$\eta$ and $\eta'$ decays into lepton pairs

TL;DR

This paper calculates the decay rates of eta and eta' mesons into lepton pairs within the Standard Model, using Canterbury approximants to improve theoretical predictions and explore potential signs of new physics.

Contribution

It introduces a data-driven method using Canterbury approximants to reliably compute decay amplitudes, addressing discrepancies and the role of resonances in eta and eta' decays.

Findings

Calculated branching ratios for eta and eta' decays into leptons.

Analyzed the impact of resonant regions on decay predictions.

Discussed potential new physics explanations for experimental discrepancies.

Abstract

In this work, we calculate the branching ratios for the $\eta(\eta')\rightarrow\bar{\ell}\ell$ decays, where $\ell = e,\mu$. These processes have tiny rates in the standard model due to spin flip, loop, and electromagnetic suppression, for what they could be sensitive to New Physics effects. In order to provide a reliable input for the Standard Model, we exploit the general analytical properties of the amplitude. For that purpose, we invoke the machinery of Canterbury approximants, which provides a systematic description of the underlying hadronic physics in a data-driven fashion. Given the current experimental discrepancies, we discuss in detail the role of the resonant region and comment on the reliability of $\chi$PT calculations. Finally, we discuss the kind of new physics which we think would be relevant to account for them.