Chiral extrapolation of the charged-pion magnetic polarizability with Pad\'e approximant

TL;DR

This paper develops a chiral extrapolation method using Padé approximants to accurately determine the charged pion's magnetic polarizability from lattice QCD data, accounting for systematic uncertainties and matching experimental results.

Contribution

It introduces a Padé approximant-based extrapolation technique that incorporates higher-order chiral perturbation theory effects to analyze lattice QCD results for pion polarizability.

Findings

Extrapolated pion magnetic polarizability agrees with experimental data.

Two-loop contributions help estimate systematic uncertainties.

Method improves the reliability of lattice QCD extrapolations.

Abstract

The background magnetic-field formalism of Lattice QCD has been used recently to calculate the magnetic polarizability of the charged pion. These $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory. In this case, the leading term proportional to $1/M_\pi$ arises at tree level from $\mathcal{L}_4$. To describe the results from lattice QCD, while maintaining the exact leading terms of chiral perturbation theory, we introduce a Pad\'e approximant designed to reproduce the slow variation observed in the lattice QCD results. Two-loop contributions are introduced to assess the systematic uncertainty associated with higher-order terms of the expansion. Upon extrapolation, the magnetic polarizability of the charged pion at the physical pion mass is found to be $\beta_{\pi^\pm}=-1.70\,(14)_{\rm stat}(25)_{\rm syst}\times 10^{-4}$ fm$^3$, in good agreement with the recent experimental measurement.