Average of R(D) and R(D^*) for ICHEP 2026

Last update on 01.08.2026

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 addition to the traditional 2-Dimensional (R(D), R(D*)) average, a 3D average of R(D), R(D*) and tau polarisation P_τ(D*) is also reported.
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.
• 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.
• 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 supersedes the published measurement: Phys.Rev. D94, 072007 (2016) [arXiv:1607.07923]
• LHCb Collaboration: Phys. Rev. Lett. 131, 111802 [arXiv:2302.02886]
  Combined measurement of R(D) and R(D^*+). Only the τ→μν_μν_τ decay mode is used.
• LHCb Collaboration: Phys. Rev. D 108, 012018 [arXiv:2305.01463] and
  Measurement of R(D^*+) where τ is reconstructed in the three-prong hadronic decay channels τ→3π(π⁰)ν.
• LHCb Collaboration: Phys. Rev. Lett. 134, 061801 (2025) [arXiv:2406.03387]
  Measurement of R(D⁺) and R(D^*+), using the τ→μν_μν_τ decay mode.
• Belle II Collaboration: Phys. Rev. D 112 (2025) 3, 032010 [arXiv:2504.11220]
  Measurement of R(D⁺) and R(D^*+), using semileptonic B tagging decay.
• Belle II Collaboration: Presented at CKM 2025 [talk]
  Measurement of R(D⁺) and R(D^*+), using hadronic B tagging decay, supersedes the Belle II Measurement of R(D*), based on the hadronic tagging sample Phys. Rev. D 110, 072020 (2024) [arXiv:2401.02840].
• Belle II Collaboration: Presented a ICHEP 2026 [talk]
  Measurement of R(D^*+) and tau polarisation, using the hadronic FEI tag and hadronic tau decays.

The preliminary BaBar result using semileptonic tagging sample presented at Moriond 2026 [talk] is not included in our nominal averages, as the systematic uncertainties and checks are still being finalised by the Collaboration ([talk at ICHEP 2026]). However we report also averages including the result for completeness. The poor quality of these averages reflects the incompatibility of the inputs (contributions to the chi2 of the average and compatibility of each measurement with the average are included for the 2D average).

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 for many HFLAV reports 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]

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. In addition, since 2023, two indipendent lattice calculations at non-zero recoil are available: from HPQCD arXiv:2304.03137[hep-lat] (R(D^*)=0.273 ± 0.015), and JLQCD arXiv:2306.05657[hep-lat] (R(D^*)=0.252 ± 0.022), have been released. Various indipendent analyses of these three lattice data has been performed by various groups. The first were performed by G. Martinelli et al. [Eur. Phys. J. C 84 (2024) 400] and I.Ray et al. [JHEP 01 (2024) 022], and the results reported in the table below. In these papers result combined with experimental inputs from Belle and Belle II on B→D^*l ν are reported along with results based on lattice only calculations.

In the following table SM predictions are reported along with the compatibility of the current 2D (R(D),R(D^*)) HFLAV average with each of them. The correlation between R(D) and R(D^*) theory prediction has been used when avaialable in the publication.

	R(D)	R(D*)	Compatibility in σ
D.Bigi, P.Gambino, Phys.Rev. D94 (2016) no.9, 094008 [arXiv:1606.08030 [hep-ph]]	0.299 ± 0.003		2.48
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	4.07
G. Martinelli, S. Simula, L. Vittorio, Phys.RevD 105 (2022) 3, 034503 [arXiv:2105.08674 [hep-ph]]	0.296 ± 0.008		2.49
F. U. Bernlochner, Z. Ligeti, M. Papucci, M. T. Prim, D. J. Robinson, C. Xiong, Phys. Rev. D 106 (2022) 096015 [arXiv:2206.11281 [hep-ph]]	0.288 ± 0.004	0.249 ± 0.003	4.61
I.Ray, S.Nandi, JHEP 01 (2024) 022 [arXiv:2305.11855 [hep-lat]]	0.304 ± 0.003	0.258 ± 0.012	2.55
FLAG Collaboration, [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054		2.65
BaBar Collaboration, Phys.Rev.Lett. 123 (2019) 9, 091801 [arXiv:1903.10002 [hep-ex]]		0.253 ± 0.005	2.27
P.Gambino, M.Jung, S.Schacht, Phys.Lett.B795 (2019) 386 [arXiv:1905.08209 [hep-ph]]		0.254 + 0.007 − 0.006	2.06
G. Martinelli, S. Simula, L. Vittorio, Eur. Phys. J. C 84 (2024) 400 [arXiv:2310.03680 [hep-ph]]		0.262 ± 0.009	1.27
Arithmetic average	0.296 ± 0.004	0.254 ± 0.005	3.73
FLAG Collaboration, R(D*) Nf=2+1 [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054	0.2582 ± 0.0051	3.47
FLAG Collaboration, R(D*) Nf=2+1+1 [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054	0.275 ± 0.015	2.31
FLAG Collaboration, R(D*) G. Martinelli et. al. [arXiv:2411.04268 [hep-lat], arXiv:2310.03680 [hep-ph]]	0.2938 ± 0.0054	0.262 ± 0.009	2.94

R(D) and R(D^*) exceed the SM predictions (arithmetic average) given above, by 2.6σ and 2.2σ respectively. Considering the R(D)-R(D^*)) correlation of -0.371, the resulting combined χ² is 17.15 for 2 degree of freedom, corresponding to a p-value of 1.89 x 10^-4. The difference with the SM predictions reported above, corresponds to about 3.7σ.

In the following table SM predictions are reported along with the compatibility of the current 3D (R(D),R(D^*),P_τ(D*)) HFLAV average with each of them. The correlation between R(D) and R(D^*) theory prediction has been used when avaialable in the publication. The SM prediction for the tau polarisation P_τ(D*)= -0.497 ± 0.007 (Phys. Rev. D 871,202 034028 (2013)) has been considered.

	R(D)	R(D*)	Compatibility in σ
D.Bigi, P.Gambino, Phys.Rev. D94 (2016) no.9, 094008 [arXiv:1606.08030 [hep-ph]]	0.299 ± 0.003		2.48
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	3.75
G. Martinelli, S. Simula, L. Vittorio, Phys.RevD 105 (2022) 3, 034503 [arXiv:2105.08674 [hep-ph]]	0.296 ± 0.008		2.49
F. U. Bernlochner, Z. Ligeti, M. Papucci, M. T. Prim, D. J. Robinson, C. Xiong, Phys. Rev. D 106 (2022) 096015 [arXiv:2206.11281 [hep-ph]]	0.288 ± 0.004	0.249 ± 0.003	4.30
I.Ray, S.Nandi, JHEP 01 (2024) 022 [arXiv:2305.11855 [hep-lat]]	0.304 ± 0.003	0.258 ± 0.012	2.22
FLAG Collaboration, [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054		2.65
BaBar Collaboration, Phys.Rev.Lett. 123 (2019) 9, 091801 [arXiv:1903.10002 [hep-ex]]		0.253 ± 0.005	2.27
P.Gambino, M.Jung, S.Schacht, Phys.Lett.B795 (2019) 386 [arXiv:1905.08209 [hep-ph]]		0.254 + 0.007 − 0.006	2.06
G. Martinelli, S. Simula, L. Vittorio, Eur. Phys. J. C 84 (2024) 400 [arXiv:2310.03680 [hep-ph]]		0.262 ± 0.009	1.27
Arithmetic average	0.296 ± 0.004	0.254 ± 0.005	3.41
FLAG Collaboration, R(D*) Nf=2+1 [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054	0.2582 ± 0.0051	3.14
FLAG Collaboration, R(D*) Nf=2+1+1 [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054	0.275 ± 0.015	1.98
FLAG Collaboration, R(D*) G. Martinelli et. al. [arXiv:2411.04268 [hep-lat], arXiv:2310.03680 [hep-ph]]	0.2938 ± 0.0054	0.262 ± 0.009	2.60

When including the latest preliminary BaBar result (BaBar^b), the compatibility with the SM (HFLAV aritmetic average) is of about 1.99σ for the 2D (R(D),R(D^*)) average, and 1.63 σ for the 3D (R(D),R(D^*),P_τ(D*)) average.

Acknowledgments