Soft Photon Theorem in QCD with Massless Quarks.

Working to all orders in dimensionally regularized QCD with massless quarks, we study the radiation of a photon whose energy is much lower than that of external partons. The conventional soft photon theorem receives corrections at leading power in the photon energy, associated with soft virtual loops of massless fermions. These additive corrections give an overall factor times the nonradiative amplitude that is infrared finite and real to all orders in α_{s}. Based on recent calculations of the three-loop soft gluon current, we identify the lowest-order three-loop correction.

Factorized power expansion for high-pT heavy quarkonium production.

We show that when the factorized cross section for heavy quarkonium production includes next-to-leading power contributions associated with the production of the heavy quark pair at short distances, it naturally reproduces all high p(T) results calculated in nonrelativistic QCD (NRQCD) factorization. This extended formalism requires fragmentation functions for heavy quark pairs, as well as for light partons. When these fragmentation functions are themselves calculated using NRQCD, we find that two of the four leading NRQCD production channels, (3)S(1)([1]) and (1)S(0)([8]), are dominated by the next-to-leading power contributions for a very wide p(T) range. The large next-to-leading order corrections of NRQCD are absorbed into the leading order of the first power correction. The impact of this finding on heavy quarkonium production and its polarization is discussed.

Heavy quarkonium production and polarization.

We present a perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum p(T) at collider energies, which includes both the leading-power (LP) and next-to-leading-power (NLP) contributions to the cross section in the m(Q)(2)/p(T)(2) expansion for heavy quark mass m(Q). We estimate fragmentation functions in the nonrelativistic QCD formalism and reproduce the bulk of the large enhancement found in explicit next-to-leading-order calculations in the color-singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization.

Color transfer in associated heavy-quarkonium production.

We study the production of heavy quarkonium in association with an additional heavy pair. We argue that important contributions may come from phase space regions where three heavy fermions are separated by relative velocities much lower than the speed of light, and to which standard effective field theories do not apply. In this region, infrared sensitive color exchange is specific to the presence of the unpaired (anti)quark. This effect vanishes as the motion of the additional particle becomes relativistic with respect to the pair, and is completely absent for massless quarks and gluons in the final state.

Two-loop anomalous-dimension matrix for soft-gluon exchange.

The resummation of soft-gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2-->n massless processes for the first time at two loops. Using color-generator notation, we show that it is proportional to the one-loop matrix. This result reproduces all pole terms in dimensional regularization of the explicit calculations of massless 2-->2 amplitudes in the literature, and it predicts all poles at next-to-next-to-leading order in any 2-->n process that has been computed at next-to-leading order. The proportionality of the one- and two-loop matrices makes possible the resummation in closed form of the next-to-next-to-leading logarithms and poles in dimensional regularization for the 2-->n processes.