The most recent measurements of the observables $R_{ D^{ (*)}}$ are in tension with the Standard Model offering hints of New Physics in $b\rightarrow c \ell \bar{ \nu}_{ \ell}$ transitions. Motivated by these results, in this work we present an analysis on their $b\rightarrow u \ell \bar{ \nu}_{ \ell}$ counterparts (for $\ell=e, ~\mu, ~\tau$). Our study has three main objectives. Firstly, using ratios of branching fractions, we assess the effects of beyond the Standard Model scalar and pseudoscalar particles in leptonic and semileptonic $B$ decays ($B^-\rightarrow \ell^- \bar{ \nu}_{ \ell}$, $\bar{ B}\rightarrow \pi \ell \bar{ \nu}_{ \ell}$ and $\bar{ B}\rightarrow \rho \ell \bar{ \nu}_{ \ell}$). Here a key role is played by the leptonic $B$ processes, which are highly sensitive to new pseudoscalar interactions. In particular, we take advantage of the most recent measurement of the branching fraction of the channel $B^-\rightarrow \mu^-\bar{ \nu}_{ \mu}$ by the Belle collaboration. Secondly, we extract the CKM matrix element $|V_{ ub}|$ while accounting simultaneously for New Physics contributions. Finally, we provide predictions for the branching fractions of yet unmeasured leptonic and semileptonic $B$ decays.
Categories: hep-ph