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Two of the elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix, $|V_{ub}|$ and $|V_{cb}|$, are extracted from semileptonic B decays. The results of the B factories, analysed in the light of the most recent theoretical calculations, remain puzzling, because for both $|V_{ub}|$ and $|V_{cb}|$ the exclusive and inclusive determinations are in clear tension. Further, measurements in the $tau$ channels at Belle, Babar, and LHCb show discrepancies with the Standard Model predictions, pointing to a possible violation of lepton flavor universality. LHCb and Belle II have the potential to resolve these issues in the next few years. This article summarizes the discussions and results obtained at the MITP workshop held on April 9--13, 2018, in Mainz, Germany, with the goal to develop a medium-term strategy of analyses and calculations aimed at solving the puzzles. Lattice and continuum theorists working together with experimentalists have discussed how to reshape the semileptonic analyses in view of the much higher luminosity expected at Belle II, searching for ways to systematically validate the theoretical predictions in both exclusive and inclusive B decays, and to exploit the rich possibilities at LHCb.
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We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlins representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the $mathcal{O}(G_Falpha)$ radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and $J^P=0^+$ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.
We study the exclusive semileptonic $B$-meson decays $Bto K(pi)ell^+ell^-$, $Bto K(pi) ubar u$, and $Btopitau u$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ outside the charmonium resonance region are 1-2$sigma$ higher than the LHCb Collaborations recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7$sigma$. Combining the Standard-Model rates with LHCbs measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|=7.45{(69)}times10^{-3}$, $|V_{ts}|=35.7(1.5)times10^{-3}$, and $|V_{td}/V_{ts}|=0.201{(20)}$, which are compatible with the values obtained from neutral $B_{(s)}$-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients ${rm Re}(C_9)$ and ${rm Re}(C_{10})$ from $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ are competitive with those from $Bto K^* mu^+mu^-$, and display a 2.0$sigma$ tension with the Standard Model. Our predictions for $Bto K(pi) ubar u$ and $Btopitau u$ are close to the current experimental limits.
Inclusive semileptonic decays of beauty baryons are studied using the heavy quark expansion to ${cal O}(1/m_b^3)$, at leading order in $alpha_s$. The case of a polarized decaying baryon is examined, with reference to $Lambda_b$. An extension of the Standard Model effective Hamiltonian inducing $b to U ell {bar u}_ ell$ transitions ($U=u,,c$ and $ell=e,,mu,,tau$) is considered, which comprises the full set of D=6 semileptonic operators with left-handed neutrinos. The effects of the new operators in several observables are described.
We discuss a method to construct observables protected against QCD uncertainties based on the angular distribution of the exclusive Bd -> K(*0}(-> Kpi) l+ l- decay. We focus on the identification and the interpretation of all the symmetries of the distribution. They constitute a key ingredient to construct a set of so-called transverse observables. We work in the framework of QCD factorization at NLO supplemented by an estimate of power-suppressed Lambda/mb corrections. A discussion of the new physics properties of two of the transverse asymmetries, AT^{(2)} and AT^{(5)}, is presented. A comparison between the transverse asymmetry AT^{(2)} and the forward-backward asymmetry shows that AT^{(2)} emerges as an improved version of it.
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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