B → τ ν



The Branching Ratio of B → τ ν can be used to determine Rb=ρ2+ η2 independently from the determination of Vub from semi-leptonic B decays. On the other side not having used BR(B → τντ) 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 Vub Vcb, adding the experimental measurement of Δmd and Δms to determine fB√BBd, and using the lattice value of BBd=1.22 ± 0.12 to obtain fB from it. In this way, the prediction is obtained without using the value of fB taken from lattice calculations, which has a larger relative uncertainty than BBd. We obtain the values quoted below:

BR(B → τντ) = (0.73 ± 0.12) × 10-4    using the rest of the contraints
   and not using Vub and lattice quantities [noVub]
BR(B → τντ) = (0.81 ± 0.12) × 10-4    using all the contraints available
   except the lattice quantities [Vub all]
BR(B → τντ) = (0.83 ± 0.12) × 10-4    using all the constraints available and
   using the inclusive value of Vub [Allincl]
BR(B → τντ) = (0.74 ± 0.12) × 10-4    using all the constraints available and
   using the exclusive value of Vub [Allexcl]

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 Vub 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.


Standard Model expectation for BR(B to τ ν) from UTfit,
                         obtained without using Vub experimental determination and LQCD inputs
(EPS) [JPG]
SM prediction on B → τ ν
using no Vub and no lattice
BR(B → τ ν) = (0.73 ± 0.12)10-4
([0.522,1.018] @ 95% prob.)

Standard Model expectation for BR(B to τ ν) from UTfit,
                         obtained without LQCD inputs
(EPS) [JPG]
SM prediction on B → τ ν
using Vub incl+excl and no lattice
BR(B → τ ν) = (0.81 ± 0.12)10-4
([0.566,1.224] @ 95% prob.)

For comparison, using all the constraints available, fB value from LQCD (fB = (200 ± 20) MeV) and the inclusive determination of Vub (Vub = (39.9 ± 1.5 ± 4.0) × 10-4), one would obtain BR(B → τντ)=(0.86 ± 0.12) × 10-4. Note that in this case, contrary to the case of Δ ms, a better agreement between the prediction and the experimental world average (BR(B → τντ)=(1.51 ± 0.33) × 10-4, combining Belle and BaBar) is found when the inclusive value of Vub is used in the fit. In other words, the experiemental measurement is in better agreement with the value of the inclusive determination of Vub.

This Branching Ratio depends upon |Vub|2 and the B decay constant fB. We show here the bound on the (ρ; η) plane (giving the total UT fit result as a reference), obtained using the 2008 HFAG average for the experimental measurement translated into a bound on Rb. 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 fB, to be compared to Lattice calculations.


Experimental likelihood of B to τ ν
(EPS) [JPG]
Experimental likelihood of B → τ ν
BR(B → τ ν) = (1.51 ± 0.33) 10-4
([0.86,2.16] @ 95% prob.)


bound from B to τ ν
(EPS) [JPG]

bound from B → τ ν on the (ρ; η) plane


1D p.d.f. of Rb from B to τ ν
(EPS) [JPG]

1D p.d.f. of Rb from B → τ ν
Rb = 0.47 ± 0.08
([0.30,0.77] @95% Prob.)


1D p.d.f. of fB from B to τ ν,
                             assuming UTfit angle result for CKM parameters
(EPS) [JPG]

1D p.d.f. of fB from B → τ ν
fB = 0.259 ± 0.042 GeV from the exp+UTfit angle fit
fB = 0.200 ± 0.020 GeV Lattice QCD




Compatibility plot for B → τ ν


The compatibility plot describes the comparison between the indirect parameter determination from the global fit excluding the B → τ ν measurement and its direct experimental value.
The plot shows the compatibility between direct and indirect determination, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty.
In more detail the distribution for the difference between direct and indirect value is first built; the ratio between central value and standard deviation for that pseudo-Gaussian distribution is then taken as compatibility indicator.

B → τ ν pull
(EPS) [JPG]


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