Magnetic field dependent ’t Hooft determinant extended Nambu–Jona-Lasinio model

Abstract

We study the implications of recent lattice QCD results for the magnetic field dependence of the quarks dynamical masses on the 't Hooft determinant extended Nambu-Jona-Lasinio model in the light and strange quark sectors (up, down and strange). The parameter space is constrained at vanishing magnetic field, using the quarks dynamical masses and the meson spectra, whereas at nonvanishing magnetic field strength the dependence of the dynamical masses of two of the quark flavors is used to fit a magnetic field dependence on the model couplings, both the four-fermion Nambu-Jona-Lasinio interaction and the sixfermion 't Hooft flavor determinant. We found that this procedure reproduces the inverse magnetic catalysis, and the strength of the scalar coupling decreases with the magnetic field, while the strength of the six-fermion 't Hooft flavor determinant increases with the magnetic field.

Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov-Nambu-Jona-Lasinio model with magnetic field dependent coupling strengths

“…Model parameters (quark current masses, mu, m d and ms, interaction coupling strengths, G and κ, and momentum integrals 3D regularization cutoff, Λ) and some properties of the low-lying pseudoscalar spectra for the set that was used in the current work as well as the vacuum dynamical masses of the quarks (Mu, M d and Ms). The fit was done in [39] and reproduces the dynamical masses of the quarks reported in [38] as well as the mass of the pion (M π ± = 140 MeV) and the eta prime mesons (M η = 958 MeV) at a vanishing magnetic field strength. For completeness the kaon mass (M K ± ), the decay width of the eta prime meson Γ η and the eta meson mass (Mη) are also presented below (for more details see [39]).…”

“…The fit was done in [39] and reproduces the dynamical masses of the quarks reported in [38] as well as the mass of the pion (M π ± = 140 MeV) and the eta prime mesons (M η = 958 MeV) at a vanishing magnetic field strength. For completeness the kaon mass (M K ± ), the decay width of the eta prime meson Γ η and the eta meson mass (Mη) are also presented below (for more details see [39]). Values used for the fitting procedure are marked with * .…”

“…Here we used our previous results from [39]. Sumarinzing, the fitting procedure can be decomposed in two parts:…”

“…The dynamical masses of the quarks dependence on the magnetic field (at vanishing temperature and quark chemical potential) resulting from lattice QCD calculations [38], were recently used to obtain a magnetic field dependence of the coupling strengths of the 't Hooft determinant extended Nambu-Jona-Lasinio model in the light and strange quark sectors (up, down and strange) [39]. In that work the parameter space is first constrained at vanishing magnetic field, using the quarks dynamical masses and the meson spectra, and then, at non-vanishing magnetic field strength, the dependence of the dynamical masses of two of the quark flavors (down and strange) is used to fit a magnetic field dependence on the model couplings, both the four-fermion Nambu-Jona-Lasinio interaction and the six-fermion 't Hooft fla-vor determinant while keeping the momentum integration regularization cutoff fixed at its vanishing magnetic field value.…”

QCD phase diagram in a constant magnetic background

“…[87] (see also Refs. [88,89]). Only T = 0 physics from the lattice is used as input to improve the model.…”