PROBING CKM PARAMETERS THROUGH UNITARITY, εK AND ΔMBd,s

Abstract

A recently carried out unitarity based analysis1,2 involving the evaluation of Jarlskog's rephasing invariant parameter J as well as the evaluation of the angles α, β and γ of the unitarity triangle is extended to include the effects of [Formula: see text] as well as [Formula: see text] mixings. The present analysis attempts to evaluate CP violating phase δ, |Vtd| and the angles α, β and γ by invoking the constraints imposed by unitarity, [Formula: see text] and [Formula: see text] mixings independently as well as collectively. By invoking the "full scanning" of input parameters, as used by Buras et al., our analysis yields the following results respectively for δ and |Vtd|, unitarity: 50°±20° (in I quadrant), 130°±20° (in II quadrant) and 5.1 × 10-3 ≤ |Vtd| ≤ 13.8 × 10-3, unitarity and εk: 33° ≤ δ ≤ 70° (in I quadrant), 110° ≤ δ ≤ 150° (in II quadrant), 5.8 × 10-3 ≤ |Vtd| ≤ 13.6 × 10-3, unitarity and Δmd: 30° ≤ δ ≤ 70°, 6.4 × 10-3 ≤ |Vtd| ≤ 8.9 × 10-3. Incorporating all the constraints together, we get 37° ≤ δ ≤ 70°, 6.5 × 10-3 ≤ |Vtd| ≤ 8.9 × 10-3, the corresponding ranges for α, β and γ are, 80° ≤ α ≤ 124°, 15.1° ≤ β ≤ 31° and 37° ≤ γ ≤ 70°, again in agreement with the recent analysis of Buras et al. as well as with other recent analyses. Our analysis yields 0.50 ≤ sin 2β ≤ 0.88, in agreement with the the recently updated BABAR results. This range of sin 2β is in agreement with the earlier result of BELLE, which however has a marginal overlap only with the lower limit of recent BELLE results. Interestingly, our results indicate that the lower limit of δ is mostly determined by unitarity, while the upper limit is governed by constraints from Δmd.