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# Including the experimental information about

The treatment of the experimental information about cannot be done by the usual uncertainty propagation, just because the simplifying hypotheses (linearization and Gaussian model for ) do not hold. In fact, the likelihood, which has the role of reweighting the probability, is open, in the sense described in Section 7 of Ref. [7], i.e. it does not go to zero at both ends of the kinematical region ( and in this case), as shown in the top plot of Fig. 7. The reason is simple: in this kind of measurement is not yet incompatible with (no oscillation). Though the open likelihood does not allow to renormalize the p.d.f. (unless strong priors forbidding high values are used), the likelihood can still be used to reweigh the points in the - plane (see Refs. [5] and [8] for other examples and discussions about the function).

It is instructive to see how the reweighting of is turned into the reweighting of the square radius of circle centered in and given by the constraint , i.e. . This is illustrated in the central plot of Fig. 7. We see that the reflection of for ps essentially kills values above , resulting in a strong sensitivity bound (in the sense of Ref. [7]) on the angle of the CKM matrix, forced to be below 90. The bottom plot of Fig. 7 shows the reweighting function in the - plane.

For small values of the reweighting function is divergent, since the whole region of high is squeezed into a small region of . This is no serious problem, since these points are already ruled out by the other constraints. The cutoff shown in the central and bottom plot of Fig. 7 is due to a cutoff at ps. Note, moreover, that the values of preferred by the data (around 15-20 ps) overlap well with the - region indicated by the other constraints. Note also that even if one goes through the academic exercise of removing by hand the peak around 15-20 ps, chopping to 1, the effect on the values of above 1 (and hence of above 90) does not change.

Next: Global combination and results Up: Inferring and of the Previous: Partial combinations of results
Giulio D'Agostini 2004-01-20