Predictions for the rare kaon decays $K_{S,L} \to \pi^0 \ell^+ \ell^-$ from QCD in the limit of a large number of colours

TL;DR

This paper uses QCD in the large number of colours limit to analyze and predict rare kaon decay rates involving $K_{S,L} o \pi^0 \, \\ell^+ \\ell^-$, clarifying CP-violation interference effects.

Contribution

It introduces a theoretical framework based on large-$N_c$ QCD to study long-distance effects in rare kaon decays and predicts decay rates and CP-violation interference.

Findings

Predicted decay rates for $K_{S} o \\pi^0 \\ell^+ \\ell^-$.

Unambiguous prediction of constructive interference in $K_L o \\pi^0 \\ell^+ \\ell^-$.

Validated the large-$N_c$ approach as suitable for these decay modes.

Abstract

The long-distance and non-local parts of the form factors describing the single-photon mediated $K_{S,L}\to\pi^0\gamma^*\to\pi^0\ell^+\ell^-$ ($\ell = e, \mu$) transitions in the standard model are addressed in QCD in the limit where the number $N_c$ of colours becomes infinite. It is shown that this provides a suitable theoretical framework to study these decay modes and that it allows to predict the decay rates for $K_{S}\to\pi^0\ell^+\ell^-$. It also unambiguously predicts that the interference between the direct and indirect CP-violating contributions to the decay rate for $K_L\to\pi^0 \ell^+ \ell^-$ is constructive.