Preliminary average of R(D) and R(D^*) for Moriond 2024

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: presented at Lepton Photon 2023 and submitted to PRD [arXiv:2401.02840]
  Measurement of R(D*), based on the hadronic tagging sample.
• LHCb Collaboration: presented at Moriond EW 2024 [Moriond 2024]
  Measurement of RD(D⁺) and R(D^*+), using the τ→μν_μν_τ decay mode.

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.

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 1.6σ and 2.5σ respectively. Considering the R(D)-R(D^*)) correlation of -0.39, the resulting combined χ² is 13.95 for 2 degree of freedom, corresponding to a p-value of 9.33 x 10^-4. The difference with the SM predictions reported above, corresponds to about 3.31σ.

Acknowledgments