  Usually, B->pi+pi- decays are expressed in terms of weak amplitudes
explicitly dependent on the CKM weak phase alpha or gamma. In this letter, we
show that the weak amplitudes can be rewritten such that a manifest dependence
on beta emerges instead. Based on this, we constrain new-physics contributions
to the CP-violating phase phi_d in B_0 anti-B_0 mixing. Further, we apply
reparametrization invariance and use QCD factorization predictions to
investigate the bounds on an additional new-physics amplitude in B->pi+pi-.
