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

We study χ_cJ → 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 χ_cJ up to higher order corrections in small velocity v. This allows us to estimate the polarisation parameters for χ_c2 → VV using data for χ_c0,1 → VV. This analysis is carried out for the available data on the χ_cJ → ϕϕ decays.