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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 ofthese anomalies beyond the Standard Model. In this paper we provide - for thefirst time - all the necessary theoretical ingredients to perform and interpretmeasurements of $R_{\Lambda_c^*}$ at the LHCb experiment. For this, we revisitthe heavy-quark expansion of the relevant hadronic matrix elements, and providetheir expressions to order $\alpha_s$ and $1/m$ accuracy. Moreover, we studythe sensitivity to the form factor parameters given the projected size andpurity of upcoming and future LHCb datasets of $\Lambda_b\to\Lambda_c^*\mu\bar{\nu}$ decays. We demonstrate explicitly the need to performa simultaneous fit to both $\Lambda_c^*$ final states. Finally, we provideprojections for the uncertainty of $R_{\Lambda_c^*}$ based on the form factoranalysis from semimuonic decays and theoretical relations based on theheavy-quark expansion.

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