Asymptotic freedom in the axial and coulomb gauges
Abstract
The sources of the negative contribution to the charge renormalization factor gB/g − 1 in Yang-Mills theories are investigated in the axial and Coulomb gauges. In the axial gauge, a Källén dispersion relation exists but the spectral function is not positive definite because of the prescription that is used to integrate the singular polarization vectors. In the Coulomb gauge, the negative contributions are (to the lowest order) isolated in the Coulomb self-energy corrections to the Coulomb field.
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Program title: SecDec 3.0
Catalogue identifier: AEIR_v3_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v3_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 123828
No. of bytes in distributed program, including test data, etc.: 1651026
Distribution format: tar.gz
Programming language: Wolfram Mathematica, perl, Fortran/C++.
Computer: From a single PC to a cluster, depending on the problem.
Operating system: Unix, Linux.
RAM: Depending on the complexity of the problem
Classification: 4.4, 5, 11.1.
Catalogue identifier of previous version: AEIR_v2_1
Journal reference of previous version: Comput. Phys. Comm. 184(2013)2552
Does the new version supersede the previous version?: Yes
Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g. kinematic thresholds).
Solution method: Algebraic extraction of singularities within dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way.
Reasons for new version:
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Improved user interface.
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Additional new decomposition strategies.
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Usage on a cluster is much improved.
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Speed-up in numerical evaluation times.
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Various new features (please see below).
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Implementation of two new decompositions strategies based on a geometric algorithm.
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Scans over large ranges of parameters are facilitated.
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Linear propagators can be treated.
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Propagators with negative indices are possible.
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Interface to reduction programs like Reduze, Fire, LiteRed facilitated.
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Option to use numerical integrator from Mathematica.
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Using CQUAD for 1-dimensional integrals to improve speed of numerical evaluations.
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Option to include epsilon-dependent dummy functions.
Running time: Between a few seconds and several hours, depending on the complexity of the problem.
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- ★
On leave of absence from Instituto de Fisica, Universidade de São Paulo, Brazil.