Colour-octet contributions to exclusive charmonium decays

Abstract

We investigate the theoretical uncertainties of $P$-wave charmonium decays into two pions, ${\chi }_{\stackrel{¸}{J}}\to {\pi }^{+}{\pi }^{-}$, ${\pi }^0{\pi }^0$. 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 $|\stackrel{¸}{\text{cbar}}\text{g}>$ of the ${\chi }_{\stackrel{¸}{J}}$ wave function is actually not power suppressed with respect to the usual colour-singlet decay arising from the dominant $|\stackrel{¸}{\text{cbar}}>$ Fock state. An explicit calculation yields an agreement with the data for a very reasonable value for the single extra non-perturbative parameter.

Comments: 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/