Automated generation of lattice QCD Feynman rules

The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams.

Program summary

Program title: HiPPY, HPsrcCatalogue identifier: AEDX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLv2 (see Additional comments below)No. of lines in distributed program, including test data, etc.: 513 426No. of bytes in distributed program, including test data, etc.: 4 893 707Distribution format: tar.gzProgramming language: Python, Fortran95Computer: HiPPy: Single-processor workstations. HPsrc: Single-processor workstations and MPI-enabled multi-processor systemsOperating system: HiPPy: Any for which Python v2.5.x is available. HPsrc: Any for which a standards-compliant Fortran95 compiler is availableHas the code been vectorised or parallelised?: YesRAM: Problem specific, typically less than 1 GB for either codeClassification: 4.4, 11.5Nature of problem: Derivation and use of perturbative Feynman rules for complicated lattice QCD actions.Solution method: An automated expansion method implemented in Python (HiPPy) and code to use expansions to generate Feynman rules in Fortran95 (HPsrc).Restrictions: No general restrictions. Specific restrictions are discussed in the text.Additional comments: The HiPPy and HPsrc codes are released under the second version of the GNU General Public Licence (GPL v2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, we ask that any publications including results from the use of this code or of modifications of it cite Refs. 1,2] as well as this paper. Finally, we also ask that details of these publications, as well as of any bugs or required or useful improvements of this core code, would be communicated to us.Running time: Very problem specific, depending on the complexity of the Feynman rules and the number of integration points. Typically between a few minutes and several weeks. The installation tests provided with the program code take only a few seconds to run.References:

• 1] 

  A. Hart, G.M. von Hippel, R.R. Horgan, L.C. Storoni, Automatically generating Feynman rules for improved lattice eld theories, J. Comput. Phys. 209 (2005) 340–353, doi:10.1016/j.jcp.2005.03.010, arXiv:hep-lat/0411026.

• 2] 

  M. Lüscher, P. Weisz, Efficient Numerical Techniques for Perturbative Lattice Gauge Theory Computations, Nucl. Phys. B 266 (1986) 309, doi:10.1016/0550-3213(86)90094-5.