Leading particles and charged particle multiplicity in annihilation and non-annihilation interactions

Using data from our K^?p experiment at 8.25 GeV/c we have investigated the charged particle multiplicity, and the variation of charged pion multiplicity as a function of the effective mass squared of all pions, for various samples of data, and compared our results with $\text{p}$p annihilation data and pp data. Evidence is presented which suggests that the difference in behaviour between the annihilation and non-annihilation data is not due to some specific mechanism such as baryon exchange, but is related to the absence of leading particles in the former case.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

Integration over instanton parameters in non-abelian gauge theories

The measure for integrating over instanton degrees of freedom in the euclidean functional integrals for non-abelian gauge theories is discussed within the context of the construction of Atiyah, Drinfeld, Hitchin and Manin, and evaluated for the SU(2) two-instanton solution of 't Hooft.     

Deep inelastic photon-photon scattering in an asymptotically free gauge theory

Two-photon scattering is analyzed assuming the strong interactions are described by an asymptotically free gauge theory. The box diagram is found to be enhanced relative to the “strong” contribution in the deep inelastic region but only as a power of ln ν. An exception is the structure function W₃ in which the box diagram dominates like a power of ν. The validity of a fixed pole sum rule is also considered.     

Testing gauge theories in electron-electron scattering

The magnitudes of the correction terms to Møller scattering in the Weinberg-Salam Model and Georgi-Glashow model are compared. The possible consequences of the variations of the free parametersM E ⁺/M _W ,E/M _φ andE/M _Z with these correction terms are carefully discussed.     

Spontaneous symmetry breaking in massless field theories: Dimensional transmutation and gauge independence

In a reformulation of the Coleman and Weinberg program, we study the parametrization of the spontaneous symmetry breaking solutions of massless field theories. Our analysis is based on a full use of the concept of the dimensional transmutation, namely the parametrization in terms of the independent invariants of the underlying renormalization group. This invariant parametrization provides a convenient setting for the operator interpretation in a given Fock space and is shown to be a powerful tool in studying general aspects of the theory beyond the one-loop approximation. In particular, the gauge independence of the physical matrix elements in the spontaneously broken solution of massless scalar electrodynamics is demonstrated to all orders in perturbation theory.     

Quark confinement and topology of gauge theories

The phenomenon of quark confinement is known to be connected with the restoration of apparently broken gauge symmetry. In this paper we focus on a special mechanism which is responsible for such restoration. The major suggestion is that in the treatment of infrared problems certain classical field trajectories are of paramount importance, which trajectories connect seemingly degenerate vacua thereby eliminating the degeneracy. Initially, we demonstrate this mechanism in certain simple non-gauge models. In order of increasing difficulty, we next examine compact quantum electro-dynamics in 2 + 1 space-time dimensions- essentially a variant of unified models of the Georgi-Glashow type. In this case we prove that charge is confined and show that the force between two charges is independent of the distance between them. For small values of the fine structure constant this force is explicitly evaluated. Finally, we turn to the more realistic case of a 3 + 1 dimensional non-Abelian gauge theory, and analyse the contribution of a single pseudoparticle to the correlation functions. It is proposed that the quantum fluctuations of the pseudoparticle are inessential, and that the one-loop approximation is effectively correct even for the large scale pseudoparticles. The emergent conclusion then is that the renormalized Yang-Mills theory is reduced to the problem of evaluating the effects of those configurations which involve many pseudoparticles, due account being taken of the interactions between them. Some aspects of this last problem are also discussed.     

Anomalous commutators in vector and chiral gauge theories

A fixed-time point-splitting regularisation employing suitable phase factors is used to derive various anomalous commutators - both in usual vector gauge theories and non-abelian chiral gauge theories in four dimensions. In the latter case, new structures for the commutators involving currents have been found. Consistency of these expressions is established by reproducing some familiar results.     

Anomalous gauge theories as constrained Hamiltonian systems

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear σ-model and later for fermionic theory. The breakdown of the Gauss law constraints and the anomalous commutators among them are studied in a systematic way. An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints. Dirac brackets between the time components of gauge fields are shown to involve anomalous terms. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.     

The rise of the cross section and the Mandelstam diagrams

We evaluate multi-pomeron exchanges based on non-planar, Mandelstam-like diagrams of an underlying field theory. We take into account both the coupling of many pomerons to the external lines and the coupling of the pomerons among themselves in a scheme that can incorporate low-energy effects in a natural way. We express the total cross section in terms of one-two-three-pomeron exchange plus a term due to the triple-pomeron interaction. We have considered two possible values for the intercept: α₀ = 1.025, α₀ = 1. In both cases we can find agreement with the observed rise of the pp total cross section.     

Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories

A new proof of Adler's theorem in finite massless QED is given and generalizations to non-Abelian gauge theories are studied.     

Measurement of the single-jet invariant cross section at Fermilab

In an experiment performed at Fermilab we have studied the production of high p_t hadron jets from 400 GeV/c pp interactions. A large solid-angle, towered calorimeter was used to trigger and reconstruct the jet events. We report results for inclusive single-jet production and compare those results with QCD predictions and results obtained at the ISR and the SPS Collider.     

Polarized lepton-hadron scattering in asymptotically free gauge theories

We analyze polarized deep inelastic electron and neutrino scattering in asymptotically free gauge theories of the strong interactions. We compute the logarithmic deviations from Bjorken scaling in the moment sum rules for the structure functions due to the leading twist-2 and -3 operators that control the light-cone expansion. We also consider continuations to the elastic limit and to the Regge region.     

Steady-state differential cross section for elastic scattering

Lower limits are found on the differential cross section for elastic scattering and on its derivatives with respect to the momentum transfer t at t = 0 at high energies on the basis of completely general considerations. The results are expressed in terms of the measurable total cross sections.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 103–108, April, 1970.     

Multiple bremsstrahlung in gauge theories at high energies: (III). Finite mass effects in collinear photon bremsstrahlung

We present a method for calculating the various spin amplitudes for QED processes in which an arbitrary number of photons is radiated in directions nearly parallel to the fermion directions. This is accomplished by introducing explicit polarization vectors for the photons and by working in the high energy limit, where finite mass effects are treated in leading order.     

Anomalous diffraction approximation for light scattering cross section: Case of ordered clusters of non-absorbent spheres

The anomalous diffraction (AD) method has proved to be an adequate approximation of the exact method (GMM code computed by Xu) to obtain the scattering cross section for aggregates whose primary particle size parameter is greater than 2. Indeed, the error of this approximated method is less than approximately 10% when the primary particles are in SiO₂.However, this method is strongly related to the aggregate morphology since it includes in its formulation the concept of chord length. We initially studied the chord distribution for various aggregates, and then we reformulated the anomalous diffraction method, to approximate the scattering cross section, now completely analytically. This new expression is entitled ADr with the r for rapid because this one is at least a hundred times faster than the standard AD method.     

Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres

We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789–810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation.