Preliminary average of R(D) and R(D^*) for Spring 2025

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.
• 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 superseeds 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.
• Belle II Collaboration: Phys. Rev. D 110, 072020 (2024) [arXiv:2401.02840]
  Measurement of R(D*), based on the hadronic tagging sample.
• LHCb Collaboration: Phys. Rev. Lett. 134, 061801 (2025) [arXiv:2406.03387]
  Measurement of RD(D⁺) and R(D^*+), using the τ→μν_μν_τ decay mode.
• Belle II Collaboration: presented at Moriond EW 2025 and submitted to PRD [arXiv:2504.11220]
  Measurement of RD(D⁺) and R(D^*+), using semileptonic B tagging decay.

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 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		1.89
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	4.13
G. Martinelli, S. Simula, L. Vittorio, Phys.RevD 105 (2022) 3, 034503 [arXiv:2105.08674 [hep-ph]]	0.296 ± 0.008		1.93
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	4.65
I.Ray, S.Nandi, JHEP 01 (2024) 022 [arXiv:2305.11855 [hep-lat]]	0.304 ± 0.003	0.258 ± 0.012	2.44
FLAG Collaboration, [arXiv:2411.04268 [hep-lat]]	0.2938 ± 0.0054		2.06
BaBar Collaboration, Phys.Rev.Lett. 123 (2019) 9, 091801 [arXiv:1903.10002 [hep-ex]]		0.253 ± 0.005	2.79
P.Gambino, M.Jung, S.Schacht, Phys.Lett.B795 (2019) 386 [arXiv:1905.08209 [hep-ph]]		0.254 + 0.007 − 0.006	2.58
G. Martinelli, S. Simula, L. Vittorio, Eur. Phys. J. C 84 (2024) 400 [arXiv:2310.03680 [hep-ph]]		0.262 ± 0.009	1.79
Arithmetic average	0.296 ± 0.004	0.254 ± 0.005	3.77

R(D) and R(D^*) exceed the SM predictions (arithmetic average) given above, by 1.9σ and 2.7σ respectively. Considering the R(D)-R(D^*)) correlation of -0.39, the resulting combined χ² is 16.92 for 2 degree of freedom, corresponding to a p-value of 2.12 x 10^-4. The difference with the SM predictions reported above, corresponds to about 3.8σ.

Acknowledgments