George F. Sterman

Transverse momentum distribution in Drell-Yan pair and W and Z boson production

Abstract We exhibit and discuss the QCD prediction for the transverse momentum distribution of W bosons, Z bosons and high-mass virtual photons produced in high-energy hadron-hadron collisions. Recent work has shown that this prediction is consistent with the structure of leading twist initial state interactions. The expression we present is expected to give results correct up to order αsN(Q) for anyQT when the boson mass Q is very large (> 108 GeV!), given only input from perturbative calculations at order αsN+2 and deeply inelastic scattering structure functions. We specify the required N = 0 coefficients, employing the order αs2 results of Kodaira and Trentadue and of Davies and Stirling. We then show how the expression should be modified to deal with current energy scales. We also discuss the connection between low-QT and high-QT formulae.

Factorization of Hard Processes in QCD

We summarize the standard factorization theorems for hard processes in QCD, and describe their proofs.

Summation of large corrections to short-distance hadronic cross sections

Abstract The large soft gluon corrections to short-distance hadronic cross sections are summed to all orders in perturbation theory. The arguments apply to any cross section whose Born contribution is initiated by quarks, including Drell-Yan and heavy vector boson cross sections. The exponentiation of leading and non-leading ln(n) terms in moments of these cross sections is verified. In particular, the ln3(n) terms computed by van Neervan at two loops are rederived on the basis of one-loop calculations.

Hard elastic scattering in QCD: Leading behavior

We derive the asymptotic behavior of elastic meson-meson and baryon-baryon scattering at high energy and fixed angle. Our results organize both Sudakov and nonleading logarithmic corrections to independent (Landshoff) scatterings of valence quarks. We show how to separate these contributions systematically from single-scattering contributions, in a manner which suggests that the complete amplitudes should be computable perturbatively down to the dimensional counting power, in terms of hadronic wave functions.

Factorization for short distance hadron-hadron scattering

Abstract We show that factorization holds at leading twist in the Drell-Yan cross section dσ/dQ2dy and related inclusive hadron-hadron cross sections. We review the heuristic arguments for factorization, as well as the difficulties which must be overcome in a proof. We go on to give detailed arguments for the all order cancellation of soft gluons, and to show how this leads to factorization.

The Perturbative pion form-factor with Sudakov suppression

Abstract We give a modified perturbative expression for the pion electromagnetic form factor in perturbative QCD, which includes Sudakov suppression of the elastic scattering of quarks that are isolated in space. Beyond momentum transfers of 20Λ QCD the perturbative calculation becomes relatively insensitive to soft gluon exchange. Our analysis involves no phenomenological parameters such as a gluon mass, and may be applied to the proton form factor.

RESUMMATION FOR QCD HARD SCATTERING

Abstract We resum distributions that are singular at partonic threshold (the elastic limit) in heavy quark production, in terms of logarithmic behavior in moment space. The method may be applied to a variety of cross sections sensitive to the edge of phase space, including transverse momentum distributions. Beyond leading logarithm, dependence on the moment variable is controlled by a matrix renormalization group equation, reflecting the evolution of composite operators that represent the color structure of the underlying hard scattering. At next-to-leading logarithmic accuracy, these evolution equations may be diagonalized, and moment dependence in the cross section is a sum of exponentials. Beyond next-to-leading logarithm, resummation involves matrix-ordering. We give a detailed analysis for the case of heavy quark production by light quark annihilation and gluon fusion.

Evolution of color exchange in QCD hard scattering

Abstract In QCD hard scattering cross sections, the color content of the underlying hard scattering evolves with a factorization scale. This evolution is controlled by an anomalous dimension matrix, specific to each hard-scattering reaction. Anomalous dimensions are determined from the renormalization of products of ordered exponentials of the gauge field, which describe the coherent radiation of gluons by incoming hadrons and the observed jets or particles of the final state. The anomalous dimensions depend on the kinematics of the underlying hard scattering, but are free of collinear singularities. A number of these matrices are available in the literature. Here, we exhibit one-loop mixing matrices for the full list of 2 → 2 reactions involving light quarks and gluons. The eight-by-eight anomalous dimension matrix for gluon-gluon scattering shows a simplified structure in the basis corresponding to definite color exchange in the t -channel.

Sudakov factorization and resummation

We present a unified derivation of the resummation of Sudakov logarithms, directly from the factorization properties of cross sections in which they occur. We rederive in this manner the well-known exponentiation of leading and non-leading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. The relevant factorization theorems are known to hold for many such cross sections of interest, and we conjecture that they apply even more widely. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of non-leading logarithms requires in general mixing in the space of the color tensors of the hard scattering. The exponentiation of Sudakov logarithms implies that many weighted cross sections obey particular evolution equations in momentum transfer, which streamline the computation of their Sudakov exponents. We illustrate this method with the resummation of soft-gluon enhancements of the inclusive Drell-Yan cross section, in both DIS and MS factorization schemes.

Single transverse-spin asymmetries in hadronic pion production

We analyze single transverse-spin asymmetries for hadronic pion production at large transverse momenta using QCD factorization. In the large