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Manuscript Title: The mu(x,beta,alpha) function and its role in the analysis of the QCD- SVZ sum rules.
Authors: C. Ayala
Program title: MUNU
Catalogue identifier: ACHH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 70(1992)401
Programming language: Fortran.
Computer: VAX 8800.
Operating system: VAX/VMS.
Word size: 32
Keywords: Particle physics, Elementary, Quantum chromodynamics, Sum rules, Asymptotic expansions.
Classification: 11.5.

Nature of problem:
The careful treatment of the QCD-SVZ sum rules requires an asymptotic analysis of those mu-functions. In study of any n-point function in QCD one expands alpha s(x) in the (1/log(x)) expansion due to their renormalization group equations to the corresponding level of perturbation theory. The improvement of that n-point function via Borel sum rules result to be linear combinations of the mu(x,beta,alpha) function (and the related nu(x,alpha)) for different values of the alpha and beta parameters. That result is again developed in a (1/log(x)) expansion, not a reliable one as the physical presented above, but one deeply asymptotic and with serious disagreements in the physical region. There is no sense sustaining that both expansions must be taken to the same order.

Solution method:
We carefully construct the mu(x,beta,alpha) and nu(x,alpha) functions as Fortran functions, and also their expansions in (1/log(x)). We show that the expansions in the physical region are noticeably asymptotic and not as reliable as the ones obtained in the perturbative parameter of QCD (alpha s). We calculate the coefficients of the expansion (of upcoming complexity) using the algebraic manipulator REDUCE. A triplet of functions from the CERN library GENLIB could be used, but to improve their performance in our particular case, we wrote specfic routines adjusted to our needs. Thus, the package is library- independent.

It effectively stops at sixth order in perturbation theory in QCD (alpha s 6). This will be more than enough for a long time. The expansions for mu and nu are developed till order twelve (1/log(x))**12, which is perfectly resonable.

Running time:
The computation of the "test run output" spend half a minute in a VAX8800. The calculation of the functions and several of its expansions need less than one minute in most of the cases. It crucially depends on the set of parameters input but is unlikely that more execution time will be needed.