Gluon fragmentation into quarkonium at next-to-leading order

We present the first calculation at next-to-leading order (NLO) in $alpha_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in $4-2epsilon$ dimensions. We also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.

Charm-pair Rescattering Mechanism for Charmonium Production in High-energy Collisions

A new mechanism for heavy quarkonium production in high-energy collisions called the s-channel cut was proposed in 2005 by Lansberg, Cudell, and Kalinovsky. We identify this mechanism physically as the production of a heavy quark and anti-quark that are on-shell followed by their rescattering to produce heavy quarkonium. We point out that in the NRQCD factorization formalism this rescattering mechanism is a contribution to the color-singlet model term at next-to-next-to-leading order in perturbation theory. Its leading contribution to the production rate can be calculated without introducing any additional phenomenological parameters. We calculate the charm-pair rescattering (or s-channel cut) contribution to the production of J/psi at the Tevatron and compare it to estimates by Lansberg et al. using phenomenological models. This contribution competes with the leading-order term in the color-singlet model at large transverse momentum but is significantly smaller than the next-to-leading-order term. We conclude that charm-pair rescattering is not a dominant mechanism for charmonium production in high-energy collisions.