Search

In this report, we present a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories., Comment: 92 pages, 7 figures

We consider high-mass systems of two or more particles that are produced by QCD hard scattering in hadronic collisions. We examine the azimuthal correlations between the system and one of its particles. We point out that the perturbative QCD computation of such azimuthal correlations and asymmetries can lead to divergent results at fixed perturbative orders. The fixed-order divergences affect basic (and infrared safe) quantities such as the total cross section at fixed (and arbitrary) values of the azimuthal-correlation angle $\varphi$. Examples of processes with fixed-order divergences are heavy-quark pair production, associated production of vector bosons and jets, dijet and diboson production. A noticeable exception is the production of high-mass lepton pairs through the Drell--Yan mechanism of quark-antiquark annihilation. However, even in the Drell--Yan process, fixed-order divergences arise in the computation of QED radiative corrections. We specify general conditions that produce the divergences by discussing their physical origin in fixed-order computations. We show lowest-order illustrative results for $\cos(n\varphi)$ asymmetries (with $n=1,2,4,6$) in top-quark pair production and associated production of a vector boson and a jet at the LHC. The divergences are removed by a proper all-order resummation procedure of the perturbative contributions. Resummation leads to azimuthal asymmetries that are finite and computable. We present first quantitative results of such a resummed computation for the $\cos(2\varphi)$ asymmetry in top-quark pair production at the LHC., Comment: 43 pages, 5 eps figures

We consider the production of a pair of heavy quarks ($Q{\bar Q}$) in hadronic collisions. When the transverse momentum $q_T$ of the heavy-quark pair is much smaller than its invariant mass, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all-orders. This behavior is well known from the simpler case of hadroproduction of colourless high-mass systems, such as vector or Higgs boson(s). In the case of $Q{\bar Q}$ production, the final-state heavy quarks carry colour charge and are responsible for additional soft radiation (through direct emission and interferences with initial-state radiation) that complicates the evaluation of the logarithmically-enhanced terms in the small-$q_T$ region. We present the all-order resummation structure of the logarithmic contributions, which includes colour flow evolution factors due to soft wide-angle radiation. Resummation is performed at the completely differential level with respect to the kinematical variables of the produced heavy quarks. Soft-parton radiation produces azimuthal correlations that are fully taken into account by the resummation formalism. These azimuthal correlations are entangled with those that are produced by initial-state collinear radiation. We present explicit analytical results up to next-to-leading order and next-to-next-to-leading logarithmic accuracy., Comment: Some comments expanded and references added. Version published on NPB

We consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. We show that the recent computation of the soft-virtual corrections to Higgs boson production at N$^3$LO [1] together with the universality structure of soft-gluon emission can be exploited to extract the general expression of the hard-virtual coefficient that contributes to threshold resummation at N$^3$LL accuracy. The hard-virtual coefficient is directly related to the process-dependent virtual amplitude through a universal (process-independent) factorization formula that we explicitly evaluate up to three-loop order. As an application, we present the explicit expression of the soft-virtual N$^3$LO corrections for the production of an arbitrary colourless system. In the case of the Drell-Yan process, we confirm the recent result of Ref.[2]., Comment: Slightly expanded text, one reference added, version published on NPB

We consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. The logarithmically-enhanced contributions at small transverse momentum are treated to all perturbative orders by a universal resummation formula that depends on a single process-dependent hard factor. We show that the hard factor is directly related to the all-order virtual amplitude of the corresponding partonic process. The direct relation is universal (process independent), and it is expressed by an all-order factorization formula that we explicitly evaluate up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. Once the NNLO scattering amplitude is available, the corresponding hard factor is directly determined: it controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy, and it can be used in applications of the q_T subtraction formalism to perform fully-exclusive perturbative calculations up to NNLO. The universality structure of the hard factor and its explicit NNLO form are also extended to the related formalism of threshold resummation., Comment: References added. Version accepted for publication on NPB

We consider the cross section for one-particle inclusive production at high transverse momentum in hadronic collisions. We present the all-order resummation formula that controls the logarithmically-enhanced perturbative QCD contributions to the partonic cross section in the threshold region, at fixed rapidity of the observed parton (hadron). The explicit resummation up to next-to-leading logarithmic accuracy is supplemented with the computation of the general structure of the near-threshold contributions to the next-to-leading order cross section. This next-to-leading order computation allows us to extract the one-loop hard-virtual amplitude that enters into the resummation formula. This is a necessary ingredient to explicitly extend the soft-gluon resummation beyond the next-to-leading logarithmic accuracy. These results equally apply to both spin-unpolarized and spin-polarized scattering processes., Comment: References added. Version published on Nucl. Phys. B

We consider QCD radiative corrections to vector-boson production in hadron collisions. We present the next-to-next-to-leading order (NNLO) result of the hard-collinear coefficient function for the all-order resummation of logarithmically-enhanced contributions at small transverse momenta. The coefficient function controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy. The same coefficient function is used in applications of the subtraction method to perform fully-exclusive perturbative calculations up to NNLO., Comment: 13, pages, no figures. arXiv admin note: text overlap with arXiv:1106.4652

We consider the production of the Standard Model Higgs boson through the gluon fusion mechanism in hadron collisions. We present the next-to-next-to-leading order (NNLO) QCD result of the hard-collinear coefficient function for the all-order resummation of logarithmically-enhanced contributions at small transverse momentum. The coefficient function controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy. The same coefficient function is used in applications of the subtraction method to perform fully-exclusive perturbative calculations up to NNLO., Comment: Few technical details added in Eqs.(34)-(38) and accompanying text, typos corrected in Eq.(23)

We consider the production of a generic system of non-strongly interacting particles with a high total invariant mass M in hadron collisions. We examine the transverse-momentum (q_T) distribution of the system in the small-q_T region (q_T << M), and we present a study of the perturbative QCD contributions that are enhanced by powers of large logarithmic terms of the type ln (M^2/q_T^2). These terms can be resummed to all orders in QCD perturbation theory. The partonic production mechanism of the final-state system can be controlled by quark-antiquark (qqbar) annihilation and/or by gluon fusion. The resummation formalism for the qqbar annihilation subprocess is well established, and it is usually extrapolated to the gluon fusion subprocess. We point out that this naive extrapolation is not correct, and we present the all-order resummation formula for the q_T distribution in gluon fusion processes. The gluon fusion resummation formula has a richer structure than the resummation formula in qqbar annihilation. The additional structure originates from collinear correlations that are a specific feature of the evolution of the colliding hadrons into gluon partonic states. In the q_T cross section at small values of q_T, these gluon collinear correlations produce coherent spin correlations between the helicity states of the initial-state gluons and definite azimuthal-angle correlations between the final-state particles of the observed high-mass system., Comment: 27 pages, no figures

We consider the transverse-momentum (q_T) distribution of Drell--Yan lepton pairs produced in hadron collisions. At small values of q_T, we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. At intermediate and large values of q_T, we consistently combine resummation with the known next-to-leading order perturbative result. All perturbative terms up to order alpha_S^2 are included in our computation which, after integration over q_T, reproduces the known next-to-next-to-leading order result for the Drell--Yan total cross section. We show and discuss the reduction in the scale dependence of the results with respect to lower-order calculations, estimating the corresponding perturbative uncertainty. We present a preliminary comparison with Tevatron Run II data., Comment: Additional details shown in Fig.3. Note added on the quantitative effect of the coefficient A^{(3)}

We consider the production of W bosons in hadron collisions, and the subsequent leptonic decay W->lnu_l. We study the asymmetry between the rapidity distributions of the charged leptons, and we present its computation up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. Our calculation includes the dependence on the lepton kinematical cuts that are necessarily applied to select W-> lnu_l events in actual experimental analyses at hadron colliders. We illustrate the main differences between the W and lepton charge asymmetry, and we discuss their physical origin and the effect of the QCD radiative corrections. We show detailed numerical results on the charge asymmetry in ppbar collisions at the Tevatron, and we discuss the comparison with some of the available data. Some illustrative results on the lepton charge asymmetry in pp collisions at LHC energies are presented., Comment: 37 pages, 21 figures

We consider QCD radiative corrections to the production of W and Z bosons in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposed version of the subtraction formalism. The calculation includes the gamma-Z interference, finite-width effects, the leptonic decay of the vector bosons and the corresponding spin correlations. Our calculation is implemented in a parton level Monte Carlo program. The program allows the user to apply arbitrary kinematical cuts on the final-state leptons and the associated jet activity, and to compute the corresponding distributions in the form of bin histograms. We show selected numerical results at the Tevatron and the LHC., Comment: 7 pages, 3 ps figures

We consider transverse-momentum (q_T) resummation for Drell--Yan lepton pair production in hadron collisions. At small values of q_T, the logarithmically-enhanced QCD contributions are resummed up to next-to-leading logarithmic accuracy. At intermediate and large values of q_T, resummation is consistently combined with the fixed-order perturbative result. We present numerical results for e^+e^- pairs from the decay of Z bosons produced at Tevatron energies. We perform a detailed study of the scale dependence of the results to estimate the corresponding perturbative uncertainty. We comment on the comparison with the available Tevatron data., Comment: 24 pages, 12 ps figures, added comments and references; results unchanged

Report of the Working Group on Higgs Bosons for the Workshop, ``Physics at TeV Colliders'', Les Houches, France, 11-29 June, 2007., Comment: 102 pages, 68 figures

We consider Higgs boson production through gluon--gluon fusion in hadron collisions. We present a numerical program that computes the cross section up to NNLO in QCD perturbation theory. The program includes the decay modes H->gamma-gamma, H->WW->lnulnu, H->ZZ->4leptons, and allows the user to apply arbitrary cuts on the momenta of the partons and of the photons or leptons that are produced in the final state., Comment: 6 pages, to appear in the proceedings of the 8th International Symposium on Radiative Corrections, RADCOR 2007, Florence, Italy

We consider Higgs boson production by gluon fusion in hadron collisions. We study the doubly-differential transverse-momentum (q_T) and rapidity (y) distribution of the Higgs boson in perturbative QCD. In the region of small q_T (q_T << M_H, M_H being the mass of the Higgs boson), we include the effect of logarithmically-enhanced contributions due to multiparton radiation to all perturbative orders. We use the impact parameter and double Mellin moments to implement and factorize the multiparton kinematics constraint of transverse- and longitudinal-momentum conservation. The logarithmic terms are then systematically resummed in exponential form. At small q_T, we perform the all-order resummation of large logarithms up to next-to-next-to-leading logarithmic accuracy, while at large q_T (q_T ~ M_H), we apply a matching procedure that recovers the fixed-order perturbation theory up to next-to-leading order. We present quantitative results for the differential cross section in q_T and y at the LHC, and we comment on the comparison with the q_T cross section integrated over y., Comment: References added

We consider higher-order QCD corrections to the production of colourless high-mass systems (lepton pairs, vector bosons, Higgs bosons,...) in hadron collisions. We propose a new formulation of the subtraction method to numerically compute arbitrary infrared-safe observables for this class of processes. To cancel the infrared divergences, we exploit the universal behaviour of the associated transverse-momentum (q_T) distributions in the small-q_T region. The method is illustrated in general terms up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. As a first explicit application, we study Higgs boson production through gluon fusion. Our calculation is implemented in a parton level Monte Carlo program that includes the decay of the Higgs boson in two photons. We present selected numerical results at the LHC., Comment: References added

This Report summarises the activities of the "SM and Higgs" working group for the Workshop "Physics at TeV Colliders", Les Houches, France, 2-20 May, 2005. On the one hand, we performed a variety of experimental and theoretical studies on standard candles (such as W, Z, and ttbar production), treating them either as proper signals of known physics, or as backgrounds to unknown physics; we also addressed issues relevant to those non-perturbative or semi-perturbative ingredients, such as Parton Density Functions and Underlying Events, whose understanding will be crucial for a proper simulation of the actual events taking place in the detectors. On the other hand, several channels for the production of the Higgs, or involving the Higgs, have been considered in some detail. The report is structured into four main parts. The first one deals with Standard Model physics, except the Higgs. A variety of arguments are treated here, from full simulation of processes constituting a background to Higgs production, to studies of uncertainties due to PDFs and to extrapolations of models for underlying events, from small-$x$ issues to electroweak corrections which may play a role in vector boson physics. The second part of the report treats Higgs physics from the point of view of the signal. In the third part, reviews are presented on the current status of multi-leg, next-to-leading order and of next-to-next-to-leading order QCD computations. Finally, the fourth part deals with the use of Monte Carlos for simulation of LHC physics., Comment: 234 pages, 173 figures. Web page of the workshop (with links to the talks): http://lappweb.in2p3.fr/conferences/LesHouches/Houches2005/

We consider the transverse-momentum (q_T) distribution of generic high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. At small q_T, we concentrate on the all-order resummation of the logarithmically-enhanced contributions in QCD perturbation theory. We elaborate on the $b$-space resummation formalism and introduce some novel features: the large logarithmic contributions are systematically exponentiated in a process-independent form and, after integration over q_T, they are constrained by perturbative unitarity to give a vanishing contribution to the total cross section. At intermediate and large q_T, resummation is consistently combined with fixed-order perturbative results, to obtain predictions with uniform theoretical accuracy over the entire range of transverse momenta. The formalism is applied to Standard Model Higgs boson production at LHC energies. We combine the most advanced perturbative information available at present for this process: resummation up to next-to-next-to-leading logarithmic accuracy and fixed-order perturbation theory up to next-to-leading order. The results show a high stability with respect to perturbative QCD uncertainties., Comment: 48 pages, 13 postscript figures

Theoretical progress in Higgs boson production and background processes is discussed with particular emphasis on QCD corrections at and beyond next-to-leading order as well as next-to-leading order electroweak corrections. The residual theoretical uncertainties of the investigated processes are estimated in detail. Moreover, recent investigations of the MSSM Higgs sector and other extensions of the SM Higgs sector are presented. The potential of the LHC and a high-energy linear e+e- collider for the measurement of Higgs couplings is analyzed., Comment: 169 pages, Proceedings 3rd Les Houches Workshop: Physics at TeV Colliders, Les Houches, France, 26 May - 6 Jun 2003

We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sudakov weights associated to the cross section kinematics. We explicitly illustrate the application to the case of Drell--Yan and prompt-photon production., Comment: 13 pages, LaTeX

We consider QCD corrections to Higgs boson production through gluon--gluon fusion in hadron collisions. We compute the cross section, performing the all-order resummation of multiple soft-gluon emission at next-to-next-to-leading logarithmic level. Known fixed-order results (up to next-to-next-to-leading order) are consistently included in our calculation. We give phenomenological predictions for Higgs boson production at the Tevatron and at the LHC. We estimate the residual theoretical uncertainty from perturbative QCD contributions. We also quantify the differences obtained by using the presently available sets of parton distributions., Comment: 44 pages, 17 postscript figures

We consider the transverse-momentum (q_T) distribution of Higgs bosons produced at hadron colliders. We use a formalism that uniformly treats both the small-q_T and large-q_T regions in QCD perturbation theory. At small q_T (q_T << M_H, M_H being the mass of the Higgs boson), we implement an all-order resummation of logarithmically-enhanced contributions up to next-to-next-to-leading logarithmic accuracy. At large q_T (q_T \gtap M_H), we use fixed-order perturbation theory up to next-to-leading order. The resummed and fixed-order approaches are consistently matched by avoiding double-counting in the intermediate-q_T region. In this region, the introduction of unjustified higher-order terms is avoided by imposing unitarity constraints, so that the integral of the q_T spectrum exactly reproduces the perturbative result for the total cross section up to next-to-next-to-leading order. Numerical results at the LHC are presented. These show that the main features of the q_T distribution are quite stable with respect to perturbative QCD uncertainties., Comment: 9 pages, 2 postscript figures

We consider Higgs boson production through gluon--gluon fusion in hadron collisions, when a veto is applied on the transverse momenta of the accompanying hard jets. We compute the QCD corrections to this process at NLO and NNLO, and present numerical results at the Tevatron and the LHC., Comment: 5 pages, 4 ps figures, presented at the XXXVIIth Rencontres de Moriond, QCD and Hadronic interactions, Les Arc1800, France

This Report documents the results obtained by the Working Group on Quantum ChromoDynamics and the Standard Model for the Workshop ``Physics at TeV Colliders'', Les Houches, France, 21 May - 1 June 2001. The account of uncertainties in Parton Distribution Functions is reviewed. Progresses in the description of multiparton final states at Next-to-Leading Order and the extension of calculations for precision QCD observables beyond this order are summarized. Various issues concerning the relevance of resummation for observables at TeV colliders is examined. Improvements to algorithms of jet reconstruction are discussed and predictions for diphoton and photon pi-zero production at the LHC are made for kinematic variables of interest regarding searches for a Higgs boson decaying into two photons. Finally, several improvements implemented in Monte-Carlo event generators are documented.

We consider the production of isolated prompt photons in hadronic collisions. We present a general discussion in QCD perturbation theory of the isolation criterion used by hadron collider experiments. The isolation criterion is implemented in a computer programme of the Monte Carlo type, which evaluates the production cross section at next-to-leading order accuracy in perturbative QCD. The calculation includes both the direct and the fragmentation components of the cross section, without any approximation of the dependence on the radius R of the isolation cone. We examine the scale dependence of the isolated cross section, the sensitivity of the cross section to the values of the isolation parameters, and we provide a quantitative comparison between the full R dependence and its small-R approximation., Comment: 29 pages, 1 figure, few comments slightly expanded, results unchanged, misprints corrected

Report of the Higgs working group for the Workshop `Physics at TeV Colliders', Les Houches, France, 21 May - 1 June 2001. It contains 7 separate sections: A. Theoretical Developments B. Higgs Searches at the Tevatron C. Experimental Observation of an invisible Higgs Boson at LHC D. Search for the Standard Model Higgs Boson using Vector Boson Fusion at the LHC E. Study of the MSSM channel $A/H \to \tau \tau$ at the LHC F. Searching for Higgs Bosons in $t\bar t H$ Production G. Studies of Charged Higgs Boson Signals for the Tevatron and the LHC, Comment: 120 pages, latex, many figures, proceedings of the Workshop `Physics at TeV Colliders', Les Houches, France, 21 May - 1 June 2001, full Author list included in paper. Typos corrected, author list and acknowledgements completed. Convernors: D. Cavalli, A. Djouadi, K. Jakobs, A. Nikitenko, M. Spira, C.E.M. Wagner, W.-M. Yao

We consider Higgs boson production through gluon--gluon fusion in hadron collisions, when a veto is applied on the transverse momenta of the accompanying hard jets. We compute the QCD radiative corrections to this process at NLO and NNLO. The NLO calculation is complete. The NNLO calculation uses the recently evaluated NNLO soft and virtual QCD contributions to the inclusive cross section. We find that the jet veto reduces the impact of the NLO and NNLO contributions, the reduction being more sizeable at the LHC than at the Tevatron., Comment: 22 pages, 12 postscript figures

We propose a method for combining QCD matrix elements and parton showers in Monte Carlo simulations of hadronic final states in $e^+e^-$ annihilation. The matrix element and parton shower domains are separated at some value $y_{ini}$ of the jet resolution, defined according to the $k_T$-clustering algorithm. The matrix elements are modified by Sudakov form factors and the parton showers are subjected to a veto procedure to cancel dependence on $y_{ini}$ to next-to-leading logarithmic accuracy. The method provides a leading-order description of hard multi-jet configurations together with jet fragmentation, while avoiding the most serious problems of double counting. We present first results of an approximate implementation using the event generator APACIC++., Comment: 21 pages, 11 figures, uses JHEP.cls

We present a QCD study of fragmentation processes for light and heavy quarks in the semi-inclusive region of large x. Large logarithmic terms, due to soft-gluon radiation, are evaluated and resummed to all perturbative orders in the QCD coupling alpha_s. Complete analytical results to next-to-leading logarithmic accuracy are given for one-particle and two-particle inclusive distributions in e+e- annihilation and DIS. Factorization of parton radiation at low transverse momenta is exploited to identify the universal (process-independent) perturbative fragmentation function that controls heavy-quark processes, and to perform next-to-leading logarithmic resummation of its soft-gluon contributions. To gauge the quantitative impact of resummation, we perform numerical studies of light- and heavy-quark fragmentation in e+e- collisions., Comment: 37 pages, Latex, axodraw, epsfig, 11 figures

We compute the soft and virtual NNLO QCD corrections to Higgs production through gluon-gluon fusion at hadron colliders. We present numerical results obtained at the LHC and at the Tevatron Run II., Comment: latex, 5 pages, presented at the XXXVIth Rencontres de Moriond, QCD and Hadronic interactions, Les Arc1800, France and at the 9th International Workshop on Deep Inelastic Scattering DIS2001, Bologna, Italy

We consider QCD corrections to Higgs boson production through gluon-gluon fusion in hadron collisions. Using the recently evaluated two-loop amplitude for this process and the corresponding factorization formulae for soft-gluon bremsstrahlung at O(alpha_s^2), we compute the soft and virtual contributions to the NNLO cross section. We also discuss soft-gluon resummation at next-to-next-to-leading logarithmic accuracy. Numerical results for Higgs boson production at the LHC are presented., Comment: 17 pages, 4 figures included. One note and one reference added

We consider the resummation of the logarithmic contributions to the region of small transverse momenta in the distributions of high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. We point out that the resummation formulae that are usually used to compute the distributions in perturbative QCD involve process-dependent form factors and coefficient functions. We present a new universal form of the resummed distribution, in which the dependence on the process is embodied in a single perturbative factor. The new form simplifies the calculation of non-leading logarithms at higher perturbative orders. It can also be useful to systematically implement process-independent non-perturbative effects in transverse-momentum distributions. We also comment on the dependence of these distributions on the factorization and renormalization scales., Comment: misprints corrected in Eqs. (6), (7) and (12), results unchanged

We study the soft limit of one-loop QCD amplitudes and we derive the process-independent factorization formula that controls the singular behaviour in this limit. This is obtained from the customary eikonal factorization formula valid at tree (classical) level by introducing a generalized soft-gluon current that embodies the quantum corrections. We compute the explicit expression of the soft-gluon current at one-loop order. It contains purely non-abelian correlations between the colour charges of each pair of hard-momentum partons in the matrix element. This leads to colour correlations between (two and) three hard partons in the matrix element squared. Exploiting colour conservation, we recover QED-like factorization for the square of the matrix elements with two and three hard partons., Comment: latex, 20 pages, 4 eps figures

The Les Houches Workshop on Physics at TeV Colliders took place from June 8-18, 1999. One of the three working groups at Les Houches concentrated on QCD issues, both at the Tevatron Collider and at the LHC. Besides the interest in QCD in its own right, QCD dynamics plays an important role in the production mechanisms for any new physics process that might be observed at either collider, as well as any processes that may form backgrounds to the new physics. This writeup serves both as a pedagogical overview of QCD as well as an update on the current status of the field., Comment: 179 pages, 65 figures

We discuss issues of QCD at the LHC including parton distributions, Monte Carlo event generators, the available next-to-leading order calculations, resummation, photon production, small x physics, double parton scattering, and backgrounds to Higgs production., Comment: 115 pages, Latex, 47 figures, to appear in the Report of the ``1999 CERN Workshop on SM Physics (and more) at the LHC'', S. Catani, M. Dittmar, D. Soper, W.J. Stirling, S. Tapprogge (convenors)

We study the infrared behaviour of tree-level QCD amplitudes and we derive infrared-factorization formulae that are valid at any perturbative order. We explicitly compute all the universal infrared factors that control the singularities in the various soft and/or collinear limits at O(as^2)., Comment: latex, 38 pages, 11 eps figures

We compute the effects of soft-gluon resummation, at the next-to-leading-logarithmic level, in the fixed-target hadroproduction cross section for prompt photons. We find in general that the corrections to the fixed next-to-leading-order results are large for large renormalization scales, and small for small scales. This leads to a significant reduction of the scale dependence of the results for most experimental configurations of interest. We compare our results to the recent measurements by the E706 and UA6 collaborations., Comment: 30 pages, Latex, epsfig, amssymb, 17 figures. Submitted to JHEP

We consider the singular behaviour of tree-level QCD amplitudes when the momenta of three partons become simultaneously parallel. We discuss the universal factorization formula that controls the singularities of the multiparton matrix elements in this collinear limit and present the explicit expressions of the corresponding splitting functions. The results fully include spin (azimuthal) correlations up to ${\cal O}(\as^2)$. In the case of spin-averaged splitting functions we confirm similar results obtained by Campbell and Glover., Comment: latex, 10 pages, minor corrections in the references

We present the explicit expressions for the resummation of large-x Sudakov effects in the transverse-energy distribution of prompt-photons produced in hadronic collisions, to next-to-leading logarithmic (NLL) accuracy. Fragmentation processes do not contribute to the Sudakov resummation at NLL level. In Mellin space, the resummed radiative factor factorizes in the product of independent radiators for the two initial and the one final coloured partons appearing in the Born process, times a simple factor describing the soft-gluon interferences between initial and final states. The formulae are given in terms of Mellin moments, and can be used for phenomenological applications using standard techniques for the inverse-Mellin transforms. The calculations presented in this work, when added to the existing works on DY and DIS production, complete the theoretical ground-work necessary to carry out global fits of parton densities with a uniform NLL accuracy in the large-x region., Comment: 1+26 pages, Latex, epsfig, 1 figure

We study the production of isolated photons in $e^+e^-$ annihilation and give the proof of the all-order factorization of the collinear singularities. These singularities are absorbed in the standard fragmentation functions of partons into a photon, while the effects of the isolation are consistently included in the short-distance cross section. We compute this cross section at order $\as$ and show that it contains large double logarithms of the isolation parameters. We explain the physical origin of these logarithms and discuss the possibility to resum them to all orders in $\as$., Comment: 18 pages, LaTex, 2 eps figures, few modifications in the text, results unchanged

We compute the effect of soft-gluon resummation, at the next-to-leading-logarithmic level, in the hadroproduction cross-section for heavy flavours. Applications to top, bottom and charm total cross-sections are discussed. We find in general that the corrections to the fixed next-to-leading-order results are larger for larger renormalization scales, and small, or even negative, for smaller scales. This leads to a significant reduction of the scale-dependence of the results, for most experimental configurations of interest., Comment: 28 pages, Latex, epsfig, 15 figures. Corrected typos in captions of Figs. 2 and 9. Corrected NLO curve in Fig. 14

We give perturbative predictions for the distribution of the $C$-Parameter event shape variable in $e^+e^-$ annihilation, including resummation of large logarithms in the two-jet (small-$C$) region, matched to next-to-leading order results. We also estimate the leading non-perturbative power correction and make a preliminary comparison with experimental data., Comment: 12 pages, LaTeX, 3 figures

We show that QCD observables defined as infrared- and collinear-safe, according to the usual Sterman-Weinberg criteria, can nevertheless be infinite at accessible points inside phase space, to any finite order of perturbation theory. Infrared finiteness is restored after resummation of divergent terms to all orders. The resulting characteristic structure, which we call a Sudakov shoulder, represents an interesting new class of QCD predictions., Comment: 16 pages, LaTeX, 2 figures

We compute the effects of soft gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell--Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important only fairly close to the threshold region. In the case of heavy flavour production we find that resummation effects are small in the experimental configurations of practical interest., Comment: 45 pages, Latex, epsfig, 10 figures. Minor corrections to text, notation and references. The previously quoted HERAb NLO bottom production cross section was wrong, and it has been fixed. Accepted for Publication on Nucl. Phys. B

We reexamine the top quark production cross section at the Tevatron and LHC, in the light of recent progress on the resummation of logarithmic soft gluon corrections. We find that resummation effects are much smaller than previously thought. We also compute Coulombic threshold effects, and find them negligible. We update the discussion of uncertainties due to scale dependence, the value of the strong coupling constant, and the parton density parametrization. Our current best estimate of the top production cross section at the Tevatron and its error is $\sigma(\mt=175\,{\rm GeV})=4.75{+0.73\atop-0.62}$., Comment: 17 pages, Latex, epsfig, 7 figures. Revised version. Updated experimental results. Minor changes in the cross section tables. To appear on Phys. Lett. B

The perturbative QCD approach to quarkonium decay into a photon and hadrons is reconsidered. It is shown that a consistent treatment within perturbative QCD calls for the introduction of a fragmentation contribution which has been neglected so far. The ensuing phenomenological implications are discussed, and, in particular, the possibility of measuring the gluon fragmentation function of the photon is addressed. *To appear in the proceedings of the workshop QCD94, Montpellier, July '94., Comment: 4 pages + 3 figures, uuencoded postscript, Cambridge preprint Cavendish-HEP-94/09

We discuss the role of sub-leading corrections to deep inelastic processes in the small-x regime, and report recent results on the calculation of coefficient functions and quark anomalous dimensions. *To appear in the proceedings of the workshop QCD94, Montpellier, July '94., Comment: 2 pages, uuencoded postscript, Cavendish-HEP-94/12

High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular at small x order by order in perturbation theory. In the singlet sector, we derive the relevant master equations for the space-like evolution of gluons and quarks. Their solution enables us to sum next-to-leading corrections to the small-x behaviour of quark anomalous dimensions and deep inelastic scattering coefficient functions. We present results in both MSbar and DIS factorization schemes., Comment: 46 pages (+ 7 figures not included, available from the authors), Latex, Cavendish-HEP-94/01