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

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 term, determined from the charge radius extracted via the kaon electromagnetic form factor, and an inelastic 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 a charged kaon electric polarizability of $α_E = (1.682 \pm 0.523) \times 10^{-4}$ fm$^3$ and a squared charge radius $r_E^2 = 0.3303 \pm 0.0028$ fm$^2$ after extrapolation to the physical pion mass. The quoted uncertainties include statistical errors and, for $α_E$, the $\boldsymbol{q}^2 \to 0$ extrapolation; they do not include systematic effects from the quenched approximation, omitted disconnected diagrams, finite volume, or the single lattice spacing, which may be comparable in size. The results at the simulated masses should therefore be regarded as the primary outcome, with the physical-point values serving as an indicative extrapolation. 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.