arXiv subjects

G. Marchesini

Publications and source records attributed to G. Marchesini.

52 records · Page 3Linked to original sources

arXiv1997

Structure functions and angular ordering at small x

We compute the gluon distribution in deep inelastic scattering at small x by solving numerically the angular ordering evolution equation. The leading order contribution, obtained by neglecting angular ordering, satisfies the BFKL equation. Our aim is the analysis of the subleading corrections. Although not complete - the exact next-to-leading contribution is not yet available - these corrections are important since they come from the physical property of coherence of QCD radiation. In particular we discuss the subleading correction to the BFKL characteristic function and the gluon distribution's dependence on the maximum available angle. Conformal invariance of the BFKL equation is lost, however this is not enough to bring the small-x gluon distribution into the perturbative regime: although large momentum regions are enhanced by angular ordering, the small momentum regions are not fully suppressed. As a consequence, the gluon anomalous dimension is finite and tends to the BFKL value $γ=1/2$ for $α_S \to 0$. The main physical differences with respect to the BFKL case are that angular ordering leads to 1) a larger gluon anomalous dimension, 2) less singular behaviour for $x \to 0$ and 3) reduced diffusion in transverse momentum.

hep-ph↗

arXiv1996

Infrared Renormalons and Finite Volume

We analyze the perturbative expansion of a condensate in the O(N) non-linear sigma model for large N on a two dimensional finite lattice. On an infinite volume this expansion is affected by an infrared renormalon. We extrapolate this analysis to the case of the gluon condensate of Yang-Mills theory and argue that infrared renormalons can be detected by performing perturbative studies even on relatively small lattices.

hep-lat↗

arXiv1996

Gauge invariant action at the ultraviolet cutoff

We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry.

hep-th↗

arXiv1996

HERWIG version 5.9

HERWIG (Hadron Emission Reactions With Interfering Gluons) is a multipurpose Monte Carlo event generator for the simulation of hard collisions between hadrons, leptons and photons. This note describes the new features of version 5.9. These include adding over 100 new particles, 1800 new decay modes and supporting new decay types. A complete space-time picture, including heavy meson mixing and secondary decays, is available for all event types and includes an optional colour rearrangement model. Initial state radition of photons in e^+e^- is is now included. Many other processes and features have been upgraded.

hep-ph↗

arXiv1996

Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory

We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings'' of the Wilsonian action $S_Ł[ϕ]$ of the exact renormalization group (RG) at the scale $Ł$. This relation involves the ultraviolet region of $Ł$ so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We also study the infrared (IR) renormalons. This formulation is particularly suited for this study since: $i$) $Ł$ plays the rôle of a IR cutoff in Feynman diagrams and non-perturbative effects could be generated as soon as $Ł$ becomes small; $ii$) by a systematical resummation of higher order corrections the Wilsonian flowing couplings enter directly into the Feynman diagrams with a scale given by the internal loop momenta; $iii$) these couplings tend to the running coupling at high frequency, they differ at low frequency and remain finite all the way down to zero frequency.

hep-th↗

arXiv1996

Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes

We consider power-behaved contributions to hard processes in QCD arising from non-perturbative effects at low scales which can be described by introducing the notion of an infrared-finite effective coupling. Our method is based on a dispersive treatment which embodies running coupling effects in all orders. The resulting power behaviour is consistent with expectations based on the operator product expansion, but our approach is more widely applicable. The dispersively-generated power contributions to different observables are given by (log-)moment integrals of a universal low-scale effective coupling, with process-dependent powers and coefficients. We analyse a wide variety of quark-dominated processes and observables, and show how the power contributions are specified in lowest order by the behaviour of one-loop Feynman diagrams containing a gluon of small virtual mass. We discuss both collinear safe observables (such as the e+e- total cross section and τhadronic width, DIS sum rules, e+e- event shape variables and the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e+e- fragmentation functions and the Drell-Yan cross section).

hep-ph↗

arXiv1995

RENORMALONS FROM EIGHT LOOP EXPANSION OF THE GLUON CONDENSATE IN LATTICE GAUGE THEORY,

We use a numerical method to obtain the weak coupling perturbative coefficients of local operators with lattice regularization. Such a method allows us to extend the perturbative expansions obtained so far by analytical Feynman diagrams calculations. In SU(3) lattice gauge theory in four dimensions we compute the first eight coefficients of the expectation value of the Wilson loop on the elementary plaquette which is related to the gluon condensate. The computed eight coefficients grow with the order much faster than predicted by the presence of the infrared renormalon associated to the dimension of the gluon condensate. However the renormalon behaviour for large order is quite well reproduced if one considers the expansion coefficients in a new coupling related to the lattice coupling by large perturbative corrections. This is expected since the lattice and continuum Lambda scales differ by almost two orders of magnitude.

hep-th↗

arXiv1994

BRS symmetry from renormalization group flow

By using the exact renormalization group formulation we prove perturbatively the Slavnov-Taylor (ST) identities in SU(2) Yang-Mills theory. This results from two properties: {\it locality}, i.e. the ST identities are valid if their local part is valid; {\it solvability}, i.e. the local part of ST identities is valid if the couplings of the effective action with non-negative dimensions are properly chosen.

hep-th↗

arXiv1994

BRS symmetry for Yang-Mills theory with exact renormalization group

In the exact renormalization group (RG) flow in the infrared cutoff $Λ$ one needs boundary conditions. In a previous paper on $SU(2)$ Yang-Mills theory we proposed to use the nine physical relevant couplings of the effective action as boundary conditions at the physical point $Λ=0$ (these couplings are defined at some non-vanishing subtraction point $μ\ne 0$). In this paper we show perturbatively that it is possible to appropriately fix these couplings in such a way that the full set of Slavnov-Taylor (ST) identities are satisfied. Three couplings are given by the vector and ghost wave function normalization and the three vector coupling at the subtraction point; three of the remaining six are vanishing (\eg the vector mass) and the others are expressed by irrelevant vertices evaluated at the subtraction point. We follow the method used by Becchi to prove ST identities in the RG framework. There the boundary conditions are given at a non-physical point $Λ=Λ' \ne 0$, so that one avoids the need of a non-vanishing subtraction point.

hep-th↗

arXiv1994

Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_μ(x) \to \exp\{A_μ(x)/\sqrtβ\}$ into the Langevin algorithm and the observables and to perform the expansion in β^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (β^{-4}) which extends by one loop the previously known series.

hep-lat↗

arXiv1994

Axial anomalies in gauge theory by exact renormalization group method

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $Ł$ and the boundary conditions for the relevant couplings. The physical theory is obtained at $Ł=0$. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point $Ł=Ł_0\to\infty$ but at the physical value $Ł=0$. As an illustration, we compute the triangle axial anomalies.

hep-th↗

arXiv1994

Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance

We study the formulation of the Wilson renormalization group (RG) method for a non-Abelian gauge theory. We analyze the simple case of $SU(2)$ and show that the local gauge symmetry can be implemented by suitable boundary conditions for the RG flow. Namely we require that the relevant couplings present in the physical effective action, \ie the coefficients of the field monomials with dimension not larger than four, are fixed to satisfy the Slavnov-Taylor identities. The full action obtained from the RG equation should then satisfy the same identities. This procedure is similar to the one we used in QED. In this way we avoid the cospicuous fine tuning problem which arises if one gives instead the couplings of the bare Lagrangian. To show the practical character of this formulation we deduce the perturbative expansion for the vertex functions in terms of the physical coupling $g$ at the subtraction point $μ$ and perform one loop calculations. In particular we analyze to this order some ST identities and compute the nine bare couplings. We give a schematic proof of perturbative renormalizability.

hep-th↗

arXiv1993

Small $x$ processes: Heavy Quark Production at High Energy

A brief summary is given of some recent perturbative QCD results on the evaluation of cross sections and on the the structure of final states in processes with incoming hadrons at small $x$. A new Monte Carlo simulation which includes these theoretical features is described together with its applications to the study of heavy quark production in $ep$ collisions at very high energy. (Talk given at the XXVIIth Rencontre de Moriond, March 1993, Les Arcs, France)

hep-ph↗

arXiv1993

QCD and high energy hadronic interaction: Summary talk (theory)

Results presented in perturbative QCD are reviewed. The topics discussed include: - struction functions, - heavy flavour production, - direct photon production, - inclusive production at LHC/SSC, - small $x$ physics, - QCD jets and - intermittency. For reference to the data in this talk see the summary presented by J.E. Augustin.

hep-ph↗

arXiv1993

Ward identities and Wilson renormalization group for QED

We analyze a formulation of QED based on the Wilson renormalization group. Although the ``effective Lagrangian'' used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's functions correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski's renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponding counterterms are generated in the process of fixing the physical conditions.

hep-th↗

arXiv1993

Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case

A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the ``relevant'' vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.

hep-th↗