arXiv subjects
Publications and source records attributed to George Sterman.
Parton distribution functions are determined by the comparison of finite-order calculations with data. We briefly discuss the interplay of higher order corrections and PDF determinations, and the use of soft-gluon resummation in global fits.
We exhibit a method for simultaneously treating recoil and threshold corrections in single-photon inclusive cross sections, working within the formalism of collinear factorization. This approach conserves both the energy and transverse momentum of resummed radiation. At moderate p_T, we find the potential for substantial enhancements from higher-order perturbative and power-law nonperturbative corrections.
We discuss a formalism in which high-$p_T$ dijet rapidity gaps are identified by energy flow in the interjet region. When the gap energy, $Q_{\rm gap}$, is sufficiently large, the cross section may be computed from standard factorization theorems. For $p_T\gg Q_T\ggΛ_{\rm QCD}$, this is a two-scale perturbative problem, in which we may resum logarithms of $Q_{\rm gap}/p_T$. The cross section computed as a function of $Q_{\rm gap}$ reproduces many of the features of the Tevatron dijet gap data. The factorized cross section gives meaning to the color content of the hard scattering.
Threshold resummation for factorizable cross sections in hadron-hadron collisions has a number of applications and extensions. We discuss factorization scale dependence, resummation at nonleading power in the moment variable, and the implications of resummation for power corrections in the hard momentum scale.
We review some techniques of resummation applied to heavy quark production in hadronic scattering and electroproduction near partonic threshold, and discuss the reduction of factorization scale dependence in resummed cross sections.
The past few years have seen remarkable progress in the theory and phenomenology of QCD, bringing perturbative and nonperturbative methods into closer contact with each other and with experiment.
A leading twist expansion in terms of bilocal operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other hard quasi-elastic processes. Operators of increasing dimensions contribute to logarithmically enhanced terms, which are suppressed by corresponding powers of $1-x$. For the longitudinal structure function in moment $(N)$ space all the logarithmic contributions of order $\ln^k N/N$ are shown to be resummable in terms of the anomalous dimension of the leading operator in the expansion.
Penguin diagrams for decays such as $b\to (s,d)γ$ involve virtual loops of $u$ or other light quarks. Logarithms of the virtual quark mass could, in principle, influence the phenomenological analysis of the decay. It is thus important to study these logarithms to all orders in QCD perturbation theory. In this paper we show that, at arbitrary order, the matrix elements of operators in the effective hamiltonian contributing to $b\to sγ$ are finite for the limit of $m_u \to 0$ in penguin loops.
I give a pedagogical introduction to resummation and power corrections, using the thrust variable in electron-positron annihilation as an example, followed by an discussion of issues of predictability in perturbative QCD.
When rapidity gaps in high-$p_T$ dijet events are identified by energy flow in the central region, they may be calculated from factorized cross sections in perturbative QCD, up to corrections that behave as inverse powers of the central region energy. Although power-suppressed corrections may be important, a perturbative calculation of dijet rapidity gaps in ${\rm p}\bar{\rm p}$ scattering successfully reproduces the overall features observed at the Tevatron. In this formulation, the average color content of the hard scattering is well-defined. We find that hard dijet rapidity gaps in quark-antiquark scattering are not due to singlet exchange alone.
We analyze single transverse-spin asymmetries for hadronic pion production at large transverse momenta using QCD factorization. In the large $x_F$ region, leading contributions to the asymmetries are naturally produced by twist-3 parton correlation functions that couple quark fields and gluon field strengths. With a simple model for these matrix elements, leading-order asymmetries calculated from QCD are consistent with data on pion production from Fermilab, and can be used to predict single-spin asymmetries at RHIC. We argue that our perturbative calculation for the asymmetries is relevant to pion transverse momenta as low as a few GeV.
We show that existing proofs of factorization imply the cancellation of certain multiladder contributions that Gotsman, Levin, and Maor had suggested would invalidate the basic factorization theorem in QCD. No modifications of the original argument are necessary, although the details of the example offer useful insight into the mechanisms of factorization.
We discuss threshold resummation for dijet production in hadronic collisions. Resummation to next-to-leading logarithmic (NLL) accuracy is given in terms of an anomalous dimension matrix for each partonic subprocess involved.
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 $2 \to 2$ 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.
We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factorization of coherent soft gluons from the hard scattering. The precise formulas depend on the partonic scattering angles and energies, as well as on the method used to define the jets in the final state. For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass. Other choices of dijet cross section can give, however, qualitatively different behavior, even at leading logarithm.
Some of the experimental and theoretical results discussed at the Fifth International Workshop on Deep Inelastic Scattering and QCD are reviewed.
The electromagnetic form factors of hadrons at large momentum transfer have been the subject of intense theoretical and experimental scrutiny over the past two decades, yet there is still not a universally-accepted framework for their description. This review is a synopsis of their current status at large momentum transfer. The basic theoretical approaches to form factors at large momentum transfer are developed, emphasizing the valence quark and Feynman (soft) pictures. The discussion includes the relation of these descriptions to the parton model, as well as the roles of factorization, evolution, Sudakov resummation and QCD sum rules. This is followed by a discussion of the experimental status of pion and nucleon elastic form factors and resonance production amplitudes in the light of recent data, highlighting the successes and shortcomings of various theoretical proposals.
We describe the resummation of singular distributions at partonic threshold in heavy quark production, generalizing results for Drell-Yan and other electroweak hard-scattering processes.