Applications of Chiral Perturbation Theory in Reactions with Heavy Particles

Abstract

Effective field theory techniques are used to describe the interaction of heavy hadrons in a model independent way. Predictability is obtained by exploiting the symmetries of QCD. Heavy hadron chiral perturbation theory is reviewed and used to describe $D^{\ast }$ decays. The phenomenologically important $D^{\ast }D\pi$ coupling is extracted from data working to first order in the chiral and heavy quark symmetry breaking parameters. A method is described for determining $|V_{ub}|$ from exclusive semileptonic $B$ and $D$ decays with 10% uncertainty. An effective field theory for two-nucleon systems is then discussed. The large S-wave scattering lengths necessitate expanding around a non-trivial fixed point. A detailed discussion of the interplay between renormalization and the power counting is given. In power counting pion interactions with nucleons it is useful to consider three classes of pion: potential, radiation, and soft. A power counting for massive radiation is developed. Finally, it is shown that the leading terms in the effective theory for nucleon-nucleon interactions are invariant under Wigner's SU(4) spin-isospin symmetry in the infinite scattering length limit.

Comments: Ph.D. thesis, 170 pages