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Register a new userPhase Transition of Finite Size Quark Droplets with Isospin Chemical Potential in the Nanbu--Jona-Lasinio Model
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Making use of the NJL model and the multiple reflection expansion pproximation, we study the phase transition of the finite size droplet with u and d quarks. We find that the dynamical masses of u, d quarks are different, and the chiral symmetry can be restored at different critical radii for u, d quark. It rovides a clue to understand the effective nucleon mass splitting in nuclear matter. Meanwhile, it shows that the maximal isospin chemical potential at zero temperature is much smaller than the mass of pion in free space.
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We derive the critical temperature in a nonlocal Nambu-Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang-Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu-Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang-Mills theory at low-energy as also confirmed by lattice computations.
We determine the volume and mass dependence of scalar and pseudoscalar two-point functions in N_f-flavour QCD, in the presence of an isospin chemical potential and at fixed gauge-field topology. We obtain these results at second order in the epsilon-expansion of Chiral Perturbation Theory and evaluate all relevant zero-mode group integrals analytically. The virtue of working with a non-vanishing chemical potential is that it provides the correlation functions with a dependence on both the chiral condensate, Sigma, and the pion decay constant, F, already at leading order. Our results may therefore be useful for improving the determination of these constants from lattice QCD calculations. As a side product, we rectify an earlier calculation of the O(epsilon^2) finite-volume correction to the decay constant appearing in the partition function. We also compute a generalised partition function which is useful for evaluating U(N_f) group integrals.
We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon number one soliton in a hot quark matter in the NJL model as well as in a hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in mean-field approximation, we find a chiral phase transition from Goldstone to Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence - at finite temperatures not close to the critical one they are less affected than in the cold matter. Whereas the quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, the nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first order phase transition. We solve the B=1 solitonic sector of the NJL model in the presence of an external hot quark and nucleon medium. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of a cold matter. At some critical temperature, which for the nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from the nucleon to the quark matter.
We compare the low eigenvalue spectra of the Overlap Dirac operator on two sets of configurations at $mu_I/mu_I^c$ = 0.5 and 1.5 generated with dynamical staggered fermions at these isospin chemical potential on $24^3 times 6$ lattices. We find very small changes in the number of zero modes and low lying modes which is in stark contrast with those across the corresponding finite temperature phases where one sees a drop across the phase transition. Possible consequences are discussed.
We investigate the phase diagram on temperature-chemical potential plane in the Nambu-Jona-Lasinio model with the dimensional regularization. While the structure of the resulting diagram shows resemblance to the one in the frequently used cutoff regularization, some results of our study indicate striking difference between these regularizations. The diagram in the dimensional regularization exhibits strong tendency of the first order phase transition.
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