Abstract
We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli-Villars regularization scheme.
Highlights
We study inverse magnetic catalysis in the Nambu–Jona-Lasinio model beyond mean field approximation
Considering the dimension reduction of fermions, the chiral symmetry breaking is enhanced by the magnetic field, which leads to an increasing critical temperature for the chiral restoration phase [26,27,28]
With a strong magnetic field, the Goldstone mode in the chiral symmetry breaking phase may play an important role for the realization of inverse magnetic catalysis [33]
Summary
We study inverse magnetic catalysis in the Nambu–Jona-Lasinio model beyond mean field approximation. By comparing the gap equation (4) for mean field quark mass mmf with the pole equation (8) for neutral meson masses mM , we have the simple relations in the chiral symmetry breaking phase, mπ0 = 0, mσ = 2mmf . The physical quark mass as the order parameter of chiral phase transition corresponds to the minimum of the thermodynamic potential of the system at fixed temperature, chemical potential and magnetic field,
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