We consider leptonic $B^-to ell^- bar u_ell$ and semileptonic $bar B to pi ell^- bar u_ell$, $bar B to rho ell^- bar u_ell$ decays and present a strategy to determine short-distance coefficients of New-Physics operators and the CKM element $|V_{ub}|$. As the leptonic channels play a central role, we illustrate this method for (pseudo)-scalar operators which may lift the helicity suppression of the corresponding transition amplitudes arising in the Standard Model. Utilising a new result by the Belle collaboration for the branching ratio of $B^-to mu^- bar u_mu$, we explore theoretically clean constraints and correlations between New Physics coefficients for leptonic final states with $mu$ and $tau$ leptons. In order to obtain stronger bounds and to extract $|V_{ub}|$, we employ semileptonic $bar B to pi ell^- bar u_ell$ and $bar B to rho ell^- bar u_ell$ decays as an additional ingredient, involving hadronic form factors which are determined through QCD sum rule and lattice calculations. In addition to a detailed analysis of the constraints on the New Physics contributions following from current data, we make predictions for yet unmeasured decay observables, compare them with experimental constraints and discuss the impact of CP-violating phases of the New-Physics coefficients.
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