Form-factor-independent test of lepton universality in semileptonic heavy meson and baryon decays

TL;DR

This paper proposes a form-factor-independent method to test lepton universality in semileptonic heavy meson and baryon decays by analyzing the convexity parameter, which isolates lepton-mass effects and identifies potential New Physics deviations.

Contribution

It introduces a novel approach using the convexity parameter to test lepton universality independently of form factors in heavy hadron decays.

Findings

The method isolates lepton-mass effects in decay distributions.

Standard Model predicts equal optimized partial rates for all leptons.

Deviations from equality indicate possible New Physics effects.

Abstract

In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic $\cos^2\theta$ coefficient of the differential $\cos\theta$ distribution. We call the corresponding normalized coefficient the convexity parameter. This observation opens the path to a test of lepton universality in semileptonic heavy meson and baryon decays that is independent of form-factor effects. By projecting out the quadratic rate coefficient, dividing out the lepton-mass-dependent factor and restricting the phase space integration to the $\tau$ lepton phase space, one can define optimized partial rates which, in the Standard Model, are the same for all three $(e,\mu,\tau)$ modes in a given semileptonic decay process. We discuss how the identity is spoiled by New Physics effects. We discuss semileptonic heavy meson decays such as $\bar{B}^0 \to D^{(\ast)+} \ell^- \bar\nu_\ell$ and $B_c^- \to J/\psi (\eta_c)\ell^- \bar\nu_\ell$, and semileptonic heavy baryon decays such as $\Lambda_b \to \Lambda_c \ell^- \bar\nu_\ell$ for each $\ell=e,\mu,\tau$.