Soft-collinear factorization and Sudakov resummation of heavy meson decay amplitudes with effective field theories

Decays of the B meson into light and energetic particles are discussed. The calculation of the corresponding decay amplitudes is non-trivial in many respects. Strong interaction effects are always present and cannot be computed reliably using analytic techniques. However, besides the intrinsic energy scale lambdaQCD of Quantum Chromo Dynamics, there also exists a much larger scale, the b-quark mass m b, at which perturbation theory can be applied. QCD-factorization is the idea of separating the contributions that arise at these different scales and performing a systematic expansion in the ratio lambdaQCD /mb. Hard processes at the large scale can be computed using perturbation theory, while soft processes are encoded in non-perturbatioe structure functions. The observation that for many decay modes the same structure functions are needed make this a useful approach. However, factorization theorems need to be proved for every single decay, since some amplitudes do not factorize. The intent of this thesis is to study examples of factorizable and non-factorizable amplitudes in a systematic framework, by using effective field theory techniques.; The advancing precision of experimental measurements of B-decays make it necessary to improve the accuracy of theoretical predictions. To achieve this, it is necessary to perform a resummation of Sudakov logarithms, which enter at every non-trivial order in perturbation theory.; In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic particles. Specifically, the factorizable amplitudes for inclusive B → Xul- n&d1; and exclusive B- → gamma l- n&d1; are calculated in renormalization-group improved perturbation theory to first non-trivial order. Form factors encoding the exclusive decay amplitudes for B¯ → Pl- n&d1; and B → Vl- n&d1; (P = light pseudoscalar meson, V = light vector meson) are studied and proved to be dominated by the non-factorizable Feynman mechanism.