Average of R(D) and R(D*) for 2021

This web page contains the averages of the ratios of Branching Fractions R(D*)=BF(B→D*τντ)/BF(B→D* l νl) and R(D)=BF(B→Dτντ)/BF(B→D l νl).
In the present average we consider the following measurements:


In the average we assume 100% correlation for the systematic uncertainties associated with the B→D(*) form factors, the D** composition and shapes, and the τ branching fractions. The other uncertainties are considered uncorrelated between the various experiments.


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 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]
LHCb 0.336 ± 0.027 ± 0.030 - - input Phys.Rev.Lett.115,111803 (2015) arXiv:1506.08614 [hep-ex]
BELLE 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]
LHCb 0.283 ± 0.019 ± 0.029 - - input Phys.Rev.Lett.120,171802 (2018) arXiv:1708.08856_[hep-ex] Phys.Rev.D 97, 072013 (2018) arXiv:1709.02505_[hep-ex]
BELLE 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]
Average .txt  0.295 ± 0.010 ± 0.010 0.339 ± 0.026 ± 0.014 -0.39/-0.34/-0.38 chi2/dof = 8.8/7 (CL = 0.28) R(D)-R(D*).pdf  .png  
(dashed curves correspond to 3 σ contour)
R(D) .pdf  .png  
R(D*) .pdf  .png  

Compatibility with SM predictions

SM predictions for R(D) based on following Lattice calculations:

The prediction obtained combining the two calculation above (FLAG Working Groups Eur.Phys.J.C80 (2019) no.113 (2020) arXiv:1902.08191 [hep-lat] ) is R(D) =0.300 ± 0.008.

P. Gambino and D. Bigi in Phys.Rev.D 94, 094008 (2016) arXiv:1606.08030 [hep-ph] combined the two lattice calculations, with the experimental Form Factor of B→ D l ν from BaBar (2010) and Belle (2016), obtaining R(D) = 0.299 ± 0.003. The result is compatible with the above calculations, but more accurate. Similar calculation were performed more recently by other groups (see table below for references).

The SM prediction for R(D*) widely used in previous HFLAV averages was:

New calculations have become available since the 2017. The most relevant input to these new calculations are: form factors obtained fitting with the BGL parameterization the unfolded spectrum from Belle with tagged B-hadron sample arXiv:1702.01521_[hep-ex] and untagged Phys.Rev.D 100 , 052007 (2019) arXiv:1809.03290_[hep-ex].

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.

Recently, FNAL/MILC released the first unquenched Lattice calculation of B→D*l ν form factors at non-zero recoil, A.Bazavov et al. [arXiv:2105.14019 [hep-lat]] , predicting a value of R(D*)=0.265 ± 0.013, using only Lattice inputs. A combined analysis with experimental inputs of both B→Dl ν and B→D*l ν would be desirable.

These new calculations are in good agreement between each other, and consistent with old predictions for R(D*), but more robust.

The central values of the SM predictions, and their uncertainty estimates, will evolve as more precise measurements of B→D(*)l ν spectra and new calculations become available. The disagreement on the treatment of the theoretical uncertaitines can be settled when further calculations of the B→D* Form Factors beyond the zero recoil limit as well as information on the pseudoscalar Form Factor will be available.

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. [arXiv:2105.14019 [hep-lat]] 0.265 ± 0.013

R(D) and R(D*) exceed the SM predictions given above, by 1.4σ and 2.8σ respectively. Considering the R(D)-R(D*)) correlation of -0.38, the resulting combined χ2 is 13.97 for 2 degree of freedom, corresponding to a p-value of 0.92 x 10-3. The difference with the SM predictions reported above, corresponds to about 3.3σ.