Resumming the color-octet contribution toe+e−→J/ψ+X

Recent observations of the spectrum of $J/\psi$ produced in $e^{+}{e}^{-}$ collisions at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance are in conflict with fixed-order calculations using the nonrelativistic QCD effective field theory. One problem is that leading order color-octet mechanisms predict an enhancement of the cross section for $J/\psi$ with a maximal energy that is not observed in the data. However, in this region of phase space large perturbative corrections (Sudakov logarithms) as well as enhanced nonperturbative effects are important. In this paper we use the newly developed soft-collinear effective theory (SCET) to systematically include these effects. We find that these corrections significantly broaden the color-octet contribution to the $J/\psi$ spectrum. Our calculation employs a one-stage renormalization group evolution rather than the two-stage evolution used in previous SCET calculations. We give a simple argument for why the two methods yield identical results to lowest order in the SCET power counting.