CP-violation in B → π+π- and the unitarity triangle
Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333, Munich, Germany
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We analyze the extraction of weak phases from CP-violation in B → π+π- decays. We propose to determine the unitarity triangle by combining the information on mixing-induced CP-violation in B → π+π-, S, with the precision observable sin2β obtained from the CP-asymmetry in B → ψK S . It is then possible to write down exact analytical expressions for and as simple functions of the observables S and sin2β and of the penguin parameters r and ϕ. As an application clean lower bounds on and can be derived as functions of S and sin2β, essentially without hadronic uncertainty. Computing r and ϕ within QCD factorization yields precise determinations of and since the dependence on r and ϕ is rather weak. It is emphasized that the sensitivity to the phase ϕ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter C of direct CP-violation in B → π+π-. Predictions and uncertainties for r and ϕ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in 1/m b and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.
© Springer-Verlag, 2006