Excluding MeV-scale QCD axions by $K_L \to \pi^0\pi^0 a$ at KTeV

TL;DR

This paper reexamines the viability of MeV-scale QCD axions coupling to quarks and electrons by analyzing kaon decay data, concluding that most of the parameter space is excluded, with only a tiny, finely-tuned region remaining possible.

Contribution

It provides new bounds on MeV-scale QCD axions from kaon decay measurements, refining previous constraints and exploring uncertainties in chiral Lagrangian calculations.

Findings

Most of the MeV-scale QCD axion parameter space is excluded by kaon decay bounds.

The KTeV experiment's measurements strongly constrain axion models with certain couplings.

A tiny, finely-tuned region remains where the scenario is not excluded.

Abstract

An interesting proposal suggests that a QCD axion $(a)$ coupling to the up quark, down quark, and electron remains viable for an axion mass near 10~MeV. In this paper, this possibility is reexamined by deriving new bounds from kaon decays. In particular, we perform a detailed analysis of the $K_L \to \pi^0 \pi^0 e^+ e^-$ measurement reported by the KTeV experiment, and reinterpret $K^+$ decay measurements at the E949 and NA62 experiments to constrain both the diphoton decay and effectively invisible decay modes of the axion. We find that, combined with the previously known bounds, the viable window for the MeV-scale QCD axion is excluded, primarily due to the KTeV bound. Uncertainties associated with the chiral Lagrangian are further examined, and the scenario remains excluded even after accounting for these uncertainties, except for a tiny region of parameter space where higher-order corrections must finely cancel the leading-order contribution, suppressing the branching ratio of $K_L\to \pi^0\pi^0 a$ by three orders of magnitude.