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 (\emph{up}, \emph{down} and \emph{strange}). The parameter space is constrained at vanishing magnetic field, using the quarks dynamical masses and the meson spectra, whereas at non-vanishing 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 six-fermion '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.
Highlights
The effect of strong magnetic fields in strongly interacting matter plays a very important role in several physical contexts such as in heavy ion collisions [1,2,3], in astronomic compact object like magnetars [4,5], and in the first phases of the early Universe [6,7]
We study the implications of recent lattice Quantum chromodynamics (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
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
Summary
The effect of strong magnetic fields in strongly interacting matter plays a very important role in several physical contexts such as in heavy ion collisions [1,2,3], in astronomic compact object like magnetars [4,5], and in the first phases of the early Universe [6,7]. Quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons whose phase diagram have been widely studied by lattice QCD (LQCD) simulations and in the context of effective models in the presence of magnetic fields (see [8] for a review). In the presence of magnetic fields, LQCD and the vast majority of effective models predict magnetic catalysis, which is the increment of the chiral order parameter, the light quark condensate, as the magnetic field, B, increases. This phenomenon is originated by the dominant contribution of the lowest Landaulevel [9].
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