Magnetism of QCD matter and the pion mass from tensor-type spin polarization and the anomalous magnetic moment of quarks

We investigate the magnetism of QCD matter and pion mass under magnetic fields, including the contribution from the tensor-type spin polarization (TSP) and the anomalous magnetic moment (AMM) of quarks. The AMM reduces the lowest Landau level (LLL) energy and the TSP lifts up the LLL energy; thus, the AMM and the TSP have opposite effects on the magnetized quark matter. It is found that the TSP enhances the magnetic catalysis of chiral condensate and induces diamagnetism (negative magnetic susceptibility) of quark matter at low temperature; both neutral and charged pion masses increase quickly with magnetic field in the case of TSP. The AMM of quarks induces magnetic inhibition, causes inverse magnetic catalysis at finite temperature, and the neutral pion mass decreases with magnetic field, while the charged pion mass shows nonmonotonic behavior with respect to the magnetic field, which qualitatively agrees with lattice result. However, the magnetic susceptibility is positive at low temperature with AMM. Also, it is found that the Gell-Mann-Oakes-Renner relation breaks down when the AMM or TSP effect is considered.