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

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 $K_L \to π^0 π^0 (X\to e^+e^-)$ decays constrain the couplings of light $X$ bosons to light quarks to be as small as $\mathcal{O}(10^{-5})$. The charged-pion modes $K^+ \to π^+ π^0 (X \to e^+e^-)$ and $K_L \to π^+ π^- (X \to e^+e^-)$ 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 $K \to πXX$ 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.

Figures (7)

• Figure 1: Leading diagram for $K^+\to \pi^+ X_\mu$ and $K_S \to \pi^0 X_\mu$ decays.
• Figure 2: Leading diagrams for $K_L\to \pi^0 \pi^0 X_\mu$, $K^+\to \pi^+ \pi^0 X_\mu$, and $K_L \to \pi^+ \pi^- X_\mu$ decays. Emissions from a single pion line or from a three-pion vertex is only significant for modes with charged pions.
• Figure 3: Leading diagrams for $K^+\to \pi^+ \gamma X_\mu$. For $K \to \pi X_\mu X_\mu$ there are two additional possibilities by swapping the vector and $\Delta S =1$ vertices of the bottom diagrams.
• Figure 4: Limits derived from kaon decay data on promptly-decaying vector bosons $X$ as a function of $m_X$ and the effective coupling $g_{\rm eff}$. For all channels except $K^+ \to \pi^+ X$ and $K^+ \to \pi^+ \gamma X$, both proportional to $g_{K\pi^+}$ defined in \ref{['eq:g_kpi']}, we only take couplings proportional to contact diagrams to contribute such that a single combination factorizes to $g_{\rm eff}$; see Table \ref{['tab:constraints']}. For $K^+ \to \pi^0 \pi^+ X_{ee}$ decays (blue), the band envelops limits across two decay model assumptions: "IB" (solid) or "M" (dashed). For $K^+ \to \pi^+ X_{ee} X_{ee}$, there are no direct limits below $m_X = 10$ MeV due to the NA62 selection.
• Figure 5: The allowed regions in the 17 MeV spin-1 boson coupled to a vector (left) or axial-vector (right) current for $g_{s}^{V,A} = 0$, setting the electron coupling to saturate the lower bound from NA64 NA64:2019auh. The $90\%$ CL allowed regions for different kaon decay channels are shown in color, together with their overlap, which is highlighted by the inset axis. Constraints from pion decays are shown as dark grey bands. For SINDRUM, the two bands correspond to different sign choices for $g_e^{V}$ (left) or $g_e^{V}$ (right). The $2\sigma$ allowed regions for the $^4$He, $^8$Be, $^{12}$C ATOMKI anomalies are shown as light shaded grey (from BarducciErratum). The preference regions for $^{12}$C in the axial-vector case are beyond the axis boundaries Mommers:2024qzy.