This web page contains the averages of the ratios of Branching Fractions
R(D*)=BF(B→D*τν_{τ})/BF(B→D* l ν_{l})
and R(D)=BF(B→Dτν_{τ})/BF(B→D l ν_{l}).
In the present average we consider the following measurements:
Experiment | R(D*) | R(D) | Rescaled Correlation (stat/syst/total) | Inputs | Remarks |
---|---|---|---|---|---|
BaBar | 0.332 ± 0.024 ± 0.018 | 0.440 ± 0.058 ± 0.042 | -0.45/-0.07/-0.27 | input | Phys.Rev.Lett. 109,101802 (2012) arXiv:1205.5442_[hep-ex] Phys.Rev.D 88, 072012 (2013) arXiv:1303.0571_[hep-ex] |
BELLE^{a} | 0.293 ± 0.038 ± 0.015 | 0.375 ± 0.064 ± 0.026 | -0.56/-0.11/-0.49 | input | Phys.Rev.D 92, 072014 (2015) arXiv:1507.03233 [hep-ex] |
BELLE^{b} | 0.270 ± 0.035 ^{+ 0.028}_{-0.025} | - | - | input | Phys.Rev.Lett.118,211801 (2017) arXiv:1612.00529 [hep-ex] Phys.Rev.D 97, 012004 (2018) arXiv:1709.00129_[hep-ex] |
BELLE^{c} | 0.283 ± 0.018 ± 0.014 | 0.307 ± 0.037 ± 0.016 | -0.53/-0.51/-0.51 | input | Phys.Rev.Lett. 124 (2020) 16, 161803 arXiv:1910.05864 [hep-ex] |
LHCb^{a} | 0.281 ± 0.018 ± 0.024 | 0.441 ± 0.060 ± 0.066 | -0.49/-0.39/-0.43 | input | Accepted by PRL [arXiv:2302.02886] |
LHCb^{b} | 0.257 ± 0.012 ± 0.018 | - | - | input | Accepted by PRD [arXiv:2305.01463] |
Belle II | 0.267 (^{+0.041} _{-0.039}) (^{+0.028} _{-0.033}) | - | - | input | Presented at Lepton Photon 2023 Lepton Photon's talk |
Average .txt | 0.284 ± 0.012 | 0.357 ± 0.029 | -0.40 | chi2/dof = 10.3/9 (CL = 0.33) |
R(D)-R(D*), Δχ^{2}=1 contours rdrds.pdf
(dashed curves correspond to 3 σ contour)
R(D)-R(D*), 68% C.L. contours rdrds.pdf
R(D) .pdf (with the SM predictions) R(D) .pdf R(D*) .pdf (with the SM predictions) R(D*) .pdf |
SM predictions for R(D) based on following Lattice calculations:
The SM prediction for R(D^{*}) widely used in previous HFLAV averages was:
The BaBar collaboration computed an indipendent prediction of R(D^{*})=0.253 ± 0.005, from a full angular analysis of B→D^{*}l ν Phys.Rev.Lett. 123 (2019) 9, 091801.
In 2021 FNAL/MILC released the first unquenched Lattice calculation of B→D^{*}l ν form factors at non-zero recoil, A.Bazavov et al. [Eur. Phys. J. C 82, 1141 (2022)] , predicting a value of R(D^{*})=0.265 ± 0.013, using only Lattice inputs. An indipendent analysis of the FNAL/MILC lattice data, performed by G. Martinelli et al. [Eur. Phys. J. C 82, 1083 (2022)], results in R(D^{*})=0.275 ± 0.008. Recently two new indipendent lattice calculations at non-zero recoil, from HPQCD arXiv:2304.03137[hep-lat] and JLQCD harXiv:2306.05657[hep-lat] have been released. The results are reported in the table below.
A combined fit of the lattice calculations for both B→Dl ν and B→D^{*}l ν has been recently released by I.Ray and S.Nandi arXiv:2305.11855[hep-ph]. The predicted values for the ratios are R(D)=0.304(3) and R(D^{*})=0.258(0.012). In this paper also inputs from LCSR (N.Gubernari, A.Kokulu, D.van Dyk, JHEP 01, 150 (2019)) and measurements of the differential distributions are considered. As expected this fit configuration gives a considerably smaller uncertainty for R(^{*}); the results are R(D)=0.300(3) and R(D^{*})=0.251(1). In the table below only the results based on Lattice calculations are reported.
These new calculations are in good agreement between each other, and consistent with
old predictions for R(D^{*}). But there are inconsistencies on the shape of some of the form factors for B→D^{*}l ν. More studies are required to
clarify the origin of the discrepancies.
Critical analyses of the various calculations and experimental inputs for both B→Dl ν and B→D^{*}l ν, as perfomed by I.Ray and S.Nandi, would be desirable.
R(D) | R(D^{*}) | |
---|---|---|
D.Bigi, P.Gambino, Phys.Rev. D94 (2016) no.9, 094008 [arXiv:1606.08030 [hep-ph]] | 0.299 ± 0.003 | |
P.Gambino, M.Jung, S.Schacht, Phys.Lett.B795 (2019) 386 [arXiv:1905.08209 [hep-ph]] | 0.254 + 0.007 − 0.006 | |
M.Bordone, M.Jung, Danny van Dyk, Eur.Phy.J.C 80 (2020) 2, 74 [arXiv:1908.09398 [hep-ph]] | 0.298 ± 0.003 | 0.247 ± 0.006 |
F.Bernlochner, Z.Ligeti, M.Papucci, D.Robinson, Phys.Rev. D95 (2017) no.11, 115008 [arXiv:1703.05330 [hep-ph]] | 0.299 ± 0.003 | 0.257 ± 0.003 |
S.Jaiswal, S.Nandi, S.K.Patra, JHEP 1712 (2017) 060 [arXiv:1707.09977 [hep-ph]] | 0.299 ± 0.004 | 0.257 ± 0.005 |
BaBar Collaboration, Phys.Rev.Lett. 123 (2019) 9, 091801 [arXiv:1903.10002 [hep-ex]] | 0.253 ± 0.005 | |
G. Martinelli, S. Simula, L. Vittorio, Phys.RevD 105 (2022) 3, 034503 [arXiv:2105.08674 [hep-ph]] | 0.296 ± 0.008 | |
Arithmetic average | 0.298 ± 0.004 | 0.254 ± 0.005 |
D.Bigi, P.Gambino, S.Schacht, JHEP 1711 (2017) 061 [arXiv:1707.09509 [hep-ph]] | 0.260 ± 0.008 | |
M.Bordone, M.Jung, Danny van Dyk, Eur.Phy.J.C 80 (2020) 2, 74 [arXiv:1908.09398 [hep-ph]] | 0.297 ± 0.003 | 0.250 ± 0.003 |
FNAL/MILC, A.Bazavov et al. Eur. Phys. J. C 82 (2022) 1141 [arXiv:2105.14019 [hep-lat]] | 0.265 ± 0.013 | |
G. Martinelli, S. Simula, L. Vittorio, Eur. Phys. J. C 82 (2022) 1083 [arXiv:2109.15248 [hep-ph]] | 0.275 ± 0.008 | |
HPQCD, J.Harrison, C.Davies, [arXiv:2304.03137 [hep-lat]] | 0.279 ± 0.013 | |
JLQCD, Y.Aoki et al. [arXiv:2306.05657 [hep-lat]] | 0.252 ± 0.022 | |
I.Ray, S.Nandi [arXiv:2305.11855 [hep-lat]] | 0.304 ± 0.003 | 0.258 ± 0.012 |
R(D) and R(D^{*}) exceed the SM predictions given above, by 2.0σ and 2.2σ respectively.
Considering the R(D)-R(D^{*})) correlation of -0.40, the resulting combined χ^{2} is 14.2 for 2 degree of freedom,
corresponding to a p-value of 0.82 x 10^{-3}. The difference with the SM predictions reported above, corresponds to about 3.34σ.