Final State Interactions in the Decay of Heavy Quarks

I discuss some recent results on the systematic behavior of final state rescattering which makes use of the limit of a heavy B meson. The results suggest that soft final state interactions do not disappear in the large mB limit. Soft and hard final state phases can both contribute to CP violating asymmetries in B decay. The way that the soft phases occur is interesting theoretically and suggests the violation of local quark-hadron duality. Some of the CP violating asymmetries that can occur in the Standard Model require the presence of strong final state interaction phases. Very little in known about final state interactions at the high energies that are relevant for B decay. What I will describe in this talk does not “solve” the problem of these interactions. However, my collaborators (Eugene Golowich, Alexey Petrov and João Soares) and I have obtained some insights that at least taught me something about this frustrating topic. I would like to share these with you. This has taken us on a path into unfashionable but surprisingly interesting physics and may shed new light on weak decays. As is now common, we use the mass of the B meson as an organizing parameter and consider the limit where the mass is very large. We can show that soft final state interaction survive in this limit and can isolate their leading cause, although in the end we cannot provide a specific number describing the magnitude of the phase. Our main conclusions rest on a few simple facts. These are: 1) The Unitarity Relation. Final state interactions in B decay involve the rescattering of physical final state particles. Unitarity of the S-matrix, S†S = 1, implies that the T -matrix, S = 1 + iT , obeys Disc TB→f ≡ 1 2i [ 〈f |T |B〉 − 〈f |T |B〉 ]