Charged pion electric polarizability from four-point functions in lattice QCD

TL;DR

This paper introduces a novel four-point function method in lattice QCD to determine the electric polarizability of charged pions, providing insights into hadron internal structure beyond traditional background field techniques.

Contribution

The work presents an alternative lattice QCD approach using four-point functions to study charged hadron polarizabilities, offering a clearer understanding of photon, quark, and gluon interactions.

Findings

Charged pion electric polarizability results suggest cancellation between elastic and inelastic contributions.

Method demonstrates feasibility with quenched Wilson action on a 24^3×48 lattice.

Results indicate potential for studying smaller pion masses in future work.

Abstract

Polarizabilities reveal valuable information on the internal structure of hadrons in terms of charge and current distributions. For neutral hadrons, the standard approach is the background field method. But for a charged hadron, its acceleration under the applied field complicates the isolation of the polarization energy. In this work, we explore an alternative method based on four-point functions in lattice QCD. The approach offers a transparent picture on how polarizabilities arise from photon, quark, and gluon interactions. We carry out a proof-of-concept simulation on the electric polarizability of a charged pion, using quenched Wilson action on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV. We show in detail the evaluation and analysis of the four-point correlation functions and report results on charge radius and electric polarizability. Our results from connected diagrams suggest that charged pion $\alpha_E$ is due to a cancellation between elastic and inelastic contributions. It would be interesting to see how the cancellation plays out at smaller pion masses in future simulations.