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

TL;DR

This paper introduces a lattice QCD method using four-point functions to accurately determine the magnetic polarizability of a charged pion, accounting for complex interactions and providing results consistent with theoretical predictions.

Contribution

The study develops and applies a novel four-point function approach in lattice QCD to compute the magnetic polarizability of charged pions, including all relevant interactions.

Findings

Magnetic polarizability ($eta_M$) is small and negative, aligning with chiral perturbation theory.

Connected diagram contributions show significant cancellation, affecting the polarizability value.

The method effectively incorporates photon, quark, and gluon interactions in lattice QCD calculations.

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 ($\alpha_E$) 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.