Axial Inverse Magnetic Catalysis

We propose a new inverse magnetic catalysis emerging around the chiral crossover regime in the thermomagnetic QCD with 2 + 1 flavors at physical point, that is, the inverse magnetic catalysis for $U(1)$ axial symmetry (AIMC: axial inverse magnetic catalysis): difference of susceptibilities for quark bilinears forming the $U(1)_A$ partner increases with respect to the applied magnetic field at zero temperature, while decreases at higher temperatures as well as its (pseudo) critical temperature. This phenomenon is compared with the already discovered IMC for the chiral $SU(2)_L \times SU(2)_R$ symmetry (CIMC: chiral IMC). We demonstrate the AIMC based on a Nambu-Jona-Lasinio model with 2 + 1 quark flavors, where introduced anomalous magnetic moments of the quarks play the essential role to drive both the CIMC and AIMC. Our finding is shortly testable on lattices. Possible phenomenological and cosmological implications are also briefly addressed.