Functional dependence of axial anomaly via mesonic fluctuations in the three flavor linear sigma model

Abstract

Temperature dependence of the $U_A(1)$ anomaly is investigated by taking into account mesonic fluctuations in the $U(3)\times U(3)$ linear sigma model. A field dependent anomaly coefficient function of the effective potential is calculated within the finite temperature functional renormalization group approach. The applied approximation scheme is a generalization of the chiral invariant expansion technique developed in [G. Fejos, Phys. Rev. D 90, 096011 (2014)]. We provide an analytic expression and also numerical evidence that depending on the relationship between the two quartic couplings, mesonic fluctuations can either strengthen of weaken the anomaly as a function of the temperature. The role of the six-point invariant of the $U(3)\times U(3)$ group, and therefore the stability of the chiral expansion is also discussed in detail.

10 pages, 3 figures, minor changes, Published in Phys. Rev. D

References in corpus (9)

• Exact evolution equation for the effective potential
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Magnetic susceptibility of a strongly interacting thermal medium with 2+1 quark flavors
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows
• Chiral phase transition in the vector meson extended linear sigma model

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