Pseudoscalar meson $P\to \tau (\to \pi \nu_\tau, \rho \nu_\tau, \ell \bar{\nu}_\ell \nu_\tau) \bar{\nu}_\tau$ decays in the Standard Model and beyond

TL;DR

This paper provides a comprehensive theoretical analysis of pseudoscalar meson decays involving tau leptons, incorporating new physics effects within an effective field theory framework, and introduces methods to extract new physics couplings from energy distributions.

Contribution

It offers model-independent predictions for decay rates, develops a novel approach to determine new physics couplings, and identifies invariant fixed points in energy distributions.

Findings

Precise Standard Model predictions for differential decay rates.

A robust methodology for extracting new physics couplings from energy moments.

Identification of fixed points invariant under new physics contributions.

Abstract

In this work, we have conducted a comprehensive and systematic theoretical investigation of the full cascade decays of charged pseudoscalar mesons, specifically $D_s$, $D$, $B$, and $B_c$, into $\tau \nu_\tau$, followed by the subsequent decay of the $\tau$ via its dominant experimentally reconstructible channels: $\tau \to \pi \nu_\tau$, $\tau \to \rho \nu_\tau$, $\tau \to e \bar\nu_e \nu_\tau$, and $\tau \to \mu \bar\nu_\mu \nu_\tau$. Our study is framed within the model-independent low-energy effective field theory approach, which incorporates the most general set of four-fermion operators, including those coupling to right-handed neutrinos. We provide precise Standard Model predictions for differential decay rate as a function of the final-state charged particle energy, develop an innovative and robust methodology for extracting the magnitudes of the new physics couplings using energy moments, and identify and characterize fixed points in the normalized energy distributions. The fixed points are invariant under new physics contributions described by the considered effective Hamiltonian.