Kaon decay constraints on vector bosons coupled to non-conserved currents

TL;DR

This paper investigates how rare kaon decays can constrain light vector bosons coupled to non-conserved currents, providing new limits on their couplings and implications for the ATOMKI experiment anomaly.

Contribution

It introduces novel constraints from kaon decay modes on light vector bosons, especially considering double emission processes and their relevance to experimental anomalies.

Findings

$K_L \to \pi^0 \pi^0 (X\to e^+e^-)$ decays constrain couplings to light quarks at $\mathcal{O}(10^{-5})$.

Double emission $K \to \pi XX$ decays provide additional constraints with a $(m_K/m_X)^2$ enhancement.

Limits impact interpretations of the ATOMKI 17 MeV boson anomaly.

Abstract

We study rare three- and four-body kaon decays as a probe of light vector and axial-vector bosons coupled to non-conserved currents. We find that searches for $K_L \to \pi^0 \pi^0 (X\to e^+e^-)$ decays constrain the couplings of light $X$ bosons to light quarks to be as small as $\mathcal{O}(10^{-5})$. The charged-pion modes $K^+ \to \pi^+ \pi^0 (X \to e^+e^-)$ and $K_L \to \pi^+ \pi^- (X \to e^+e^-)$ provide weaker limits, but constrain complementary combinations of couplings to the $u$, $d$, and $s$ quarks at the level of $\mathcal{O}(10^{-4})$. Finally, we also find that double emission of $X$ in $K \to \pi XX$ decays can provide yet additional constraints on the parameter space of light $X$ bosons due to a double $(m_K/m_X)^2$ enhancement to the rate. For a 17 MeV boson, these limits add to the known tension between spin-1 bosons coupled to vector and axial-vector currents interpretations of the results of the ATOMKI experiment with meson decay data. Finally, we also comment on negative pion capture on hydrogen and deuterium as a source of light particles and discuss the prospects for testing the 17 MeV boson hypothesis.