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

We investigate the magnetism of QCD matter and pion mass under magnetic field considering the contribution from the tensor-type spin polarization and the anomalous magnetic moment (AMM) of quarks. It is found that the tensor-type spin polarization (TSP) induces the magnetic catalysis of chiral condensate and 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 anomalous magnetic moment (AMM) of quarks induces magnetic inhibition and a magnetic dependent AMM 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 the magnetic field, which is qualitatively in agreement with lattice result. However, the magnetic susceptibility is positive at low temperature with AMM. In the current framework, our results show the irreconcilable contradiction between the diamagnetism and inverse magnetic catalysis.