The Branching Ratio of B → τ ν can be used to determine R_b=ρ²+ η² independently from the determination of V_ub from semi-leptonic B decays. On the other side not having used BR(B → τν_τ) as an input in the analysis, we can indirectly determine its value as an output of our fit. This is obtained starting from the UTangles determination of ρ and η, combined with the experimental determination of V_ub V_cb, adding the experimental measurement of Δm_d and Δm_s to determine f_B√B_Bd, and using the lattice value of B_Bd=1.28 ± 0.05 ± 0.09 to obtain f_B from it. In this way, the prediction is obtained without using the value of f_B taken from lattice calculations, which has a larger relative uncertainty than B_Bd. We obtain the values quoted below:

Although all the predictions above are compatible within the errors, a comparison of the values obtained from the above determinations gives the measure of the correlation of this prediction with V_ub in the overall UT fit, since all other input quantities are the same. The result p.d.f., obtained using all the informations in the fit, is given in the plot below.

(EPS) [JPG]

For comparison, using f_B value from LQCD (f_B = (189 ± 27) MeV) and the inclusive determination of V_ub (V_ub = (44.9 ± 3.3) × 10^-4), one would obtain BR(B → τν_τ)=(1.39 ± 0.44) × 10^-4. Note that in this case, contrary to the case of Δ m_s, a better agreement between the prediction and the experimental world average (BR(B → τν_τ)=(1.31 ± 0.48) × 10^-4, combining Belle and BaBar) is found when the inclusive value of V_ub. This suggests that the experiemental measurement is in agreement with the value of the inclusive determination of V_ub.

This Branching Ratio depends upon |V_ub|² and the B decay constant f_B. We show here the bound on the (ρ; η) plane (giving the total UT fit result as a reference), obtained using the experimental measurements from BaBar (BR(B → τν) = 0.88^+0.68+0.11_-0.67-0.11)x10^-4) Belle (BR(B → τν) = 1.79^+0.56+0.39_-0.49-0.46)x10^-4) translated into a bound on R_b. An other interesting exercise consists in assuming the output of the UT analysis and translate the measurement of the Branching Fraction into a determination of f_B, to be compared to Lattice calculations.

(EPS) [JPG] Experimental likelihood of B → τ ν BR(B → τ ν) = (1.31 ± 0.48)10-4 ([0.38,2.25] @ 95% prob.)

(EPS) [JPG] bound from B → τ ν on the (ρ; η) plane

(EPS) [JPG] 1D p.d.f. of Rb from B → τ ν Rb = 0.55 ± 0.11 ([0.34,0.83] @95% Prob.)

(EPS) [JPG] 1D p.d.f. of fB from B → τ ν fB = 0.237 ± 0.037 GeV from the exp+UTfit fB = 0.189 ± 0.027 GeV Lattice QCD