Speaker
Description
We investigate the $U(1)_{A}$ symmetry and the chiral separation effect (CSE) in the presence of a strong background magnetic field within the three-flavor Nambu-Jona-Lasinio (NJL) model. To incorporate the inverse magnetic catalysis (IMC) effect, we introduce a magnetic-field-dependent scalar coupling $G_{s}(eB)$. We evaluate the susceptibility splittings $\chi_{\pi_{0}}-\chi_{\delta_{0}}$ and $\chi_{\pi_{0}}-\chi_{\sigma}$ related to the singlet $U(1)_{A}$ symmetry and the surviving neutral non-singlet axial symmetry, respectively. Our results for these susceptibility splittings are qualitatively consistent with Lattice-QCD calculations. At low temperatures, both susceptibility splittings are enhanced by the magnetic field, whereas near the crossover they decrease at sufficiently large $eB$, reflecting the transition from magnetic catalysis (MC) to inverse magnetic catalysis (IMC) behavior. We further calculate the CSE conductivity and its higher-order coefficients. At low temperatures, the CSE conductivity is nearly zero and then increases with increasing temperature, gradually approaching its chiral-limit value. By combining the NJL and hadron gas descriptions, we reproduce the Lattice-QCD behavior of the CSE conductivity. Although the higher-order contributions are minor, they exhibit enhanced sensitivity to the chiral crossover region. These findings provide further insight into the realization of chiral and $U(1)_{A}$ symmetries in strongly magnetized matter.
