Improved description of di-lepton production in \(\tau^-\to\nu_\tau P^-\) decays

• Published in: arXiv.org
• Main Authors: Guevara, Adolfo, Gabriel López Castro, Roig, Pablo
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.03.2022
• Subjects: Broken symmetry; Decay; Evaluation; Flavor (particle physics); Leptons; Mathematical analysis; Pions; Strangeness
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2111.09994

Recently, the Belle collaboration reported the first measurements of the \(\tau^- \to\nu_{\tau}\pi^-e^+e^-\) branching fraction and the spectrum of the pion-dielectron system. In an analysis previous to Belle's results, we evaluated this branching fraction which turned out to be compatible with that reported by Belle, although with a large uncertainty. This is the motivation to seek for improvements on our previous evaluation of \(\tau^- \to \nu_{\tau}\pi^-\ell^+\ell^-\) decays (\(\ell=e,\,\mu\)). In this paper we improve our calculation of the \(WP^-\gamma^*\) vertex by including flavour symmetry breaking effects in the framework of the Resonance Chiral Theory. We impose QCD short-distance behaviour to constrain most parameters and data on the \(\pi^-e^+e^-\) spectrum reported by Belle to fix the remaining free ones. As a result, improved predictions for the branching ratios and hadronic/leptonic spectra are reported, in good agreement with observations. Analogous calculations for the strangeness-changing \(\tau^- \to \nu_{\tau}K^-\ell^+\ell^-\) transitions are reported for the first time. Albeit one expects the \(m_{\pi\mu^+\mu^-}\) spectrum to be measured in Belle-II and the observables with \(\ell=e\) can be improved, it is rather unlikely that the \(K\) channels can be measured due to the suppression factor \(|V_{ud}/V_{us}|^2=0.05\).