Colour-octet contributions to exclusive charmonium decays

We investigate the theoretical uncertainties of $P$-wave charmonium decays into two pions, $\chi_{\c J}\rightarrow \pi^+\pi^-$, $\pi^0\pi^0$. Constraining the pion distribution-amplitude from the recent precise data on $F_{\pi\gamma}(Q^2)$, we find an order-of-magnitude discrepancy between data and prediction. The disagreement persists even after inclusion of transverse degrees of freedom and Sudakov suppressions. We propose the colour-octet mechanism as the solution to the puzzle. The colour-octet decay contribution arising from the higher Fock component $|\c \cbar \g >$ of the $\chi_{\c J}$ wave function is actually not power suppressed with respect to the usual colour-singlet decay arising from the dominant $|\c \cbar >$ Fock state. An explicit calculation yields an agreement with the data for a very reasonable value for the single extra non-perturbative parameter.