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Manuscript Title: An extended version of the simple and fast Feynman diagram generator EasyFeynDiag
Authors: Bo Xiao, Hao Wang
Program title: EasyFeynDiag
Catalogue identifier: AEPD_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 186(2015)108
Programming language: C.
Computer: Platforms on which an ANSI C compiler is available.
Operating system: Operating Systems on which an ANSI C compiler is available.
RAM: 236000 bytes for a typical two-loop order uubar → ttbar process in the QCD model.
Keywords: Feynman diagram, Effective theory, Perturbative expansion, Scattering process.
PACS: 12.38.Bx, 12.15.Lk.
Classification: 4.4.

Does the new version supersede the previous version?: The new version generates Feynman diagrams better, but is more time consuming, than the previous version.
Overall, the new version supersedes the previous version.

Nature of problem:
Automatic generation of Feynman diagrams from given interactions, scattering process, and number of loops.

Solution method:
The algorithm of EasyFeynDiag is translated from the perturbative expansion formula of the S-matrix [1]. It follows an ordered iterative traversing procedure to find all the possible combinations of the fields and creation/annihilation operators.
Two selection rules are adopted in turn, to suppress equivalent Feynman diagrams originating from vertices relabelling, and from multiple identical particles of an interaction term, respectively. This simple algorithm prohibits equivalent diagrams to one-loop order.
To further prohibit equivalent diagrams to higher order, more careful treating of the identical particles is required. By introducing one additional "order rule" for the identical particles and one additional "selection rule" for identical vertices, the equivalent diagrams are prohibited to two-loop order. Those two rules are explained briefly below:
1. order rule for identical particles
When identical particles from the same vertex are to connect to other legs, those connections must be ordered: the second identical particle must connect to a leg equal or behind the leg connected by the first identical particle, and so on the Nth to the (N - 1)th identical particle. At the same time, proper symmetry factors need to be generated to count for this ordering.
2. selection rule for identical vertices
When m identical particles from the same vertex have connected to m new vertices that are of the same interaction type, these m vertices are defined as identical vertices. If later another particle is to connect to one of these identical vertices, it is only permitted to connect to the most front one, the other (m - 1) connections are represented by a factor m.

Reasons for new version:
High energy calculations to two-loop order are becoming more and more common, e.g. [2]. To introduce, into EasyFeynDiag, the ability to prohibit equivalent diagrams to two-loop order would make it more attractive to workers in High Energy Physics.

Summary of revisions:
  1. the code is organized in a totally new way, more convenient for people to read and modify;
  2. the algorithm for Feynman diagram generation in the program is extended to a version that prohibits equivalent diagrams to two-loop order (the previous version is to one-loop order).

Restrictions:
  1. There are default values for the maximum external particles and internal vertices for a scattering process, and maximum legs or leg types for an interaction term. Users need to modify the corresponding values in the code to get larger limits.
  2. Equivalent Feynman diagrams arise at three-loop order or higher, although this fact does not hurt the correctness of the Feynman amplitudes to be obtained from those diagrams.

Unusual features:
Allow for arbitrary physical model and arbitrary number of loops. Symmetry factors are naturally generated. Small and fast.

Running time:
About 0.139 seconds to generate all the Feynman diagrams of a typical two-loop order uubar → ttbar process in the QCD model.

References:
[1] Bo Xiao, Hao Wang, Shou-hua Zhu, A simple algorithm for automatic Feynman diagram generation, Computer Physics Communications 184 (2013) 1966
[2] Barnreuther, Peter and Czakon, Michal and Mitov, Alexander, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to qqbar → ttbar + X, Phys.Rev.Lett. 109, 132001 (2012)