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.