Magnetic polarizability of a charged pion from four-point functions in lattice QCD

Electromagnetic dipole polarizabilities are fundamental properties of a hadron that represent its resistance to deformation under external fields. For a charged hadron, the presence of acceleration and Landau levels complicates the isolation of its deformation energy in the conventional background field method. In this work, we explore a general method based on four-point functions in lattice QCD that takes into account all photon, quark and gluon interactions. The electric polarizability (${\alpha }_E$) has been determined from the method in a previous proof-of-principle simulation. Here we focus on the magnetic polarizability (${\beta }_M$) using the same quenched Wilson action on a ${24}^3\times 48$ lattice at $\beta =6.0$ with pion mass from 1100 to 370 MeV. The results from the connected diagrams show a large cancellation between the elastic and inelastic contributions, leading to a relatively small and negative value for ${\beta }_M$ consistent with chiral perturbation theory. We also discuss the mechanism for ${\alpha }_E+{\beta }_M$ from combining the two studies.