Study Of Quark Isovector Interaction Based On The NJL Model

Quantum Chromodynamics?QCD?is a basic gauge field theory to describe strong inter-actions.Lattice QCD calculations predict that the transition between the hadronic phase and the partonic phase is a smooth crossover at nearly zero baryon chemical potential.Although Lattice QCD suffers from the fermion sign problem at finite baryon chemical potential,the hadron-quark phase transition can be a first-order one at large baryon chemical potentials based on studies from effective theoretical models,e.g.,the Nambu-Jona-Lasinio?NJL?model and its extensions.Studying the phase structure of QCD matter and searching for the signal of the critical point between the crossover and the first-order transition are the fundamental goals of relativistic heavy-ion collision experiments.Recently,the beam-energy scan?BES?program was carried out at the relativistic heavy-ion collider?RHIC?of the Brookhaven National Lab-oratory?BNL?,in order to search for the signal of the critical point of the hadron-quark phase transition.Despite the lack of definitive signals for the critical point in experiments,several properties of the strong interaction of quark matter in the case of high temperature and high density have been observed.In addition,the study of compact stars in nature provide another effective way to explore the interaction of quark matter at high baryon number density and low temperature.Isospin asymmetric quark matter consisting of different net numbers of u and d quarks is produced in high-energy relativistic heavy-ion collision experiments,which can lead to isospin-dependent dynamics in the Quark-Gluon Plasma?QGP?.In the case of compact stars,the isospin asymmetry of the quark matter inside the star may be larger.Thus,exploring the properties of the isospin-dependent properties of quark matter is of great significance to understand the isospin dependence of the hadron-quark phase transition,the isospin effect of the parton dynamics of the RHIC high energy physics experiment,and the nature of compact stars.In this thesis,we will explore the properties of isospin asymmetric quark matter based on a 3-flavor NJL model from four aspects:the phase diagram and the symmetry energy of quark matter,isospin effect on baryon and charge fluctuations,isospin properties of quark matter in compact stars and isospin splitting of pion elliptic flow.First of all,we study the the phase diagram in the?_q-T plane based on a 3-flavor NJL model.According to the analysis of the phase diagram,we can know the dynamics of spontaneous breaking of chiral symmetry in vac-uum and its restoration at low temperatures and baryon chemical potentials.Choosing quark condensate as an order parameter for chiral phase transition,we can find that the transition be-tween the hadronic phase and the partonic phase is a smooth crossover at low baryon chemical potential as well as at high temperature,and the transition can be a first-order transition at larger baryon chemical potential as well as at low temperature.The critical point between the crossover and the first-order transition for the chiral phase transition is??_q=354 MeV,T=45MeV?.With the isovector interaction,the phase boundaries as well as the critical points of u and d begin to separate.And we found that the isospin splittings of chiral phase transition and the critical point are more sensitive to the scalar-isovector coupling,while the quark matter sym-metry energy is more sensitive to the vector-isovector coupling.In addition to chiral symmetry,quantum chromodynamics has two important characteristics:one is the asymptotic freedom,and the other is the color confinement.When the momentum scale of the strong interaction in-creases,the coupling constant??_s?of the strong interaction tends to zero and the hadron-quark phase transition can be a deconfinement phase transition.Thus,we introduce the Polyakov loop into the NJL model to compensate effectively the gluon contribution,and it can serve as an or-der parameter for deconfinement phase transition.The phase diagram obtained from the pNJL model has two important features:?1?the critical point moves to a higher temperature and a slightly smaller quark chemical potential??_q=347 MeV,T=93 MeV?;?2?the phase boundary of deconfinement transition is mostly independent of the isovector coupling.Experimentally,the non-Gaussian fluctuation of conserved quantities?net-baryon and net-charge?in relativis-tic heavy-ion collisions can be a signal of the phase transition critical point.We thus have studied the higher order susceptibilities?skewness and kurtosis?of net-baryon and net-charge fluctuations based on 3-flavor pNJL model.With isovector coupling constants,the peaks of the net-baryon and net-charge susceptibilities move to the low-temperature or low-energy side.On the other hand,the shape of the net-charge susceptibilities is largely changed with the isovec-tor couplings,i.e.,an additional negative peak appear in the skewness results and two positive peaks peaks appear in the kurtosis results along the hypothetical chemical freeze-out line,if it is very close to the phase boundary.Recently,‘low-energy'relativistic heavy-ion collisions were carried out in the beam-energy scan?BES?program at the relativistic heavy-ion collider?RHIC?,in order to search for the signal of the critical point of the hadron-quark phase transition.Among various interest-ing phenomena different from those observed in relativistic heavy-ion collisions is the splitting of v₂between protons and antiprotons,K⁺and K^-,and?⁺and?^-,showing the break-down of the NCQ scaling law.The v₂splitting between protons and antiprotons as well as between K⁺and K^-can be attributed to the different mean-field potentials for particles and their antiparti-cles.Further,we will explain the v₂splitting between?⁺and?^-based on the framework of an extended multiphase transport model,in which the partonic mean-field potentials are obtained from a 3-flavor NJL model including isovector couplings.Since heavy-ions are neutron-rich nuclei,the produced matter is not only baryon-rich but also neutron-rich or d-quark-rich,where d??u?quarks are expected to have a more repulsive potential than u??d?in the presence of a vector-isovector interaction.Using an improved coalescence model to convert quarks and antiquarks to hadrons at hadronization,the vector-isovector interaction will enhance the v₂of?^-while reduce the v₂of?⁺,qualitatively consistent with that observed experimentally.Finally,we use the NJL model to discuss the effects of vector interactions and isovec-tor interactions on the equation of state?EOS?of quark matter in strange quark stars.We find the EOS is more sensitive to the strength of the vector-isoscalar interaction,with a larger vector-isoscalar coupling constant R_Vleading to a stiffer EOS.The vector-isovector interaction characterized by the reduced coupling constant R_IVslightly stiffens the EOS at higher baryon densities,but the scalar-isovector interaction affects the EOS only around 2?₀,but has negli-gible effects at higher baryon densities.In addition,we can also know that a stiffer equation of state can give a larger mass of compact star,and the tidal deformabilities of the star will be larger.According to the mass-radius relation and tidal deformabilities from the GW170817event as well as the v₂splitting results,we thus gives an allowed area for the coupling strengths of the vector and isovector interactions.