Reparametrization invariance of B decay amplitudes and implications for new physics searches in B decays

When studying $B$ decays within the standard model (SM), it is customary to use the unitarity of the CKM matrix in order to write the decay amplitudes in terms of only two of the three weak phases which appear in the various diagrams. Occasionally, it is mentioned that those two weak phases can be used in order to describe any decay amplitude, even beyond the standard model. Here we point out that, when describing a generic decay amplitude, the two weak phases can be chosen completely at will, and we study the behavior of the decay amplitudes under changes in the two weak phases chosen as a basis. Of course, physical observables cannot depend on such reparametrizations. This has an impact on discussions of the SM and on attempts to parametrize new physics effects in the decay amplitudes. We illustrate these issues by looking at $B\ensuremath{\rightarrow}\ensuremath{\psi}{K}_{S}$ and the isospin analysis in $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$.