Tests of the Standard Model in $B \to D\ell \nu_\ell$, $B \to D^* \ell \nu_\ell$ and $B_c \to J/\psi \, \ell \nu_\ell$

TL;DR

This paper investigates lepton universality in semileptonic B meson decays by analyzing differential decay rates and proposing methods to test the Standard Model's predictions independent of lepton mass effects.

Contribution

It introduces a technique to extract lepton-universality ratios from decay rates that are independent of lepton mass, enabling more robust tests even with limited data.

Findings

Ratios of helicity amplitude combinations equal unity in the Standard Model.

Method allows testing lepton universality with sparse data.

Provides a framework for analyzing differential decay rates.

Abstract

A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell \nu_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several such processes, and show how to extract combinations of the underlying helicity amplitudes that are completely independent of $m_\ell$. Ratios of these combinations for different $\ell$ (as well as some combinations for a single value of $\ell$) therefore equal unity in the Standard Model and provide stringent tests of lepton universality. Furthermore, the extractions assume the form of weighted integrals over the differential decay rates and therefore are useful even in situations where data in some regions of allowed phase space may be sparse.