Power Corrections and Nonlocal Operators
We discuss power corrections to infrared safe cross sections and event shapes, and identify a nonperturbative function that governs 1/Q corrections to these quantities.
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arXiv subjects
George Sterman
Publications and source records attributed to George Sterman.
Resummation for QCD Hard Scattering
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.
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PQCD Analysis of Hard Scattering in Nuclei
We review the extension of the factorization formalism for perturbative QCD to soft initial- and final-state scattering associated with hard processes in nuclei.
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Hard Scattering in QCD
Recent developments in the theory and experiment of QCD hard scattering are described.
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Resummation in Heavy Quark and Jet Cross Sections
We discuss corrections from the elastic limit (partonic threshold) in hadronic hard-scattering cross sections. We show why these corrections can be large at all orders in perturbation theory, and describe their resummation to arbitrary logarithmic accuracy. In particular, we discuss the role of color exchange in the hard scattering. This enables us to generalize the resummation of the Drell-Yan cross section to QCD reactions. As an example, we give the explicit resummed hard-scattering cross section for heavy-quark production through light quark annihilation, which takes into account next-to-leading logarithms to all orders.
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Partons, Factorization and Resummation, TASI95
I review the treatment of high-energy QCD in Minkowski space, with an emphasis on factorization theorems as extensions of the operator product expansion. I discuss how the factorization properties of high-energy cross sections and amplitudes lead to evolution equations that resum large logarithms for two-scale problems.
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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 nonleading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of nonleading 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 $\overline{\rm MS}$ factorization schemes.
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On the Resummation of Singular Distributions in QCD Hard Scattering
We discuss the resummation of distributions that are singular at the elastic limit of partonic phase space (partonic threshold) in QCD hard-scattering cross sections, such as heavy quark production. We show how nonleading soft logarithms exponentiate in a manner that depends on the color structure within the underlying hard scattering. This result generalizes the resummation of threshold singularities for the Drell-Yan process, in which the hard scattering proceeds through color-singlet annihilation. We illustrate our results for the case of heavy quark production by light quark annihilation, and briefly discuss its extension to heavy quark production through gluon fusion.
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Soft Gluon Resummation
I discuss some of the basic techniques and results of soft gluon resummation, and their applications to scattering at collider energies.
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Proton-Proton Near-Forward Hard Elastic Scattering
We calculate the leading twist contribution to near-forward proton-proton (and proton-antiproton) elastic scattering with large momentum transfer, in the multiple scattering (Landshoff) mechanism. The amplitude in the near-forward region is dominated by singlet exchange for all three valence quark-quark scatterings. We assume the existence of a hard singlet quark-quark amplitude, which we estimate to be ${\cal O}(α_s^2/t)$. For a three-quark state whose transverse size is less than $1/Λ_{\rm QCD}$, Sudakov resummation accounts for both approximate $\d σ^{pp}/ \d t \sim t^{-8}$ at moderate $t$, and $\d σ^{pp}/ \d t \sim t^{-10}$ at larger $t$. The transition from approximate $t^{-8}$ to $t^{-10}$ behavior is strongly correlated with the transverse size of the valence three-quark state in the proton.
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Principal Value Resummation
We present a new resummation formula for the Drell-Yan cross section. The formal resummation of threshold corrections in Drell-Yan hard-scattering functions produces an exponent with singularities from the infrared pole of the QCD running coupling. Our reformulation treats such `infrared renormalons' by a principal value prescription, analogous to a modified Borel transform. The resulting expression includes all large threshold corrections to the hard scattering function as an asymptotic series in $α_s$, but is a finite function of $Q^2$. We find that the ambiguities of the resummed perturbation theory imply the presence of higher twist corrections to quark-antiquark hard-scattering functions that begin at $Λ_{QCD}/Q$. This suggests an important role for higher twist in the phenomonolgy of hadron-hadron inclusive cross sections. We also discuss the numerical evaluation of the exponent and its asymptotic perturbation series for representative values of $Q^2$.
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Color Exchange in Near-forward Hard Elastic Ecattering
We study the large-$t$ small angle behavior of quark-quark elastic scattering. We employ a factorization procedure previously developed for fixed angle scattering, which depends on the color structure of the factorized hard subprocess. We find an evolution in $t$ that (in leading logarithmic approximation) becomes diagonal in a singlet-octet basis in the $t$-channel as $s\rightarrow \infty$. Octet exhange in the hard scattering is associated with the familiar `reggeized', $s^{α_g(t)}$ behavior, which arises from $s$-dependence in Sudakov suppression. In contrast, Sudakov suppression for $t$-channel singlet exchange in the hard scattering is $s$-independent. In general, these contributions are mixed by soft corrections, which, however, cancel in many experimental amplitudes and cross sections.
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QCD Sum Rules and Compton Scattering
We extend QCD sum rule analysis to moderate energy fixed angle Compton scattering. In this kinematic region there is a strong similarity to the sum rule treatment of electromagnetic form factors, although the four-point amplitude requires a modification of the Borel transform. To illustrate our method, we derive the sum rules for helicity amplitudes in pion Compton scattering and estimate their large-$t$ behavior in the local duality approximation.
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