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Register a new user$Bto K^ast_2(1430)ell^+ell^-$ distributions in Standard Model at large recoil
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We study the rare decay $Bto K_2^ast(1430)(to Kpi)ell^+ell^-$ in the Standard Model and beyond. Working in the transversity basis, we exploit the relations between the heavy-to-light form factors in the limit of heavy quark ($m_bto infty$) and large energy ($E_{K_2^ast}to infty$) of the $K^ast_2$ meson. This allows us to construct observables where at leading order in $Lambda_{rm QCD}/m_b$ and $alpha_s$ the form factor dependence involving the $Bto K^ast_2$ transitions cancels. Higher order corrections are systematically incorporated in the numerical analysis. In the Standard Model the decay has a sizable branching ratio and therefore a large number of events can be expected at LHCb. Going beyond the Standard Model, we explore the implications of the global fit to presently available $bto sell^+ell^-$ data on the $Bto K_2^ast ell^+ell^-$ observables.
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We predict the amplitude of the $Bto K ell^+ell^-$ decay in the region of the dilepton invariant mass squared $0<q^2leq m_{J/psi}^2$, that is, at large hadronic recoil. The $Bto K$ form factors entering the factorizable part of the decay amplitude are obtained from QCD light-cone sum rules. The nonlocal effects, generated by the four-quark and penguin operators combined with the electromagnetic interaction, are calculated at $q^2<0$, far below the hadronic thresholds. For hard-gluon contributions we employ the QCD factorization approach. The soft-gluon nonfactorizable contributions are estimated from QCD light-cone sum rules. The result of the calculation is matched to the hadronic dispersion relation in the variable $q^2$, which is then continued to the kinematical region of the decay. The overall effect of nonlocal contributions in $Bto Kell^+ell^-$ at large hadronic recoil is moderate. The main uncertainty of the predicted $Bto K ell^+ell^-$ partial width is caused by the $Bto K$ form factors. Furthermore, the isospin asymmetry in this decay is expected to be very small. We investigate the deviation of the observables from the Standard Model predictions by introducing a generic new physics contribution to the effective Hamiltonian.
We calculate the amplitude of the rare flavour-changing neutral-current decay $Bto piell^+ell^-$ at large recoil of the pion. The nonlocal contributions in which the weak effective operators are combined with the electromagnetic lepton-pair emission are systematically taken into account. These amplitudes are calculated at off-shell values of the lepton-pair mass squared, $q^2<0$, employing the operator-product expansion, QCD factorization and light-cone sum rules. The results are fitted to hadronic dispersion relations in $q^2$, including the intermediate vector meson contributions. The dispersion relations are then used in the physical region $q^2>0$. Our main result is the process-dependent addition $Delta C^{(Bpi)}_9(q^2)$ to the Wilson coefficient $C_9$ obtained at $4m_ell^2<q^2lesssim m_{J/psi}^2$. Together with the $Bto pi$ form factors from light-cone sum rules, this quantity is used to predict the differential rate, direct CP-asymmetry and isospin asymmetry in $Bto piell^+ell^-$. We also estimate the total rate of the rare decay $Bto pi ubar{ u}$.
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 propose measurements of weighted differences of the angular observables in the rare decays $B to K^*ell^+ell^-$. The proposed observables are very sensitive to the difference between the Wilson coefficients $mathcal{C}_9^{(e)}$ and $mathcal{C}_9^{(mu)}$ for decays into electrons and muons, respectively. At the same time, the charm-induced hadronic contributions are kinematically suppressed to $lesssim 7% (4%)$ in the region $1,$GeV$^2 leq q^2 leq 6,$GeV$^2$, as long as LFU breaking occurs only in $mathcal{C}^{(ell)}_{9}$. This suppression becomes stronger for the region of low hadronic recoil, $q^2 geq 15,$GeV$^2$.
This article analyses the available inputs in $btopilnu$ and $btorholnu$ decays which include the measured values of differential rate in different $q^2$-bins (lepton invariant mass spectrum), lattice, and the newly available inputs on the relevant form-factors from the light-cone sum rules (LCSR) approach. We define different fit scenarios, and in each of these scenarios, we predict a few observables in the standard model (SM). For example, $R(M) =frac{mathcal{B}(B to Mell_i u_{ell_i})}{mathcal{B}(Bto Mell_j u_{ell_j})} $, $R^{ell_i}_{ell_j}(M) =frac{mathcal{B}(Bto ell_i u_{ell_i})}{mathcal{B}(B to Mell_j u_{ell_j})}$ with M = $pi$ or $rho$ and $ell_{i,j} = e, mu$ or $tau$. We also discuss the new physics (NP) sensitivities of all these observables and obtain bounds on a few NP Wilson coefficients in $bto u tau u_{tau}$ decays using the available data. We have noted that the data at present allows sizeable NP contributions in this mode. Also, we have predicted a few angular observables relevant to these decay modes.
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