MathQCDSR: A Mathematica package for QCD sum rules calculations

Abstract We present a software package written in Mathematica for standard QCD sum rules calculations. Two examples are given to demonstrate how to use the package. One is for the mass spectrum of octet baryons from two-point correlation functions; the other for the magnetic moments of octet baryons in the external-field method. The free package FeynCalc is used to handle the gamma-matrix algebra. In addition to two notebooks for the construction of the QCD sum rules, two corresponding notebooks are provided for a Monte Carlo-based numerical analysis, complete with in-line graphical display of sum rule matching, error distributions, and scatter plots for correlations. Program summary Program title: MathQCDSR Catalogue identifier: AEJA_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJA_v1_0.html Program obtainable from: CPC Program Library, Queenʼs 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.: 93 897 No. of bytes in distributed program, including test data, etc.: 631 481 Distribution format: tar.gz Programming language: Mathematica Computer: PCs and Workstations Operating system: Any OS that supports Mathematica. The package has been tested under Windows XP, Macintosh OS X, and Linux Classification: 11.5 External routines: FeynCalc ( http://www.feyncalc.org/ ). It is a freely available Mathematica package for high-energy physics calculations. Here it is used primarily to handle gamma-matrix algebra. Nature of problem: The QCD sum rule method is a nonperturbative approach to solving quantum chromodynamics (QCD), the fundamental theory of the strong force. The approach establishes a direct link between hadron phenomenology and the QCD vacuum structure via a few QCD parameters called vacuum condensates and susceptibilities. It has been widely applied in nuclear and particle physics to gain insight into various aspects of strong-interaction physics. Solution method: First, QCD sum rules are constructed by evaluating correlation functions from two perspectives. On the quark level, it leads to a function of QCD parameters and the Borel mass parameter M . On the hadronic level, it leads to a function of phenomenological parameters and the same M . By numerically matching the two sides over a range in M , the phenomenological parameters can be extracted. The construction involves a large amount of gamma-matrix algebra, Fourier transform, and Borel transform. The matching usually involves searching for minimum χ 2 . We employ a Monte Carlo-based procedure to perform the analysis which allows for realistic error estimates. Restrictions: The package deals with only standard (SVZ) QCD sum rule calculations. It can be easily adapted to handle other variants of the method (like finite-energy sum rules). Due to the use of FeynCalc, two of the notebooks (qcdsr2pt-construction.nb and qcdsr3pt-construction.nb) only run on version 6.0 of Mathematica. The other two can run on any version. Additional comments: The package consists of the following 4 notebooks: • qcdsr2pt-construction.nb – This notebook constructs the QCD sum rules for octet baryon masses and outputs them, one particle at a time, to disk in plain text for analysis. For reference, we include all the output files (named Mass-*.txt ) as part of the package, totaling 8 files in about 20 lines. The user should generate the outputs on their own computer and check against the supplied ones. • qcdsr2pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr2pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats. • qcdsr3pt-construction.nb – This notebook constructs the QCD sum rules for the octet baryon magnetic moments and outputs them, one particle at a time, to disk in plain text for analysis. Again, for reference, we include all the output files (named Mag-*.txt ), totaling 24 files in about 400 lines. The user should generate the outputs on their own computer and check against the supplied ones to make sure the program is running properly. • qcdsr3pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr3pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats. Each notebook can be run separately, apart from the simple interface between the construction and analysis programs via plain text files written to disk. Running time: For mass calculations, qcdsr2ptconstruction.nb and qcdsr2pt-analysis.nb take about a minute each to run on a laptop. For magnetic moment calculations, qcdsr3pt-construction.nb can take up to 10 minutes for a given particle, and qcdsr3pt-analysis.nb typically a few minutes, depending on the number of Monte Carlo samples.