Colour-octet contributions to exclusive charmonium decays

Abstract

We investigate the theoretical uncertainties of $P$-wave charmonium decays into two pions, $\ddot{I}{‡}_{\stackrel{¸}{J}}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$, $\ddot{I}{€}^0\ddot{I}{€}^0$. Constraining the pion distribution-amplitude from the recent precise data on $F_{\ddot{I}€{\hat{I}}^3}(Q^2)$, 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 $\ddot{I}{‡}_{\stackrel{¸}{J}}$ 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.

12 pages Latex, 3 PS-files of figures, uses macros 'amstex' and 'psfig'; also available by anonymous ftp from ftp://wpts0.physik.uni-wuppertal.de/pub/bolz/pwav/