An analysis of the time-dependent CP asymmetry in B → ππ decays in the standard model

Measurements of the time-dependent CP-asymmetry in the decay B-d(0)(t) --> pi(+)pi(-) and its charge conjugate by the BELLE and BABAR collaborations currently yield C-pipi(+-) = -0.46 +/- 0.13 and S-pipi(+-) = -0.74 +/- 0.16, characterizing the direct and mixing-induced CP-asymmetries, respectively. We study the implication of these measurements on the CKM phenomenology taking into account the available information in the quark mixing sector. Our analysis leads to the results that the ratio \P-c/T-c\ involving the QCD-penguin and tree amplitudes and the related strong phase difference delta(c) = delta(c)(P) - delta(c)(T) in the B-d(0)/(B) over bar (0)(d) --> pi(+)pi(-) decays are quite substantial. Using the isospin symmetry to constrain \P-c/T-c\ and cos(2theta), where 2theta parameterizes the penguin-induced contribution, we present a fit of the current data including the measurements of S-pipi(+-) and C-pipi(+-). Our best-fits yield alpha = 92degrees, beta = 24degrees, gamma = 64degrees, \P-c/T-c\ = 0.77, and delta(c) = -43degrees. At 68% C.L., the ranges are 81degrees less than or equal to alpha less than or equal to 103degrees, 21.9degrees less than or equal to beta less than or equal to 25.5degrees, 54degrees less than or equal to gamma less than or equal to 75degrees, 0.43 less than or equal to \P-c/T-c\ less than or equal to 1.35 and -64degrees less than or equal to delta(c) less than or equal to -29degrees. Currently en vogue dynamical approaches to estimate the hadronic matrix elements in B --> pipi decays do not provide a good fit of the current data.