Relativistic correction to e+e- → J/Ψ plus gg at B factories and constraint on color-octet matrix elements

We calculate the relativistic correction to J/Psi production in the color-singlet process e(+)e--> J/Psi gg at B factories. We employ the nonrelativistic QCD factorization approach, where the short-distance coefficients are calculated perturbatively and the long-distance matrix elements are extracted from the decays of J/Psi into e(+)e-and light hadrons. We find that the O(v(2)) relativistic correction can enhance the cross section by a factor of 20-30%, comparable to the enhancement due to the O(alpha(s)) radiative correction obtained earlier. Combining the relativistic correction with the QCD radiative correction, we find that the color-singlet contribution to ee(+)e--> J/Psi + gg can saturate the latest observed cross section sigma(e(+)e--> J/Psi + Chi(non-c (c) over bar)) = 0.43 +/- 0: 09 +/- 0. 09 pb by Belle, thus leaving little room to the color-octet contributions. This gives a very stringent constraint on the color-octet contribution, and may imply that the values of color-octet matrix elements are much smaller than expected earlier by using the naive velocity scaling rules or extracted from fitting experimental data with the leading-order calculations.