Theory determination of $$\varvec{\bar{B}\rightarrow D^{(*)}\ell ^-\bar{\nu }}$$ form factors at $$\varvec{\mathcal {O}(1/m_c^2)}$$

Abstract

We carry out an analysis of the full set of ten B → D (*) form factors within the framework of the Heavy-Quark Expansion (HQE) to order O α s , 1/m b , 1/m 2 c , both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD lightcone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions inB → D (*) {e − , μ − }ν measurements. The coefficients entering at the 1/m 2 c level are found to be of O(1), indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of |V cb | in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios R D (*) , the τ polarization observables P D (*) τ , and the longitudinal polarization fraction F L. Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.

Challenges in semileptonic $${\varvec{B}}$$ decays

“…Indeed, based on that data set the central values for |V cb | varied by up to 6% between CLN and BGL fits [54,55,77]. By floating some additional parameters of the less flexible CLN parametrization, the agreement between BGL and CLN could be restored [54,76] [36,75,77,80,86]: varying the coefficients of the HQE consistently allows for a simultaneous description of the available experimental and lattice data in B → D, while the parametrization dependence in the extraction of V cb from Ref. [53] remains [75].…”

“…[53] remains [75]. Including additionally contributions at O(1/m 2 c ) and higher orders in the z expansion, the extracted values for V cb using the BGL parametrization and the HQE become compatible [80].…”

Standard-Model Prediction of εK with Manifest Quark-Mixing Unitarity

“…Moreover, the dominant perturbative uncertainty no longer originates from η ct but from the top-quark contribution, η tt . Note that using the exclusive determination jV cb;excl j ¼ 0.0403ð8Þ [21] and the lattice value κ ϵ ¼ 0.923ð6Þ [22] we find ϵ K ¼ 1.81ð14Þ × 10 −3 in tension with the experimental measurement [23]. Discussion and conclusions.-In this Letter, we showed that a manifest implementation of CKM unitarity in the effective jΔS ¼ 2j Hamiltonian dramatically improves the convergence behavior of the perturbative series for its imaginary part, by removing a spurious long-distance charm-quark contribution.…”

Implications for new physics from a novel puzzle in B¯(s)0→Iguro1, Kitahara2 2020Phys. Rev. D311240View full textAdd to dashboardCite

“…These SM predictions are obtained by the QCD factorization (QCDF) [3][4][5] at leading power in Λ QCD =m b , where the Wilson coefficients at next-to-nextto-leading logarithmic accuracy are used [6]. Compared to the previous estimations [7], the theoretical uncertainties are significantly reduced thanks to recent developments in theB ðsÞ → D ðÃÞ ðsÞ form factors including order Oð1=m 2 c Þ corrections within the framework of the heavy-quark expansion [8][9][10][11].…”

“…For jV cb j, the authors of Ref. [1] use an average of the inclusive and exclusive determinations in the B-meson semileptonic decays: jV cb j ¼ ð41.1 AE 0.5Þ × 10 −3 [9,10]. If one adopts the exclusive jV cb j, jV cb j ¼ ð39.25 AE 0.56Þ × 10 −3 [12], amplitudes of the above processes are uniformly reduced by 4.5%.…”