CKM-UT Angles: Mixing and CP violation at the B Factories

The B Factories have demonstrated since the beginning of this decade that CP violation in the B meson system is consistent with the Standard Model (SM) description in terms of the complex phase in the three-by-three CabibboKobayashi-Maskawa (CKM) matrix [1]. With one single phase, the SM predicts clear patterns for quark mixing and CP violations, to be satisfied by all processes. The unitarity relation VudV ∗ ub +VcdV ∗ cb + VtdV ∗ tb = 0 among the first and third columns of the CKM matrix is represented in the complex plane by a Unitarity Triangle (UT) with angles α = arg[−VtdV ∗ tb/VudV ∗ ub], β = arg[−VcdV ∗ cb/VtdV ∗ tb], γ = arg[−VudV ∗ ub/VcdV ∗ cb]. Physics beyond the SM could in general change the picture; for this reason it is very important to make many independent measurements to possibly find inconsistencies of the SM. In the evolution of BB pairs, we reconstruct the decay of one meson to final f at proper time tf , and identify (tag) its flavor using information from the other B meson in the event, decaying at time ttag. The time-dependent CP asymmetry of B 0 (B) mesons decaying to final state f can be defined as ACP (∆t) ≡ (Nf − Nf )/(Nf + Nf ) = Sf sin(∆md∆t) − Cf cos(∆md∆t). Here ∆t ≡ tf − ttag, and ∆md is the mass difference of the B meson mass eigenstates.. The sine term re-