Tests of lepton flavour universality with semileptonic decays at LHCb

The observable $\mathcal{R} \left( D^{(*)} \right) = \mathcal{B}\left( B^{0}\to D^{(*)-} \tau^{+} \nu_{\tau} \right) / \mathcal{B}\left( B^{0}\to D^{(*)-} \mu^{+} \nu_{\mu} \right)$ is a probe for Lepton Universality violation, so it is sensitive to New Physics processes. The current combination of the measurements of $\mathcal{R} \left( D^{(*)} \right)$ differs from Standard Model predictions with a $4\sigma$ significance. A measurement of $\mathcal{R} ( D^* )$ using three-prong $\tau$ decays has been performed at LHCb, resulting in $\mathcal{R}(D^*) = 0.285 \pm 0.019 (\text{stat}) \pm 0.025(\text{syst}) \pm 0.014 (\text{ext})$. This value, combined with the LHCb result obtained with $\tau \to \mu \nu_\tau \bar{\nu}_\mu$ decays, gives ${\mathcal{R}}(D^*) = 0.306 \pm 0.016 (\text{stat}) \pm 0.022 (\text{syst})$, consistent with the world average and 2.1 standard deviations above the SM prediction.