Topics in Heavy Particle Effective Theories

Abstract

This thesis gives several applications of effective field theory to processes involving heavy particles. The first is a standard application of heavy quark effective theory to exclusive B decays. It involves two sum rules giving constraints on the curvature of the B→D Isgur-Wise function. This thesis calculates order alpha corrections to these constraints, increasing the accuracy of the resultant constraints on the physical form factors. The second application involves matching SCETI onto SCETII at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. The work described here gives a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in SCETII are sufficient to reproduce all the infrared divergences of SCETI. We explain the relationship between IR regulators and an additional mode proposed for SCETII. Next we consider top production at large energies. The production process is characterized by three disparate energy scales: the center-of-mass energy (E), the mass (m), and the decay width (Gamma). At the scale E we match onto massive soft-collinear effective theory (SCET). The SCET current is run from E to m, thereby summing Sudakov logarithms of the form logn(m/E), where n=2,1. At the scale m, the top quark mass is integrated out by matching SCET jet functions onto a boosted version of heavy quark effective theory (bHQET). The jet functions in bHQET are then run from m to Gamma, summing powers of single logarithms of the ratio m/Gamma. Under certain assumptions factorization formulas can be derived for differential distributions in processes involving highly energetic jets, such as jet energy distributions. As a final topic, we show how to test these assumptions using semileptonic or radiative decays of heavy mesons, by relating the jet P⁺ distribution derived under these assumptions to other differential distributions in these decays, which are better understood.