Effect of the anomalous magnetic moment of quarks on magnetized QCD matter and meson spectra

We systematically investigate the effects made by the anomalous magnetic moment (AMM) of quark in the magnetized QCD matter, including the magnetic susceptibility, the inverse magnetic catalysis around the critical temperature and the modified neutral and or charged pion and rho meson's spectra. The dynamical AMM of quark, coupling with magnetic field, causes Zeeman splitting in the energy dispersion of quark and thus changes the magnetism properties and masses of magnetized mesons. Unfortunately, we found that the lattice results of the quark matter under magnetic fields cannot fully be explained via including the AMM interaction. It is observed that the AMM of quark reduces the dynamical quark mass and therefore induces the inverse magnetic catalysis around Tc. The neutral pion is very sensitive to the AMM term and its mass decreases with magnetic field quickly. On the contrary, the charged pion mass shows a nontrivial behavior, i.e., linearly increases with the weak and moderate magnetic fields and then saturates at strong region. For rho mesons, AMM coupling modifies the masses of neutral rho particles for all sz consistently, while it reduces the masses of charged rho mesons for sz=+1, 0 but enhances the mass of sz=-1 state. The magnetic susceptibility at low temperatures can be either positive or negative with different strengths of AMM interaction.