G. Marchesini

Monte Carlo Simulation of General Hard Processes with Coherent QCD Radiation

Abstract In this paper we extend our previous work on the simulation of coherent soft-gluon radiation to hard collisions that involve incoming as well as outgoing coloured partons. Existing simulations correctly sum the leading collinear singularities for initial- and final-state radiation, and in some cases the leading infrared contributions from outgoing partons, but not those for incoming (or the interference between incoming and outgoing). Asymptotically, however, the leading infrared and collinear contributions are comparable, the bulk of gluon emission occuring in the soft region. Furthermore, a correct treatment of leading infrared terms is necessary for the inclusive cancellation of singularities in the Sudakov form factor. We show how such a treatment ,ay be formulated in terms of an angular ordering procedure applicable to all hard processes. We then describe a new Monte Carlo program which incorporates this procedure, together with other new features such as azimuthal correlations due to gluon polarization and interference. The program is designed as a general-purpose event generator, simulating hard lepton-lepton, lepton-hadron and hadron-hadron scattering in a single package. Simulation of soft hadronic collisions and underlying events is also included. We present the predictions of the program for a wide variety of processes, and compare them with analytical results and experimental data.

Simulation of QCD jets including soft gluon interference

Abstract We present a new Monte Carlo simulation scheme for jet evolution in perturative QCD which takes into account the results of recent analyses of soft-gluon interference. Therefore, this scheme accounts correctly not only for the leading collinear singularities, as in previous schemes, but also for leading infrared singularities. In this first paper we study the basic features of gluon jet evolution such as: (i) the interference effects and the corresponding depletion of the parton distributions in the soft region; (ii) the approach to asymptopia; (iii) the efficiency of colour screening (preconfinement), which has been questioned recently by Bjorken.

Jet structure and infrared sensitive quantities in perturbative QCD

Abstract Infrared sensitive measurements in hard scattering include x - and p ⊥ -distributions at the phase space boundary (where soft emision is depressed) and jet multiplicity distributions (where it is emphasized). We review QCD results for these quantities and the corresponding infrared resummation techniques. Particular emphasis is put on the structure of the jet final state and its phenomenological consequences.

Small-x behaviour of initial state radiation in perturbative QCD☆

We analyze in perturbative QCD the asymptotic behaviour of deep inelastic processes in the semi-hard region x→0. The study is done by extending the soft gluon insertion techniques. We confirm and extend the analysis recently performed by Ciafaloni. The main results are the following: (i) Soft gluon emission from the incoming parton takes place in a region where the angles between incoming and outgoing partons are ordered. This is due to coherent effects similar to the ones in the x→1 region. (ii) Virtual corrections involving an internal line with energy fraction x give rise, for x→0, to a new form factor of non-Sudakov type. This regularizes collinear singularities when an emitted gluon is parallel to the incoming parton. (iii) At the complete inclusive level, the new form factor plays the same role as the virtual corrections in the Lipatov equation for the Regge regime. We show that, in the semi-hard regime, the gluon anomalous dimension coincides with the Lipatov ansatz. (iv) We identify the branching structure of initial-state radiation including the semi-hard regime. The branching is formulated as a probability process given in terms of Sudakov and non-Sudakov form factors. This process, in principle, can be used to extend the existing simulations of QCD cascades to the semi-hard regime.

Partonic distributions for large x and renormalization of Wilson loop

Abstract We discuss the relation between partonic distributions near the phase space boundary and Wilson loop expectation values calculated along paths partially lying on the light-cone. Due to additional light-cone singularities, multiplicative renormalizability for these expectation values is lost. Nevertheless we establish the renormalization group equation for the light-like Wilson loops and show that it is equivalent to the evolution equation for the physical distributions. By performing a two-loop calculation we verify these properties and show that the universal form of the splitting function for large x originates from the cusp anomalous dimension of Wilson loops.We discuss the relation between partonic distributions near the phase space boundary and Wilson loop expectation values calculated along paths partially lying on the light-cone. Due to additional light-cone singularities, multiplicative renormalizability for these expectation values is lost. Nevertheless we establish the renormalization group equation for the light like Wilson loops and show that it is equivalent to the evolution equation for the physical distributions. By performing a two-loop calculation we verify these properties and show that the universal form of the splitting function for large x originates from the cusp anomalous dimension of Wilson loops.

QCD coherent branching and semi-inclusive processes at large χ☆

Using the QCD coherent branching algorithm, we compute the Deep Inelastic Scattering and Drell-Yan hard cross sections in the semi-inclusive region of large χ. The calculation is done to next-to-leading logarithmic accuracy in the resummation of perturbative QCD. We compare the results with the known analytical expressions to the same accuracy in the MS subtraction scheme. They coincide if one defines an improved branching algorithm suitable for Monte Carlo simulation, in which the two-loop running coupling constant and Altarelli-Parisi splitting function are used. Therefore such a simulation can be used to measure ΛMS from these semi-inclusive cross sections. Moreover we show that the same results can also be obtained using the usual one-loop splitting function, provided the scale parameter ΛMC used in the Monte Carlo simulation is related to ΛMS by a computed factor: ΛMC=1.569 ΛMS (for five flavours).

QCD coherence in initial state radiation

Abstract We describe a unified method to analyze the structure of QCD coherence in a hard process with incoming hadrons. In particular we discuss in detail the regimes of x→0 and x→1 where x is the Bjorken variable. The multiparton emission is formulated as a factorized branching process which can be used to extend the existing simulations of QCD cascades to the semi-hard regime.

A Treatment of Hard Processes Sensitive to the Infrared Structure of QCD

Abstract We propose a modified jet evolution equation which resums large corrections to the usual leading logarithmic approximation when phase-space constraints expose the singular infrared structure of QCD. The modification, which consists simply of a rescaling of the argument of the running coupling constant, is based on perturbative arguments verified at the fourth-order level. Processes analyzed by this method include the quark (Sudakov) form factor, the large moments of structure and fragmentation functions, the asymptotic behaviour of multiplicities and the clustering of final quanta in colourless systems which occupy finite regions of (momentum and position) phase space.

Jet Multiplicity and Soft Gluon Factorization

Abstract On the basis of a factorization theorem for soft gluon insertions it is shown that leading log contributions to the multiplicity anomalous dimension come from ladder diagrams in a restricted region of phase space, in agreement with previous conjectures. This leads to a finite anomalous dimension ∼ α s and to a multiplicity behaviour ∼ exp ([ 2N c πb ] log [ Q 2 Λ 2 ]) 1 2 .

Resummation of large infrared corrections using Wilson loops

Abstract We discuss a method to resum systematically large soft gluon corrections to hard hadronic cross sections such as the structure function F ( x , Q 2 ) for x → 1. We show that all singularities as x → 1 are factorized into a Wilson loop expectation value which is a function of the ratio of the infrared scale (1− x ) Q 2 and the short distance cutoff μ 2 introduced by the factorization procedure. Thus we obtain the x → 1 behavior by studying the appropriate renormalization group equation which controls the μ-dependence of Wilson loops. Next-to-leading corrections are calculated. The method can be generalized to other distributions.