Tests of Lepton Flavour Universality with Semileptonic Decays at LHCb

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