Reducing the Error on alpha in B-> pi pi, rho rho, rho pi
M. Gronau, E. Lunghi, D. Wyler
Abstract
Theoretical errors in the extraction of alpha from B -> pi+ pi-, rho+ rho-, rho pi decays are usually given in terms of upper bounds on alphaeff-alpha obtained from isospin or from SU(3) relations, where alphaeff is measured through CP asymmetries. We show that mild assumptions about magnitudes and strong phases of penguin and tree amplitudes (|P/T| < 1 and |delta| < pi/2) in B -> pi pi and B -> rho rho, imply alphaeff > alpha, thus reducing by a factor two the error in alpha. Similarly, the assumptions |p+-/t+-| < 1, |δ-| < pi/2 <|δ+| in B -> rho pi lead to a cancellation between two terms in alphaeff-alpha. Current data support these conditions.
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