Effective field theories for inclusive B decays

Abstract

In this thesis, we study inclusive decays of the B meson. These allow one to determine CKM elements precisely and to search for physics beyond the Standard Model. We use the framework of effective field theories, in particular the Soft-Collinear Effective Theory, which is a suitable method when the decay products include a jet-like set of hadronic states. We derive factorization theorems for ... corrections (including all orders in a,) to ... in the shape function region, where ... A complete enumeration of ... contributions is provided. We also point out the presence of new shape functions that arise from four-quark operators. These induce an additional uncertainty in certain inclusive determinations of ... Next, we derive the triply differential spectrum for ... in the shape function region, consideration of which is necessitated by experimentally required cuts. It is shown that the same universal jet and shape functions appear as in the decays ... We also show that one can treat the perturbative power counting above and below the scale ... independently, using a procedure we call "split matching".

(cont.) This resolves the conflict between what is suitable in each of these regions. Finally, we use these results to calculate the fraction of the total rate that is measured in the presence of a cut on the hadronic invariant mass, mx. We find that the effect of this cut depends strongly on the value of mt and is approximately universal for all short-distance contributions. This feature can be exploited to minimize hadronic uncertainties and thereby maintain sensitivity to new physics.