Search Results (44 total)

We study the transfer of color between a heavy quark pair and an unpaired heavy quark or antiquark moving at a nonrelativistic velocity with respect to the pair. We find that the open heavy quark or antiquark can catalyze the transformation of the pair from octet representation at short distances to singlet at long distances. This process is infrared sensitive in general, and we exhibit double poles in dimensional regularization at next-to-next-to-leading order in the transition probability. Because of their dependence on kinematic variables, these poles cannot be matched to the nonperturbative matrix elements of effective field theories based on a single heavy quark pair.

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.

The distributions of two-jet event shapes contain information on hadronization in QCD. Near the two-jet limit, these distributions can be described by convolutions of nonperturbative event shape functions with the same distributions calculated in resummed perturbation theory. The shape functions, in turn, are determined by correlations of momentum flow operators with each other and with lightlike Wilson lines, which describe the coupling of soft, wide-angle radiation to jets. We observe that leading power corrections to the mean values of event shapes are determined by the correlation of a single momentum flow operator with the relevant Wilson lines. This generalizes arguments for the universality of leading power corrections based on the low-scale behavior of the running coupling or resummation. We also show how a study of the angularity event shapes can provide information on correlations involving multiple momentum flow operators, giving a window to the system of QCD dynamics that underlies the variety of event shape functions. In deriving these results, we review, develop and compare factorization techniques in conventional perturbative QCD and soft-collinear effective theory (SCET). We give special emphasis to the elimination of double counting of momentum regions in these two formalisms.

We show that certain general properties of threshold and joint resummations in Drell-Yan cross sections hold as well for their crossed analogs in semi-inclusive deep-inelastic scattering and double-inclusive leptonic annihilation. We show that all plus-distribution corrections near threshold have the same structure, and are determined to all logarithmic order by two anomalous dimensions, one of which is a generalization of the D-term previously derived in Drell-Yan. We also discuss the possibility of universality in power corrections implied by the resummation.

We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order in heavy quarkonium production. We show that the infrared singularities in this process are consistent with nonrelativistic QCD factorization to all orders in the heavy quark relative velocity v. This factorization requires the gauge-completed matrix elements that we introduced previously to prove next-to-next-to-leading-order factorization to order v².

We extend the resummation of dimensionally regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that they are proportional to the corresponding one-loop matrices. Using the color-generator notation, we reproduce the two-loop single-pole quantities H⁽²⁾ introduced by Catani for quark and gluon elastic scattering. Our results also make possible threshold and a variety of other resummations at next-to-next-to-leading logarithm. All of these considerations apply to 2→n processes with massless external lines.

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.

We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the nonrelativistic QCD (NRQCD) formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include non-Abelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at next-to-next-to-leading order, and verify that they are absorbed into the new, gauge-invariant matrix elements.

It has recently been suggested that collisions of transversely polarized protons and antiprotons at the GSI could be used to determine the nucleon’s transversity densities from measurements of the double-spin asymmetry for the Drell-Yan process. We analyze the role of higher-order perturbative QCD corrections in this kinematic regime, in terms of the available fixed-order contributions as well as of all-order soft-gluon resummations. We find that the combined perturbative corrections to the individual unpolarized and transversely polarized cross sections are large. We trace these large enhancements to soft-gluon emission near partonic threshold, and we suggest that with a physically motivated cutoff enhancements beyond lowest order are moderated relative to resummed perturbation theory, but still significant. The unpolarized dilepton cross section for the GSI kinematics may therefore provide information on the relation of perturbative and nonperturbative dynamics in hadronic scattering. The spin asymmetry turns out to be rather robust, relatively insensitive to higher orders, resummation, and the cutoffs.

We study a class of nonperturbative corrections to single-inclusive photon cross sections at measured transverse momentum p_T, in the large-x_T limit. We develop an extension of the joint (threshold and transverse momentum) resummation formalism, appropriate for large x_T, in which there are no kinematic singularities associated with recoil, and for which matching to fixed-order and to threshold resummation at next-to-leading logarithm (NLL) is straightforward. Beyond NLL, we find contributions that can be attributed to recoil from initial-state radiation. Associated power corrections occur as inverse powers of p_T² and are identified from the infrared structure of integrals over the running coupling. They have significant energy-dependence and decrease from typical fixed-target to collider energies. Energy conservation, which is incorporated into joint resummation, moderates the effects of perturbative recoil and power corrections for large x_T.

We study the application of the joint resummation formalism to Higgs boson production via gluon-gluon fusion at the CERN LHC, defining inverse transforms by analytic continuation. We work at next-to-leading logarithmic accuracy. We find that at low Q_T the resummed Higgs Q_T distributions are comparable in the joint and pure-Q_T formalisms, with a relatively small influence from threshold enhancement in this range. We find a modest (about ten percent) decrease in the inclusive cross section, relative to pure threshold resummation.

We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. These correlations are formulated for a general set of event shapes, which includes jet broadening and thrust as special cases. We illustrate the method for e⁺e^- dijet events, and calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at a measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Fermilab Tevatron collider.

We study the distribution of transverse energy, Q_Ω, radiated into an arbitrary interjet angular region Ω in high-p_T two-jet events. Using an approximation that emphasizes radiation directly from the partons that undergo the hard scattering, we find a distribution that can be extrapolated smoothly to Q_Ω=Λ_QCD, where it vanishes. This method, which we apply numerically in a valence quark approximation, provides a class of predictions on transverse energy radiated between jets, as a function of jet energy and rapidity, and of the choice of the region Ω in which the energy is measured. We discuss the relation of our approximation to the radiation from unobserved partons of intermediate energy, whose importance was identified by Dasgupta and Salam.

We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic energy. It reproduces threshold resummation for high-p_T single-particle cross sections, when recoil is neglected, and Q_T resummation at low Q_T, when higher-order threshold logarithms are suppressed. We exhibit explicit resummed cross sections, accurate to next-to-leading logarithm, for electroweak annihilation and prompt photon inclusive cross sections.

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 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 BNL RHIC. We argue that our perturbative calculation for the asymmetries is relevant to pion transverse momenta as low as a few GeV.

A leading twist expansion in terms of bilocal operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit x→1, which is also applicable to a range of other 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^kN/N are shown to be resummable in terms of the anomalous dimension of the leading operator in the expansion.

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 pp̅ scattering, using a valence quark approximation, reproduces the overall features observed at the Fermilab 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.

The elements, theoretical basis, and experimental status of perturbative quantum chromodynamics are presented. Relevant field-theoretic methods are introduced at a nonspecialist level, along with a review of the basic ideas and methods of the parton model. This is followed by an account of the fundamental theorems of quantum chromodynamics, which generalize the parton model. Summaries of the theoretical and experimental status of the most important hard-scattering processes are then given, including electron-positron annihilation, deeply inelastic scattering, and hard hadron-hadron scattering, as induced both by electoweak interactions and by quantum chromodynamics directly. In addition, a discussion is presented of the global fitting approach to the determination of parton distributions in nucleons.

We derive the anomalous nuclear dependence of jet cross sections in deeply inelastic scattering and photoproduction, in terms of twist-four parton distributions in nuclei. This paper presents details of the use of factorization at higher twist to describe multiple scattering in nuclei, and the methods described here are applicable to a variety of other high-p_T cross sections.

Using heavy quark effective field theory, exponentiation of Sudakov double logarithms, and perturbative factorization theorems for exclusive processes, we calculate the amplitude for the semileptonic decay of mesons with a single, very heavy quark into π and ρ for a large hadronic recoil momentum. A formula for these large-recoil widths is obtained in terms of two-particle wave functions of the heavy and light mesons and applied to semileptonic decays of the B.

We analyze anomalous nuclear enhancement in the photoproduction of jets as a higher-twist process in perturbative QCD. We use the Fermilab E683 data on dijet momentum imbalance to estimate the size of the relevant twist-4 parton distributions. We find that twist-4 matrix elements are of the order of 0.05-0.1 GeV² times typical twist-2 parton distributions. We discuss a physical interpretation of the nuclear enhancement as a measure of the average net transverse color force on an off-shell parton moving through nuclear matter, and give an order-of-magnitude estimate for the typical squared transverse field strengths encountered by a fast moving parton.

Using generalized factorization theorems, we calculate the leading single transverse spin asymmetry for high transverse-momentum direct-photon production in pp collisions, in terms of partonic matrix elements. The leading contribution comes from a ‘‘twist-3’’ parton distribution, involving the correlation between quark fields and the gluonic field strength. With simple assumptions for this matrix element, the asymmetry increases with x_F, naturally giving effects of 10% or more at large x_F.

We exhibit a solution to the evolution equation for the Sudakov form factor in QCD with massless quarks, which exponentiates infrared poles in dimensional continuation as well as logarithms of momentum transfer. We use this solution to construct an expression for the absolute value of the ratio of timelike to spacelike form factors, in which the infrared finiteness of the ratio is manifest. Finally, we compare this result to explicit calculations of the form factor available in the literature. Most of the large two-loop corrections to the absolute value of the ratio come from the exponentiation of one-loop corrections, including the effect of the running coupling.