A description of $\chi_{cJ}\to VV$ decays within the effective field theory framework

We study $\chi_{cJ}\to VV$ 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 $\chi_{cJ}$ up to higher order corrections in small velocity $v$. This allows us to estimate the polarisation parameters for $\chi_{c2}\to VV$ using data for $\chi_{c0,1}\to VV$. This analysis is carried out for the available data on the $\chi_{cJ}\to \phi\phi$ decays.