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Register a new userSoft contribution to $Bto gamma ell u_ell$ and the $B$-meson distribution amplitude
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The $Bto gamma ell u_ell$ decay at large energies of the photon receives a numerically important soft-overlap contribution which is formally of the next-to-leading order in the expansion in the inverse photon energy. We point out that this contribution can be calculated within the framework of heavy-quark expansion and soft-collinear effective theory, making use of dispersion relations and quark-hadron duality. The soft-overlap contribution is obtained in a full analogy with the similar contribution to the $gamma^* gamma to pi$ transition form factor. This result strengthens the case for using the $Bto gamma ell u_ell$ decay to constrain the $B$-meson distribution amplitude and determine its most important parameter, the inverse moment $lambda_B$.
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We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $Bto K^{(*)} ell^+ell^-$ decays. At the lepton-pair invariant masses far below the $bar{c}c$-threshold, $q^2ll 4m_c^2$, we use OPE near the light-cone. The nonfactorizable soft-gluon emission from $c$-quarks is cast in the form of a nonlocal effective operator. The $Bto K^{(*)}$ matrix elements of this operator are calculated from the QCD light-cone sum rules with the $B$-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to $Bto K^*gamma$ beyond the local-operator approximation. To describe the charm-loop effect at large $q^2$, we employ the hadronic dispersion relation with $psi=J/psi,psi (2S), ...$ contributions, where the measured $ Bto K^{(*)}psi $ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the $J/psi$ and $psi(2S)$ contributions. The resulting charm-loop effect is represented as a $q^2$-dependent correction $Delta C_9(q^2)$ to the Wilson coefficient $C_9$. Within uncertainties of our calculation, at $q^2$ below the charmonium region the predicted ratio $Delta C_9(q^2)/C_9$ is $leq 5% $ for $Bto K ell^+ell^-$, but can reach as much as 20% for $Bto K^*ell^+ell^-$, the difference being mainly caused by the soft-gluon contribution.
We reconsider the QCD predictions for the radiative decay $Bto gamma ell u_ell$ with an energetic photon in the final state by taking into account the $1/E_gamma, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $phi_+(omega)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of $phi_+(omega)$, including the first inverse moment, $1/lambda_B$, from the expected high-statistics data of the BELLE II experiment.
Besides being important to determine Standard Model parameters such as the CKM matrix elements $|V_{cb}|$ and $|V_{ub}|$, semileptonic $B$ decays seem also promising to reveal new physics (NP) phenomena, in particular in connection with the possibility of uncovering lepton flavour universality (LFU) violating effects. In this view, it could be natural to connect the tensions in the inclusive versus exclusive determinations of $|V_{cb}|$ to the anomalies in the ratios $R(D^{(*)})$ of decay rates into $tau$ vs $mu, e$. However, the question has been raised about the role of the parametrization of the hadronic $B to D^{(*)}$ form factors in exclusive $B$ decay modes. We focus on the fully differential angular distributions of $bar B to D^* ell^-{bar u}_ell$ with $D^* to D pi$ or $D^* to D gamma$, the latter mode being important in the case of $B_s to D_s^*$ decays. We show that the angular coefficients in the distributions can be used to scrutinize the role of the form factor parametrization and to pin down deviations from SM. As an example of a NP scenario, we include a tensor operator in the $b to c$ semileptonic effective Hamiltonian, and discuss how the angular coefficients allow to construct observables sensitive to this structure, also defining ratios useful to test LFU.
After improving the knowledge about residua of the semileptonic form factor at its first two poles we show that $f_+^{Dpi}(q^2)$ is not saturated when compared with the experimental data. To fill the difference we approximate the rest of discontinuity by an effective pole and show that the data can be described very well with the position of the effective pole larger than the next excitation in the spectrum of $D^ast$ state. The results of fits with experimental data also suggest the validity of superconvergence which in the pole models translates to a vanishing of the sum of residua of the form factor at all poles. A similar discussion in the case of $Bto pi ell u_ell$ leads to the possibility of extracting $vert V_{ub}vert$, the error of which appears to be dominated by $g_{B^ast Bpi}$, which can be nowadays computed on the lattice. In evaluating the residua of the form factors at their nearest pole we needed the vector meson decay constants $f_{D^ast}$ and $f_{B^ast}$, which we computed by using the numerical simulations of QCD on the lattice with $N_{rm f}=2$ dynamical quarks. We obtain, $f_{D^ast}/f_D=1.208(27)$ and $f_{B^ast}/f_B=1.051(17)$.
In this article, we perform a sensitivity study of an un-binned angular analysis of the $Bto D^*ell u_ell$ decay, including the contributions from the right-handed current. We show that the angular observable can constrain very strongly the right-handed current without the intervention of the yet unsolved $V_{cb}$ puzzle.
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