Simulating rare kaon decays $K^{+}\to\pi^{+}\ell^{+}\ell^{-}$ using domain wall lattice QCD with physical light quark masses

TL;DR

This paper presents the first lattice QCD calculation of the electromagnetic form factor for rare kaon decays using physical light-quark masses, providing insights into long-distance contributions with improved realism.

Contribution

It introduces a novel lattice QCD approach to compute the form factor for $K^+ o ext{pi}^+ ext{l}^+ ext{l}^-$ decays with physical quark masses, including charm-quark extrapolation.

Findings

First calculation of $V(z)$ with physical light-quark masses.

Achieved a bound for $V(z=0.013)$ despite large statistical errors.

Implemented charm-quark extrapolation to account for GIM cancellation.

Abstract

We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the $K^+\to\pi^+\ell^+\ell^-$ decay amplitude. The calculation is performed on a 2+1 flavor domain wall fermion ensemble with inverse lattice spacing $a^{-1}=1.730(4)$GeV. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=-0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quark loops.