Lattice QCD confronts the Unitarity Triangle Fit

Abstract

Before the starting of the B factories, the Unitarity Triangle (UT) analysis relied on the results of lattice QCD simulations to relate the experimental determinations of semileptonic B decays, K 0 − K ¯ 0 and B d , s 0 − B ¯ d , s 0 mixing to the CKM parameters. In the last years, much more information has been obtained from the direct determination of the UT angles from non-leptonic B decays. In this talk, we compare the results of the “classical” UT analysis (UTlattice) with the analysis based on the angles determinations (UTangles). We show that the recent measurement of Δ m s , combined with Δ m d and e K , allows from this comparison a quite accurate extraction of the values of the lattice parameters, B ˆ K , f B s B ˆ B s 1 / 2 , ξ and f B . These values, obtained “experimentally” by assuming the validity of the Standard Model, can be compared with the theoretical predictions from lattice QCD. We also discuss the different determinations of V u b and show that current data do not favor the value measured in inclusive decays. Finally, we present updated predictions for the leptonic branching fraction B R ( B → τ ν τ ) , and compare them with the recent experimental determination. We take the opportunity of this write up to update the results of ref. [M. Bona et al. [UTfit Collaboration], arXiv:hep-ph/0606167 ] with the most recent results presented at the ICHEP'06 conference.