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Register a new userVolume and Quark Mass Dependence of the Chiral Phase Transition
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We investigate chiral symmetry restoration in finite spatial volume and at finite temperature by calculating the dependence of the chiral phase transition temperature on the size of the spatial volume and the current-quark mass for the quark-meson model, using the proper-time Renormalization Group approach. We find that the critical temperature is weakly dependent on the size of the spatial volume for large current-quark masses, but depends strongly on it for small current-quark masses. In addition, for small volumes we observe a dependence on the choice of quark boundary conditions.
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We consider the quark-meson-model in a finite three-dimensional volume using the Schwinger proper-time renormalization group. We derive and solve the flow equations for finite volume in local potential approximation. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. The corresponding effective meson potential breaks chiral O(4) symmetry explicitly, depending on sigma and pion fields separately. We calculate the volume dependence of the pion mass and of the pion decay constant with the renormalization group flow equations and compare with recent results from chiral perturbation theory in a finite volume.
Near the critical temperature of the chiral phase transition, a collective excitation due to fluctuation of the chiral order parameter appears. We investigate how it affects the quark spectrum near but above the critical temperature. The calculated spectral function has many peaks. We show this behavior can be understood in terms of resonance scatterings of a quark off the collective mode.
We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $chi_{rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition is not first order but a continuous cross-over for $m_pi=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_Ltimes SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.
We investigate finite volume effects on the pion mass and the pion decay constant with renormalization group (RG) methods in the framework of a phenomenological model for QCD. An understanding of such effects is important in order to interpret results from lattice QCD and extrapolate reliably from finite lattice volumes to infinite volume. We consider the quark-meson-model in a finite Euclidean 3+1 dimensional volume. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. In the corresponding effective potential for the meson fields, the chiral O(4)-symmetry is broken explicitly, and the sigma and pion fields are treated individually. Using the proper-time renormalization group, we derive renormalization group flow equations in the finite volume and solve these equations in the approximation of a constant expectation value. We calculate the volume dependence of pion mass and pion decay constant and compare our results with recent results from chiral perturbation theory in finite volume.
We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $sigma$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K;xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $mu$, which is not surprising because at small $mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.
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