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Manuscript Title: QCD corrections to vector boson self-energies in the standard model.
Authors: B.A. Kniehl
Program title: QCDPI
Catalogue identifier: ABRC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 58(1990)293
Programming language: Fortran.
Computer: IBM 4381.
Operating system: VM/SP.
Word size: 32
Keywords: Particle physics, Elementary, Radiative corrections, Standard model of Electroweak interactions, Quantum chromodynamics, Vacuum polarization, Gauge boson, Quark, Gluon, Running coupling Constant, Dispersion relation.
Classification: 11.5.

Nature of problem:
In principle, one can calculate self-energy graphs by using ordinary Feynman integral techniques and e.g. the dimensional regularization method. However, the direct calculation of the considered two-loop amplitude disregards important physical features such as the energy dependence of the strong coupling constant alpha s and the existence of boundstate resonances in the threshold region. Dispersion relations, which allow to compute the real part of an analytic function from its imaginary part, provide a convenient tool to incorporate all these modifications. The required absorptive part of the vacuum polarization is obtained by the application of Cutkosky's rules.

Solution method:
The program solves the Cauchy principal value integrals numerically using adaptive Gaussian quadrature. In general, even after introducing the proper subtraction prescription, there are still logarithmic ultra- violet divergences present which are regularized by a high energy cutoff A. Due to the renormalizability of the standard model these residual singularities cancel in the expressions for physical observables. Here, for the sake of numerical stability, appropriate functions are already subtracted from the integrands which exactly suppress these logarithms. One is then left with an unphysical finite scale lambda on which physical results do not depend.

The program is optimized so as to avoid abundances. The imaginary parts of the self-energies are substituted by interpolating formulas just above threshold and in the high energy region. In between they are given by rather complicated functions the numerical integration of which clearly is a possible limitation of the program.

Running time:
The running time delicately depends on the required accuracy for the numerical integration. The test run took 3 min 4s total CPU time.