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

Average of R(D) and R(D*) for FPCP 2017

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. D94, 072007 (2016):arXiv:1607.07923
Measurement of R(D^*+) based on a semileptonic tagging method.
Belle Collaboration: Phys.Rev.Lett. 118, 211801 (2017)arXiv:1612.00529
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: presented at FPCP 2017 Slides
Measurement of R(D*) where τ is reconstructed in the hadronic decay channels τ→3πν.

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)	Parameters	Remarks
BaBar	0.332 +/- 0.024+/- 0.018	0.440 +/- 0.058 +/- 0.042	-0.45/-0.07/-0.27	input	Phys.Rev.Lett. 109,101802 (2012) [arXiv:1205.5442 [hep-ex]] Phys.Rev.D 88, 072012 (2013) [arXiv:1303.0571]
BELLE	0.293 +/- 0.038 +/- 0.015	0.375 +/- 0.064 +/- 0.026	-0.56/-0.11/-0.49	input	Phys.Rev.D 92, 072014 (2015) [arXiv:1507.03233 [hep-ex]]
BELLE	0.302 +/- 0.030 +/- 0.011	-	-	input	Phys.Rev. D94,072007 (2016) [arXiv:1607.07923 [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]]
LHCb	0.285 +/- 0.019 +/- 0.029	-	-	input	Presented at FPCP2017 [Slides]
Average	0.304 +/- 0.013 +/- 0.007	0.407 +/- 0.039 +/- 0.024	-0.20	chi2/dof = 3.71/6 (CL = 0.716)	R(D)-R(D).pdf .png .C (dashed curves correspond to 2 and 4 σ contours) R(D) .pdf .png .C R(D) .pdf .png .C

SM predictions for R(D) based on recent 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.

The most recent SM prediction for R(D*):

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

R(D) and R(D*) exceed the SM predictions by 2.3σ and 3.4σ respectively (comparing R(D) with FLAG average). Considering the R(D)-R(D*) correlation of -0.20, the resulting combined χ² is 20.60 for 2 degree of freedom, corresponding to a p-value of 4.13 x 10^-5. The difference with the SM predictions reported above, corresponds to about 4.1σ.