On-shell parameter fixing in the quark-meson model

Abstract

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$ and baryon chemical potential ${\mu }_B$. The parameters in the quark-meson model can be found by expressing them in terms of the sigma mass $m_{\sigma }$, the pion mass $m_{\pi }$, the constituent quark mass $m_q$ and the pion decay constant $f_{\pi }$. In practice, this matching is done at tree level, which is inconsistent once we take loop effects of the effective potential into account. We show how to properly perform the matching in the quark-meson model by using the on-shell and the modified minimal subtraction renormalization schemes relating the physical masses and the pion decay constant to the running mass parameter and couplings. We map out the phase diagram in the ${\mu }_B$--$T$ plane and compare our results with other approximations.

9 pages and 10 figs. v2: revised parameter fixing and updated results

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Cited by in corpus (12)

• Meson condensation
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Inhomogeneous chiral condensate in the quark-meson model
• Sound velocity peak and conformality in isospin QCD
• Multicomponent meson superfluids in chiral perturbation theory
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Exploring axial $U(1)$ restoration in a modified 2+1 flavor Polyakov quark meson model
• Finite Density Two Color Chiral Perturbation Theory Revisited
• QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model
• On-shell versus curvature mass parameter fixing schemes in the quark-meson model and its phase diagrams
• Thermal effects on sound velocity peak and conformality in isospin QCD
• Dissecting the moat regime at low energies I: Renormalization and the phase structure