Thermomagnetic modification of the anomalous magnetic moment of quarks using the NJL model

The effective photon-quark-antiquark ($\ensuremath{\gamma}q\overline{q}$) vertex function is evaluated at finite temperature in the presence of an arbitrary external magnetic field using two-flavor gauged Nambu--Jona-Lasinio model mean approximation. lowest order diagram contributing to form factor and anomalous moment (AMM) quarks calculated imaginary time formalism theory Schwinger proper formalism. propagator, including all Landau levels with nonzero AMM dressed quarks, considered while calculating loop diagram. Using sharp as well smooth three-momentum cutoff, we regularize UV divergences arising from parameters our are chosen reproduce well-known phenomenological quantities zero field, such pion-decay constant (${f}_{\ensuremath{\pi}}$), vacuum quark condensate, pion mass (${m}_{\ensuremath{\pi}}$), moments proton neutron. We then study dependence constituent quark. found that large chiral symmetry broken phase low region. Around pseudo-chiral transition, they decrease rapidly high temperatures both them approach vanishingly small values restored phase.