Effect of quark anomalous magnetic moment on neutral dense quark matter under magnetic field

Abstract We discuss the effect of the quark anomalous magnetic moment (AMM) on the neutral dense quark matter under magnetic fields based on the Nambu–Jona–Lasinio (NJL) model at finite baryon density. To address its correlation with the chiral symmetry, we consider a simplified situation: the model includes the two-quark flavors under constant magnetic fields, and incorporates the effective interaction of the quark AMM linked to the spontaneous chiral symmetry breaking. It has been found that the magnetization is affected by the presence of the quark AMM, which can lead to alter the sign of the magnetization, particularly immediately after the phase transition with relatively large magnetic fields. We then examine the equation of state (EoS) in cases with and without magnetization for anatomizing the thermodynamic quantities. Without the magnetization, a small magnetic field stiffens the EoS, but with increasing the magnetic field, the EoS tends to soften. The stiffness of the EoS is found to be influenced by the magnetic effect on the critical chemical potential of the chiral phase transition and the quark number density at this critical point. As a result, the mass and radius of the neutron star composed of quark matter increase with the small magnetic field but turn to decrease as the magnetic field further increases. By including the quark AMM, the critical chemical potential is decreased and the quark number density takes a smaller value. Thus, for the stronger magnetic fields, the quark AMM suppresses the softening effect of the magnetic field on the EoS, leading to increased mass and radius compared to when the quark AMM is absent. In contrast, for the small magnetic field, the contribution of the quark AMM to the EoS is marginal. When the magnetization is taken into account, the magnetic effect on the stiffness of the EoS is overshadowed by the contribution of the magnetization. However, this overshadowing occurs regardless of whether the magnetization affected by the quark AMM takes negative or positive values. As a result, the effect of the quark AMM is not evident in the mass-radius relation.