Magnetic polarizability of a charged pion from four-point functions

Abstract

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 (𝛼 𝐸 ) has been determined from the method in a previous proof-of-principle simulation. Here we focus on the magnetic polarizability (𝛽 𝑀 ) using the same quenched Wilson action on a 24 3 × 48 lattice at 𝛽 = 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 𝛽 𝑀 consistent with chiral perturbation theory.