Testing lepton flavour universality in semileptonic $\Lambda_b \to \Lambda_c^*$ decays

TL;DR

This paper develops theoretical tools and projections for measuring lepton flavor universality in $ ext{Lambda}_b o ext{Lambda}_c^*$ decays, aiding the investigation of anomalies similar to those in $R_{D^{(*)}}$.

Contribution

It provides the first comprehensive theoretical framework for $R_{ ext{Lambda}_c^*}$ measurements, including form factor expressions and sensitivity analysis for future LHCb data.

Findings

Explicit form factor expressions to order $oldsymbol{ ext{alpha}_s}$ and $oldsymbol{1/m}$.

Sensitivity analysis for upcoming LHCb datasets.

Projections for the uncertainty in $R_{ ext{Lambda}_c^*}$ measurements.

Abstract

Lepton Flavour Universality tests with semileptonic $\Lambda_b\to\Lambda_c^*$ decays are important to corroborate the present anomalies in the similar ratios $R_{D^{(*)}}$, and can provide complementary constraints on possible origins of these anomalies beyond the Standard Model. In this paper we provide - for the first time - all the necessary theoretical ingredients to perform and interpret measurements of $R_{\Lambda_c^*}$ at the LHCb experiment. For this, we revisit the heavy-quark expansion of the relevant hadronic matrix elements, and provide their expressions to order $\alpha_s$ and $1/m$ accuracy. Moreover, we study the sensitivity to the form factor parameters given the projected size and purity of upcoming and future LHCb datasets of $\Lambda_b\to \Lambda_c^*\mu\bar{\nu}$ decays. We demonstrate explicitly the need to perform a simultaneous fit to both $\Lambda_c^*$ final states. Finally, we provide projections for the uncertainty of $R_{\Lambda_c^*}$ based on the form factor analysis from semimuonic decays and theoretical relations based on the heavy-quark expansion.