Applications of Chiral Perturbation Theory in Reactions with Heavy Particles

TL;DR

This paper reviews how effective field theories, especially chiral perturbation theory, describe heavy hadron interactions, decays, and nucleon systems, providing methods to extract key parameters and explore symmetries.

Contribution

It introduces a comprehensive application of heavy hadron chiral perturbation theory to decay processes and develops a new power counting scheme for pion interactions in nucleon systems.

Findings

Extracted $D^*D\pi$ coupling from data.

Proposed a method to determine $|V_{ub}|$ with 10% uncertainty.

Showed invariance of leading nucleon-nucleon interaction terms under SU(4) symmetry.

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 $D^*$ decays. The phenomenologically important $D^*D\pi$ 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.