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

TL;DR

This paper calculates the electric polarizability of the charged kaon using lattice QCD with a four-point function approach, separating elastic and inelastic contributions, and demonstrates the method's applicability to strange mesons.

Contribution

It introduces a four-point function framework for charged kaon polarizability in lattice QCD, extending previous methods and laying groundwork for future, more precise studies.

Findings

Charged kaon electric polarizability: (0.988 ± 0.534) × 10^{-4} fm^3.

Kaon charge radius squared: 0.3303 ± 0.0028 fm^2.

Method demonstrated with 500 quenched lattice configurations, focusing on connected diagrams.

Abstract

We present a lattice QCD calculation of the electric polarizability of the charged kaon using a four-point function approach, which is the Euclidean analog of low-energy Compton scattering. In the case of the charged kaon, the polarizability is separated into an elastic (Born) term, determined from the charge radius extracted via the kaon electromagnetic form factor, and an inelastic (non-Born) term obtained from the time-integrated difference of four-point correlation functions. Our study employs 500 configurations of Wilson quenched $24^3\times 48$ lattices, and we compute connected diagrams as a proof of principle. From this analysis, we obtain values for the charged kaon electric polarizability of $\alpha_E = (0.988 \pm 0.534) \times 10^{-4}\;\mathrm{fm}^3$ as well as $\langle r_E^2\rangle =0.3303\pm 0.0028\;\mathrm{fm}^2$ for the squared kaon charge radius, after extrapolation to the physical pion mass. The study demonstrates the applicability of the four-point function framework to strange mesons, extends previous four-point function polarizability studies, and provides a foundation for future calculations with increased statistics, dynamical fermions, and improved control of systematic uncertainties.