Neutral pion polarizabilities from four-point functions in lattice QCD

TL;DR

This paper demonstrates a lattice QCD approach to compute neutral pion polarizabilities using four-point functions, highlighting the method's consistency for electric but discrepancies for magnetic polarizability, possibly due to disconnected diagrams.

Contribution

It introduces a four-point function method for calculating neutral pion polarizabilities in lattice QCD and compares results with other methods, emphasizing the role of disconnected diagrams.

Findings

Electric polarizability results agree with background field method and ChPT.

Magnetic polarizability results differ significantly among methods.

Disconnected diagrams may play an important role in neutral pion polarizability calculations.

Abstract

We report a proof-of-principle lattice QCD simulation of the electric and magnetic polarizabilities for a neutral pion in the four-point function method. The results are based on the same quenched Wilson ensembles on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV previously used for a charged pion. For electric polarizability, the results are largely consistent with those from the background field method and ChPT. In contrast, there are significant differences for magnetic polarizability among the four-point function method, the background field method, and ChPT. The situation points to the potentially important role of disconnected diagrams for a neutral pion. We elucidate a transparent quark decomposition in the four-point function method that can be used to shed light on the issue.