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

Average of R(D) and R(D^*+) for Spring 2019

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) = 5.08 ± 0.02 ± 0.12 %.
Belle Collaboration: Preliminary result presented at Moriond EW 2019 [arXiv:1904.08794]
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]

In the average we assume 100% correlation for the systematic uncertainties associated with the 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/-0.31	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/-0.50	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	0.280 ± 0.018 ± 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	Moriond EW 2019, Preliminary result arXiv:1904.08794 [hep-ex]
Average .txt	0.295 ± 0.011 ± 0.008	0.340 ± 0.027 ± 0.013	-0.39/-0.34/-0.38	chi2/dof = 8.7/7 (CL = 0.27)	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:

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 prediction obtained combining the two calculation above (FLAG Working Groups Eur.Phys.J.C77 (2017) no.2,112 arXiv:1607.00299 [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(Di^*) 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]

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 arXiv:1702.01521_[hep-ex]. These new calculations are in good agreement between each other, and consistent with the old predictions for R(D^*), but more robust. There are differences in the evaluation of the theoretical uncertainty associated mainly with assumptions on the pseudoscalar Form Factor. 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 calculation 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(Di^*)
D.Bigi, P.Gambino, Phys.Rev. D94 (2016) no.9, 094008 [arXiv:1606.08030 [hep-ph]]	0.299 ± 0.003
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
D.Bigi, P.Gambino, S.Schacht, JHEP 1711 (2017) 061 [arXiv:1707.09509 [hep-ph]]		0.260 ± 0.008
S.Jaiswal, S.Nandi, S.K.Patra, JHEP 1712 (2017) 060 [arXiv:1707.09977 [hep-ph]]	0.299 ± 0.004	0.257 ± 0.005
Arithmetic average	0.299 ± 0.003	0.258 ± 0.005

The arithmetic average is used only for illustration and doesn't imply consent from the authors of the calculations. The SM uncertainty is currently subject to debate that HFLAV is following without taking a stance in this.

R(D) and R(D^*) exceed the SM predictions given in the last row of the table above, by 1.4σ and 2.5σ respectively. Considering the R(D)-R(D^*)) correlation of -0.38, the resulting combined χ² is 12.33 for 2 degree of freedom, corresponding to a p-value of 2.07 x 10^-3. The difference with the SM predictions reported above, corresponds to about 3.08σ.

Average of R(D) and R(D*+) for Spring 2019

Compatibility with SM predictions

Average of R(D) and R(D^*+) for Spring 2019