Constraining new physics in with reparametrization invariance and QCD factorization

Usually, B⁰→π⁺π⁻ decays are expressed in terms of weak amplitudes explicitly dependent on the CKM weak phase α or γ. In this Letter, we show that the weak amplitudes can be rewritten such that a manifest dependence on β emerges instead. Based on this, we constrain new-physics contributions to the CP-violating phase _d in mixing. Further, we apply reparametrization invariance and use QCD factorization predictions to investigate the bounds on an additional new-physics amplitude in B⁰→π⁺π⁻.