Heavy-Quark expansion for $${{\bar{B}}_s\rightarrow D^{(*)}_s}$$ form factors and unitarity bounds beyond the $${SU(3)_F}$$ limit

Abstract

We carry out a comprehensive analysis of the full set ofBq → D ( * ) q form factors for spectator quarks q = u, d, s within the framework of the Heavy-Quark Expansion (HQE) to order O αs, 1/m b , 1/m 2 c . In addition to the available lattice QCD calculations we make use of two new sets of theoretical constraints: we produce for the first time numerical predictions for the full set ofBs → D ( * ) s form factors using Light-Cone Sum Rules with Bs-meson distribution amplitudes. Furthermore, we reassess the QCD three-point sum rule results for the Isgur-Wise functions entering all our form factors for both q = u, d and q = s spectator quarks. These additional constraints allow us to go beyond the commonly used assumption of SU (3)F symmetry for theBs → D ( * ) s form factors, especially in the unitarity constraints which we impose throughout our analysis. We find the coefficients of the IW functions emerging at O 1/m 2 c to be consistent with the naive O (1) expectation, indicating a good convergence of the HQE. While we do not find significant SU (3) breaking, the explicit treatment of q = s as compared to a simple symmetry assumption renders the unitarity constraints more effective. We find that the (pseudo)scalar bounds are saturated to a large degree, which affects our theory predictions. We analyze the phenomenological consequences of our improved form factors by extracting |V cb | fromB → D ( * ) ν decays and producing theoretical predictions for the lepton-flavour universality ratios R(D), R(D * ), R(Ds) and R(D * s ), as well as the τ -and D * q polarization fractions for theBq → D ( * ) q τ ν modes.

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

“…Results from [34] improve on the uncertainties obtained in [33] with NRQCD b quarks and this promising all-HISQ approach is now being extended to other processes. It is interesting to observe that the B s → D s form factors are very close to the B → D form factors over the entire kinematic range, see also [35,36].…”

“…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].…”

A puzzle in $$\varvec{\bar{B}_{(s)}^0 \rightarrow D_{(s)}^{(*)+} \lbrace \pi ^-, K^-\rbrace }$$ decays and extraction of the $$\varvec{f_s/f_d}$$ fragmentation fraction

“…First, we revisit the QCD factorization framework for the non-leptonic decaysB 0 → D ( * )+ K − andB 0 s → D ( * )+ s π − beyond leading power. We update the values of theB q → D ( * ) q form factors based on a recent analysis within the heavy-quark expansion (HQE) [3]. We also provide, for the first time, conservative numerical estimates for the necessary hadronic matrix elements that enter at next-to-leading-power in QCD /m b .…”

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%.…”