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Register a new userVolume Dependence of the Pion Mass in the Quark-Meson-Model
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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.
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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 examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the rho to pions is largely independent of the quark mass while the quark mass dependence of the rho--mass is given by recent lattice data. By employing the Omnes representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the rho-pi-pi coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely <r^4> = 0.73 +- 0.09 fm^4 or equivalently c_V=4.00pm 0.50 GeV^{-4}.
We calculate the mass shift for the pion in a finite volume with renormalization group (RG) methods in the framework of the quark-mesons model. In particular, we investigate the importance of the quark effects on the pion mass. As in lattice gauge theory, the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes, in addition to the shift due to pion interactions. We compare our results to chiral perturbation theory calculations and find differences due to the fact that chiral perturbation theory only considers pion effects in the finite volume.
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.
We study the thermodynamic geometry of the Quark-Meson model, focusing on the curvature, $R$, around the chiral crossover at finite temperature and baryon chemical potential. We find a peculiar behavior of $R$ in the crossover region, in which the sign changes and a local maximum develops; in particular, the height of the peak of $R$ in the crossover region becomes large in proximity of the critical endpoint and diverges at the critical endpoint. The appearance of a pronounced peak of $R$ close to the critical endpoint supports the idea that $R$ grows with the correlation volume around the phase transition. We also analyze the mixed fluctuations of energy and baryon number, $langleDelta UDelta Nrangle$, which grow up substantially in proximity of the critical endpoint: in the language of thermodynamic geometry these fluctuations are responsible for the vanishing of the determinant of the metric, which results in thermodynamic instability and are thus related to the appearance of the second order phase transition at the critical endpoint.
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