David G. Robertson

TSIL: a program for the calculation of two-loop self-energy integrals

Abstract TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasovs recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge–Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C/C++ or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups. Program summary Title of program: TSIL Version number: 1.0 Catalogue identifier: ADWS Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWS Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Programming language: C Platform: Any platform supporting the GNU Compiler Collection (gcc), the Intel C compiler (icc), or a similar C compiler with support for complex mathematics No. of lines in distributed program, including test data, etc.: 42 730 No. of bytes in distributed program, including test data, etc.: 297 101 Distribution format: tar.gz Nature of physical problem: Numerical evaluation of dimensionally regulated Feynman integrals needed in two-loop self-energy calculations in relativistic quantum field theory in four dimensions. Method of solution: Analytical evaluation in terms of polylogarithms when possible, otherwise through Runge–Kutta solution of differential equations. Limitations: Loss of accuracy in some unnatural threshold cases that do not have vanishing masses. Typical running time: Less than a second.

Discretized light-cone quantization of electrodynamics.

Discretized light-cone quantization of (3+1)-dimensional electrodynamics is discussed, with careful attention paid to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed, and the corresponding relations that determine the zero modes of the gauge field are obtained. One particularly natural gauge choice in the zero mode sector is identified, for which the constraint relations are simplest and the fields may be taken to satisfy the usual canonical commutation relations. The constraints are solved in perturbation theory, and the Poincare generators [ital P][sup [mu]] are constructed. The effect of the zero mode contributions on the one-loop fermion self-energy is studied.

Evaluation of the general three-loop vacuum Feynman integral

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite basis integrals that are particularly convenient for expressing renormalized quantities. The basis integrals can be computed numerically by solving coupled first-order differential equations, using as boundary conditions the analytically known special cases that depend on only one mass scale. We provide the results necessary to carry this out, and introduce an implementation in the form of a public software package called 3VIL (3-loop Vacuum Integral Library), which efficiently computes the numerical values of the basis integrals for any specified masses. 3VIL is written in C, and can be linked from C, C++, or FORTRAN code.

Light-front QCD1+1 coupled to chiral adjoint fermions

Abstract We consider SU ( N ) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually SU(N) Z N , which possesses nontrivial topology. In particular, there are N distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization for the case N = 2, using discretization as an infrared regulator. In the discretized form of the theory the nontrivial vacuum structure is associated with the zero momentum mode of the gauge field A + . We find exact expressions for the degenerate vacuum states and the analog of the θ vacuum. The model also possesses a condensate which we calculate. We discuss the difference between this chiral light-front theory and the theories that have previously been considered in the equal-time approach.

The Vacuum in Light Cone Field Theory

This is an overview of the problem of the vacuum in light-cone field theory, stressing its close connection to other puzzles regarding light-cone quantization. I explain the sense in which the light-cone vacuum is “trivial,” and describe a way of setting up a quantum field theory on null planes so that it is equivalent to the usual equal-time formulation. This construction is quite helpful in resolving the puzzling aspects of the light-cone formalism. It furthermore allows the extraction of effective Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space in which the vacuum state is simple. The discussion is fairly informal, and focuses mainly on the conceptual issues. Additional technical details of the construction described here will appear in a forthcoming paper written with Kent Hornbostel.

The Mandelstam-Leibbrandt prescription in light-cone quantized gauge theories

Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.

Renormalization Scale Invariant pQCD Predictions for R(e+ e-) and the Bjorken Sum Rule at Next-to-Leading Order

We discuss application of the physical QCD effective charge

Physical Coupling Schemes and QCD Exclusive Processes

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Optimal renormalization scale and scheme for exclusive processes

, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the

Vacuum structure of two-dimensional gauge theories on the light front

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