Testing lepton flavour universality in semileptonic \(\Lambda_b \to \Lambda_c^\) decays

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.