On-shell versus curvature mass parameter fixing schemes in the three flavor quark-meson model with vacuum fluctuations

TL;DR

This paper compares on-shell and curvature mass parameter fixing schemes in the three-flavor quark-meson model, demonstrating the importance of consistent renormalization and vacuum fluctuation inclusion for accurate phase diagram predictions.

Contribution

It introduces the first application of an on-shell parameter fixing scheme to the three-flavor quark-meson model, highlighting differences from the traditional curvature mass approach.

Findings

The on-shell scheme yields consistent physical meson masses and decay constants.

Vacuum effective potential and phase diagrams are identical under certain sigma meson mass conditions.

The study emphasizes the impact of renormalization schemes on model predictions.

Abstract

The vacuum effective potential and phase diagram for the three (2+1) flavor quark-meson model have been computed and compared in an extended mean-field approximation (e-MFA) where the model parameters are fixed by using different renormalization prescriptions after including quark one-loop vacuum fluctuations. When the vacuum one-loop divergence is regularized in the minimal subtraction scheme and the curvature masses of the scalar and pseudo-scalar mesons are used for fixing the parameters, the setting of the quark-meson model with the vacuum term (QMVT) turns out to be inconsistent as one notes that the curvature masses are defined by the evaluation of self-energy at zero momentum. This work constitutes the first application of the consistent on-shell parameter fixing scheme to the three flavor quark-meson (QM) model. In this setting of the renormalized quark-meson (RQM) model, the physical (pole) masses of the $\pi, K, \eta$ and $\eta^{\prime}$ pseudo-scalar mesons and the scalar $\sigma$ meson,the pion decay constant and kaon decay constant are put into the relation of the running mass parameter and couplings by using the on-shell and the minimal subtraction renormalization schemes. The nonstrange direction normalized vacuum effective potential plots for both the RQM model and QMVT model, are exactly identical for the $m_\sigma=$ 658.8 MeV while the nonstrange direction order parameter temperature variations and phase diagrams for both the models RQM and PQMVT are identical when the $m_\sigma $ value is smaller by 10 MeV i.e. $m_\sigma=$ 648 MeV. This happens because the normalized vacuum effective potential variation in the nonstrange direction is somewhat influenced by its variation in the strange direction.