A description of χcJ → VV decays within the effective field theory framework

Abstract

We study χcJ → VV decays using the QCD effective field theory approach. The helicity suppressed decay amplitudes are also considered. The colour-singlet contributions of these amplitudes suffer from the endpoint singularities, it is shown that they can be absorbed into renormalisation of the nonfactorisable colour-octet matrix element. The latter can be associated with the colour-octet component of the charmonium wave function. The heavy quark spin symmetry makes it possible to establish the relationships between colour-octet matrix elements for different states χcJ up to higher order corrections in small velocity v. This allows us to estimate the polarisation parameters for χc2→ VV using data for χc0,1→ VV. This analysis is carried out for the available data on the χcJ→ ϕϕ decays.