Leptophobic dark photon interpretation of the ${\eta }^{\left(\prime \right)}\to {\pi }^0\left(\eta \right)\gamma \gamma$ puzzle

Abstract

The decays of $\eta$ and ${\eta }^{\prime }$ mesons provide unique opportunities for testing the properties of low energy Quantum Chromodynamics and for the search of new physics beyond the Standard Model. However, recent experimental results on the rare decays of ${\eta }^{\left(\prime \right)}\to {\pi }^0\left(\eta \right)\gamma \gamma$ cannot be self-consistently described by the combination of the Vector Meson Dominance and Linear Sigma Model employing the same set of parameters. We show that this tension can be attributed to the presence of a leptophobic dark photon $\mathcal{B}$, and find representative values of the parameters which provide consistent description of these three decays, simultaneously. Unlike existing strategies of Dalitz analysis searching for the bump at $m_{\mathcal{B}}$, we propose the usage of mismatch between these decays to constrain the parameters of the hypothetical dark photon.

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