B → Dℓνℓ form factors beyond leading power and extraction of |Vcb| and R(D)

Abstract

We investigate the subleading-power corrections to the exclusive B → Dℓνℓ form factors at $$ \mathcal{O} $$ O ($$ {\alpha}_s^0 $$ α s 0 ) in the light-cone sum rules (LCSR) framework by including the two- and three-particle higher-twist contributions from the B-meson light-cone distribution amplitudes up to the twist-six accuracy, by taking into account the subleading terms in expanding the hard-collinear charm-quark propagator, and by evaluating the hadronic matrix element of the subleading effective current "Image missing". Employing further the available leading-power results for the semileptonic B → D form factors at the next-to- leading-logarithmic level and combining our improved LCSR predictions with the recent lattice determinations, we then carry out a comprehensive phenomenological analysis on the semi-leptonic B → Dℓνℓ decay. We extract $$ \left|{V}_{cb}\right|=\left({40.2}_{-0.5}^{+0.6}{\left|{{}_{\mathrm{th}}}_{-1.4}^{+1.4}\right|}_{\mathrm{exp}}\right)\times {10}^{-3}\left(\left|{V}_{cb}\right|=\left({40.9}_{-0.5}^{+0.6}{\left|{{}_{\mathrm{th}}}_{-1.0}^{+1.0}\right|}_{\mathrm{exp}}\right)\times {10}^{-3}\right) $$ V cb = 40.2 − 0.5 + 0.6 th − 1.4 + 1.4 exp × 10 − 3 V cb = 40.9 − 0.5 + 0.6 th − 1.0 + 1.0 exp × 10 − 3 using the BaBar (Belle) experimental data, and particularly obtain for the gold-plated ratio R(D) = 0.302 ± 0.003.

Light-cone Sum Rule Analysis of Semileptonic Decays $Λ_b^0 \to Λ_c^+ \ell^- \overlineν_\ell$

“…Similar to the lightcone sum rule analysis of B → D ( * ) transition form factors, the correlation function is expanded near the light-cone with the finite charm quark mass, and the light-cone dominance region of the momentum of final charm baryon p and momentum transfer q. With the same discussion in reference [20] and the applications in references [21][22][23][24][25], the light-cone sum rule is convinced fulfilled in this work. This approach introduces the light-cone distribution amplitudes with increasing twists in the operator product expansion of SVZ QCD sum rules to substitute the vacuum condensate operator with increasing dimensions, which gives an easy way to calculate the three-point correlation function in the QCD sum rule method.…”

Precision calculations of Bd,s → π, K decay form factors in soft-collinear effective theory

“…An attractive advantage of this alternative version of QCD sum rules on the light-cone consists in the very appearance of the universal B-meson distribution amplitudes in heavy quark effective theory (HQET) for the obtained expressions of all the bottom-meson decay form factors, independent of the particular light-hadron in the final states. Along the same vein, both the higher-order perturbative corrections and the subleading-power contributions to the heavy-to-light B-meson decay form factors [33][34][35][36][37][38], the heavy-to-heavy B-meson decay form factors [36,39,40], as well as the semileptonic heavy-baryon decay form factors [41][42][43] have been computed from the LCSR method with the heavy-hadron distribution amplitudes.…”

Deciphering the long-distance penguin contribution to $\bar B_{d, s} \to γγ$ decays

“…at the reference scale µ 0 = 1.0 GeV, motivated from the suggested three-parameter ansatz for the twist-two distribution amplitude φ + B (ω, µ 0 ) [56]. The remaining shape parameters ω 0 , α and β can be further determined by enforcing the first and second normalization relations in (13) and employing the concrete model of the twist-four and twist-five light-cone distribution amplitudes Φ 4, 5 (ω 1 , ω 2 , µ 0 ) as implemented in [34]. The conventional HQET distribution amplitudes on the lightcone appearing in the established factorization formulae of the helicity form factors F (p) i,L(R) from [3] will be also in demand in the subsequent numerical investigations, and we will apply the same phenomenological model as presented in this reference, with the exceptions of updated intervals for the inverse moments λ B d = (275 ± 75) MeV and λ Bs = (325 ± 75) MeV [57] (see [55] for a recent determination of λ Bs /λ B d with the method of QCD sum rules).…”

“…According to the numerical hierarchy between the bottom and charm quark masses, we will apply the favored power counting scheme [12,[31][32][33][34] in establishing the perturbative factorization formulae for the penguin contractions of the effective four-quark operators accompanied by the soft gluon emission, instead of the alternative counting scheme m b ∼ m c Λ implemented in the exclusive two-body B-meson decays [35,36]. Subsequently, we will report on a novel observation on the very hadronic matrix element responsible for the soft gluon radiation off the penguin diagrams.…”