Exclusive decays $\chi_{cJ}\to K^*(892)K$ within the effective field theory framework

TL;DR

This paper investigates the decay processes of $ ext{chi}_{cJ}$ particles into $K^*(892)K$ using effective field theory, analyzing color contributions, infrared singularities, and spin symmetry to improve phenomenological predictions.

Contribution

It introduces a comprehensive effective field theory approach to describe $ ext{chi}_{cJ}$ decays, incorporating color-octet contributions and spin symmetry relations to address infrared issues.

Findings

Infrared singularities are absorbed into color-octet matrix elements.

Heavy quark spin symmetry relates color-octet matrix elements.

Results improve the phenomenological description of decay branching fractions.

Abstract

We study hadronic decays $\chi_{cJ}\rightarrow K^*(892)\bar{K} $ within the effective field theory framework. We consider the colour-singlet and colour-octet contributions and study their properties using (p)NRQCD effective theory. We show that infrared singularities in collinear integrals of the colour-singlet amplitudes can be absorbed into the renormalisation of the colour-octet matrix elements. The heavy quark spin symmetry allows us to establish a relation between the colour-octet matrix elements and to define the spin symmetry breaking corrections which are free from infrared singularities. We apply obtained results for a phenomenological description of the branching fractions.