Compatibility plots for the Unitarity Triangle parameters

This section describes how the comparison between indirect parameter determinations and their (hypothetical) direct experimental measurement can be used as a test for SM description of flavour physics.
The indirect determination of a particular parameter obtained using our fit and including all the available constraints gives a prediction based on formulas which are valid in the Standard Model; the comparison between this prediction and a direct measurement can thus result in an evidence of new physics phenomena.

In the following five cases are treated:
sin 2β , Vub , γ , α , Δms .
In each case, a plot shows the compatibility between direct and indirect determinations, 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 values is first built; the ratio between central value and standard deviation for that pseudo-Gaussian distribution is then taken as compatibility indicator.

sin2β pull (EPS) [JPG]
sin2β from B0 → J/ψ K0

Since at present the experimental uncertainty on the direct measurement of sin2β (using time dependent CP asymmetry in b → cc s decays) has been reduced to 0.026 and the theoretical error has been evaluated to be 0.012, the study of this parameter is the most suitable for a significant test of the SM. The cross in the plot shows the HFAG average for sin2β from B0 → J/ψ K0, combined with the theoretical error. The current direct measurement is not fully compatible with the SM prediction because of the large value of Vub from inclusive measurement.

Vub pull (EPS) [JPG]
Vub from inclusive and exclusive measurements

The present value of sin2β favours a value of Vub more compatible with the exclusive determination than with the inclusive one. The exclusive determination is still limited by the precision of the determination of the B → π form factor from LQCD . The inclusive measurement has a smaller error and a larger central value, marginally compatible with the World Average of sin2β. In the plot we compare the indirect determination from the other constraints to the experimental measurements from exclusive (+) and inclusive (*) decays.

γ pull

The plot shows that the comparison of indirect determination obtained from the fit and the direct determination, obtained combining all the experimental informations. To obtain a value in the 3σ region, a sizable shift in the experimental measurement is needed. This fact provides the most important evidence of the success of the Standard Model, after the first measurement of sin 2β.

α pull

The situation for α is similar to the case of γ, with the additional complication that the experimental measurement comes from an SU(2) analysis of several channels, introducing a theoretical uncertainty on top of the experimental one. Moreover, a channel dependent ambiguity in the determination of the angle is intrinsic in the method.

Δm_s pull

The new measurement of Δms can be compared to the prediction from rest of the fit. The two values are in very good agreement. The effectiveness of the comparison is limited by the precision on the theoretical inputs, inducing a big error (compared to the experimental one) on the prediction from the rest of the fit.

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