Pseudoscalar decays into lepton pairs from rational approximants

TL;DR

This paper introduces a model-independent method using Canterbury approximants to analyze pseudoscalar decays into lepton pairs, revealing larger uncertainties and challenging existing experimental discrepancies, with implications for fundamental physics.

Contribution

It applies Canterbury approximants to pseudoscalar decay form factors, providing a systematic, model-independent framework that incorporates data and theoretical constraints, improving uncertainty estimates.

Findings

Previous estimates underestimated uncertainties.

Experimental discrepancies cannot be explained by current form factor models.

Implications for lepton magnetic moments and new physics.

Abstract

The pseudoscalar decays into lepton pairs $P\rightarrow\overline{\ell}\ell$ are analyzed with the machinery of Canterbury approximants, an extension of Pad\'e approximants to bivariate functions. This framework provides an ideal model-independent approach to implement all our knowledge of the pseudoscalar transition form factors driving these decays, can be used for data analysis, and allows to include experimental data and theoretical constraints in an easy way, and determine a systematic error. We find that previous theoretical estimates for these branching ratios have underestimated their theoretical uncertainties. From our updated results, the existing experimental discrepancies for $\pi^0\rightarrow e^+e^-$ and $\eta\rightarrow \mu^+\mu^-$ channels cannot be explained unless the doubly-virtual transition form factors behavior -not yet measured- are out of theoretical expectations, which is an interesting result both for anomalous magnetic moments of leptons, and for physics beyond the standard model.