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*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:

• BaBar Collaboration: Phys.Rev.Lett 109, 101802 (2012) [arXiv:1205.5442] and Phys.Rev.D 88, 072012 (2013) [arXiv:1303.0571]
  Combined measurement of R(D) and R(D^*+) based on the hadronic tagging sample and it is a combined. We use the results obtained imposing the isospin relations R(D⁰)=R(D⁺) and R(D^*0)=R(D^*+).
• Belle Collaboration: Phys.Rev. D92, 072014 (2015) [arXiv:1507.03233]
  Similar to the BaBar analysis: combined measurement of R(D) and R(D*), based on the hadronic tagging sample.
• LHCb Collaboration: Phys.Rev.Lett. 115, 111803 (2015), Addendum: Phys.Rev.Lett. 115, 159901 (2015) [arXiv:1506.08614]
  Measurement of R(D^*+). Only the τ→μν_μν_τ decay mode is used.
• Belle Collaboration: Phys.Rev.Lett. 118, 211801 (2017) [arXiv:1612.00529] and Phys.Rev.D 97, 012004 (2018) [arXiv:1709.00129]
  Measurement of R(D^*+) based on an hadronic tagging sample. The τ is reconstructed in the hadronic decay channels τ→πν and τ→ρν. This is a simultaneous measurement of R(D*) and the τ polarization.
• LHCb Collaboration: Phys.Rev.Lett. 120, 171802 (2018) [arXiv:1708.08856] and Phys.Rev.D 97, 072013 (2018) [arXiv:1711.02505]
  Measurement of R(D^*+) where τ is reconstructed in the three-prong hadronic decay channels τ→3π(π⁰)ν. This measurement has been updated to the latest HFLAV average of BF(B⁰→ D^*+ l^- ν) = 4.97 ± 0.02 ± 0.12 %.
• Belle Collaboration: Phys.Rev.Lett. 124 (2020) 16, 161803 [arXiv:1910.05864]
  Combined measurement of R(D) and R(D^*+), based on a semileptonic tagging method. This superseeds the published measurement: Phys.Rev. D94, 072007 (2016) [arXiv:1607.07923]

Compatibility with SM predictions

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

• R(D) =0.299 ± 0.011, J.A.Bailey et al. [FNAL/MILC Collaboration], Phys.Rev.D 92, 034506 (2015)arXiv:1503.07237 [hep-lat]
• R(D) =0.300 ± 0.008, H. Na et al., Phys.Rev.D 92, 054410 (2015) arXiv:1505.03925 [hep-lat]

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

• R(D^*)=0.252 ± 0.003, S.Fajfer, J.F.Kamenik, and I.Nisandzic, Phys.Rev.D85(2012) 094025 arXiv:1203.2654 [hep-ph]

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.