Mass spectra of neutral mesons $K_0,{\pi }_0,\eta ,{\eta }^{\prime }$ at finite magnetic field, temperature and baryon chemical potential

Abstract

The mass spectra of neutral mesons $K_0,{\pi }_0,\eta ,{\eta }^{\prime }$ on temperature-quark chemical potential $(T-\mu )$ plane in the presence of a constant magnetic field is investigated in the $SU(3)$ NJL model. As a Goldstone boson of chiral symmetry breaking, the mass of $K_0$ meson increases with temperature and/or quark chemical potential, and we observe two kinds of mass jumps of $K_0$ meson in media, which is induced by the mass jump of constituent quarks and the magnetic field, respectively. Due to the breaking of isospin symmetry between $u$ and $d$ quarks in magnetic fields, the mixing of ${\pi }_0-\eta -{\eta }^{\prime }$ mesons occurs and this leads to rich structures of their mass spectra. For instance, ${\pi }_0$ mass is influenced by the strange quark. There appear the change of increase ratio of ${\pi }_0$ mass at high $\mu$ and vanishing $T$ and the ${\pi }_0$ mass jump crossing over the threshold of two times of strange quark mass at finite $T$ and $\mu$. The mass ordering of ${\pi }_0,\eta ,{\eta }^{\prime }$ mesons varies in media, due to their mass jumps, which are induced by the mass jump of constituent quarks or the magnetic field.

arXiv comment8 pages, 4 figures

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