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

TL;DR

This work tests the viability of a QCD axion with mass in the MeV range, coupled to first-generation fermions, by translating kaon decay data into stringent bounds. It combines a detailed chiral Lagrangian treatment of axion–meson mixing with a dedicated Monte Carlo study of the KTeV measurement of $K_L \to \pi^0 \pi^0 e^+ e^-$ to constrain $K_L \to \pi^0 \pi^0 a$ with $a \to e^+ e^-$. It also reinterprets $K^+ \to \pi^+ a$ constraints from E949 and NA62 and examines axion-electron and other decay channels. The main result is that the MeV axion window is excluded in the leading and many subleading scenarios, with only a tiny finely-tuned region remaining possible, implying that viable QCD axions must be at much higher decay constants or involve different mass mechanisms. This demonstrates the power of kaon-decay observables as probes of low-mass axions and informs the parameter space for beyond-Standard-Model axion theories.

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 $K_L \to π^0 π^0 e^+ e^-$ 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 $K_L\to π^0π^0 a$ by three orders of magnitude.

Figures (10)

• Figure 1: Top: Summary of current experimental constraints on our axion scenario in the $(m_a,\,|Q_e|/f_a)$ plane. The red curves show contours of constant $|Q_e|$, while the black dashed curves represent constant axion lifetimes. The shaded gray regions correspond to the previously existing exclusion limits from electron beam-dump experiments and $e^+ e^-$ collider experiments Bross:1989mpRiordan:1987awDavier:1986qqAndreev:2021fzdNA64:2021aiqGninenko:2017yusCCM:2021jmkBjorken:1988asDavier:1989wzBaBar:2014zliAnastasi:2015qla. In contrast, the purple region indicates the NA62 constraint NA62:2025upx, while the shaded pink region shows the bound derived in this work from the experimental limit on the radiative kaon decay ${\rm Br}(K^+\to\pi^+\gamma\gamma)\lesssim 5.0\times10^{-7}$ set by E949. The blue solid (dashed) curve shows the constraint from the electron anomalous magnetic moment, obtained by requiring $|\Delta a_e|<10^{-12}$ for $Q_e>0$ ($Q_e<0$). Bottom: Same as in the top panel, with the additional constraint from the KTeV experiment derived in our work. The KTeV bound is derived employing the axion mixing with $\eta_{ud}$ and $\eta_{s}$ at the leading order in the chiral Lagrangian. The hatched region above the black solid line is excluded by the KTeV result. The gray contour indicates the upper limit from the electron anomalous magnetic moment for $Q_e>0$, obtained by requiring $|\Delta a_e|<10^{-12}$. Three benchmark points $(m_a, Q_e)$ adopted in our analysis are highlighted by black crosses.
• Figure 2: The function $f(m_a)$ encoding the $m_a$ dependence in ${\rm Br}(K_L \to \pi^0 \pi^0 a)$ given in eq. \ref{['eq:BR_KLpi0pi0a']}.
• Figure 3: Schematic pictures of the KTeV detector: (a) the $K_L$ beam line with related detectors and (b) the CsI calorimeter view. These figures are taken from ref. KTeV:2008nqz.
• Figure 4: The momentum distribution of the incoming $K_L$ flux at the KTeV experiment. The blue curve corresponds to a smooth fit to the $K_L$ momentum spectrum adopted in the KTeV analysis KTeV:2008nqz. The histogram shows the momentum distribution of $K_L$ mesons that decay within the fiducial region $121~\mathrm{m} \le z \le 158~\mathrm{m}$.
• Figure 5: Decay-vertex distribution of reconstructed $K_L$ decays within the fiducial volume $95~\mathrm{m} \le z \le 158~\mathrm{m}$. A sharp turn-on is visible near $z \simeq 121~\mathrm{m}$. This plot is taken from ref. KTeV:2008nqz.