T. Grandou

The Role of Soft Gluons in Lepton Pair Production

Abstract We derive expressions for the exponentiation of soft gluon effects in lepton pair production and discuss their phenomenological implications for the rapidity and Q 2 dependence of the so-called “K- factor ” . Predictions are given for scaling violations to be seen in the determination of the pion structure function.

Electron-positron annihilation in thermal QCD

We present a two loop calculation of e+−e− annihilation into quarks and gluons at finite temperature in the framework of the real time formalism. We give a self-contained and pedagogical description of the calculation which relies on finite temperature cutting rules. Using a simpler infrared regularization than those of previous works, we confirm the cancellation of mass and infrared singularities, and give in addition a complete analytical and numerical evaluation of finite terms. Some delicate points linked to wave function renormalization are treated in full detail.

Thermal field theory and infinite statistics

Abstract We construct a quantum thermal field theory for scalar particles in the case of infinite statistics. The extension is provided by working out the Fock space realization of a “quantum algebra”, and by identifying the hamiltonian as the number operator. We examine the perturbative behavior of this theory and in particular the possible extension of the KLN theorem, and argue that it appears as a stable structure in a quantum field theory context.

A new approach to analytic, non-perturbative and gauge-invariant QCD

Abstract Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional “idealistic” description of QCD and a more “realistic” description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green’s functional G c ( x , y | A ) and the vacuum functional L [ A ] . Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called “Effective Locality”, in which the interactions between quarks by the exchange of a “gluon bundle”–which “bundle” contains an infinite number of gluons, including cubic and quartic gluon interactions–display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that “non-perturbative” here refers to the effective summation of all gluons between a pair of quark lines–which may be the same quark line, as in a self-energy graph–but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the “Bundle Diagram”. As an example of the power of these methods we offer as a first analytic calculation the quark–antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon–nucleon binding potential to form a model deuteron, will appear separately.

Analytic, non-perturbative, gauge-invariant quantum chromodynamics: Nucleon scattering and binding potentials

Abstract Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define the transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized quantum chromodynamics (QCD) coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD.

Non-perturbative QCD amplitudes in quenched and eikonal approximations

Abstract Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality . The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.

Mass singularities at finite temperature in a scalar field theory

Using as a model the φ3 field theory in space-time dimensionD=6, we show the validity of the Kinoshita-Lee-Nauenberg theorem at finite temperature to first order in the coupling constant.

Remarks on infrared singularities of relativistic thermal field theories

Abstract We show that self-energy insertions in relativistic thermal field theories lead to severe infrared divergences in higher order calculations. However, these singularities seem to cancel out in the computation of total rates.

The role of soft gluons in lepton pair production (II). Scaling violations

Abstract We propose a way of testing scaling violations and subsidiarily soft gluons present in pp and π N induced reactions.

Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen...