Two-loop QCD penguin contribution to the width difference in Bs − $$ {\overline{B}}_s $$ mixing

We consider two-loop QCD corrections to the element $$ {\Gamma}_{12}^q $$ Γ 12 q of the decay matrix in Bq−$$ {\overline{B}}_q $$ B ¯ q mixing, q = d, s, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γs matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in mc/mb up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γs.

SU(3) analysis of four-quark operators: K → ππ and vacuum matrix elements

Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in τ-decay analyses. Using an SU(3)L ⊗ SU(3)R decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio ε′/ε, using the measured hadronic spectral functions in τ decay. Second, we fit our SU(3) dynamical parameters to the most recent lattice data on K → ππ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the ∆I = $$ \frac{1}{2} $$ 1 2 enhancement, confirming old suggestions about its underlying dynamical origin.

Constraints on the CKM angle α in the B → ρρ decays

Using a data sample of 122 million [Formula: see text] decays collected with BABAR detector at the PEP-II asymmetric B factory at SLAC, we measure the time-dependent-asymmetry parameters of the longitudinally polarized component in the B0 → ρ+ρ- decay as CL = -0.23 ± 0.24 ( stat ) ± 0.14 ( syst ) and SL = -0.19 ± 0.33 ( stat ) ± 0.11 ( syst ). The B0 → ρ0ρ0 decay mode is also searched for in a data sample of about 227 million [Formula: see text] pairs. No significant signal is observed, and an upper limit of 1.1 × 10-6 (90% C.L.) on the branching fraction is set. The penguin contribution to the CKM angle α uncertainty is measured to be 11°. All results are preliminary.