Mass spectra of neutral mesons <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi>η</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>η</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> at finite magnetic field, temperature and quark chemical potential

Abstract

The mass spectra of neutral mesons ${K}_{0},{\ensuremath{\pi}}_{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$ on the temperature-quark chemical potential ($T\text{\ensuremath{-}}\ensuremath{\mu}$) plane under a constant magnetic field is investigated in the $SU(3)$ Nambu-Jona-Lasinio model. As a Goldstone boson of chiral symmetry breaking, the mass of ${K}_{0}$ meson generally increases with temperature and/or quark chemical potential, and we observe two kinds of mass jumps of the ${K}_{0}$ meson in medium, one of which is induced by the mass jump of constituent quarks and the other by the magnetic field. Due to the breaking of isospin symmetry between $u$ and $d$ quarks in the presence of magnetic fields, a flavorless neutral meson mixing involving the ${\ensuremath{\pi}}_{0}\ensuremath{-}\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mesons occurs (in the isospin symmetric case the mixing involves only $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$) and a rich structure is found in the mass spectra of these mesons. For instance, the ${\ensuremath{\pi}}_{0}$ mass is influenced by the strange quark. A change in the slope of the $\ensuremath{\mu}$ dependency of the ${\ensuremath{\pi}}_{0}$ mass at high $\ensuremath{\mu}$ and vanishing T can be associated with the crossing of the threshold of two times of strange quark mass. In the finite T case, this behavior is changed into the appearance of a critical chemical potential at which a jump over the threshold of $2{m}_{s}$ occurs. The mass ordering of ${\ensuremath{\pi}}_{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$ mesons varies in medium, due to their mass jumps, which are induced by the mass jump of constituent quarks or the magnetic field.

Topics & Concepts