TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3-point functions in momentum space. Program summary Program Title: TripleK CPC Library link to program files: http://dx.doi.org/10.17632/5sz4bt28vr.1 Developer's repository link: https://triplek.hepforge.org/ Licensing provisions: GNU General Public License v3.0 Programming language: Wolfram Language [1] (Mathematica 10.0 or higher) Supplementary material: The package includes five Mathematica notebooks containing bulk of the results regarding the structure of conformal 3-point functions. Nature of problem: Triple-K integrals were introduced in [2] as a convenient tool for the analysis of conformal 3-point functions in momentum space. All 3-point functions of scalar operators, conserved currents and stress tensor can be expressed in terms of triple-K integrals. Furthermore, a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators is expressible in terms of triple-K integrals as well. Since the expressions are usually long and unwieldy, an automated tool is essential for efficient manipulations. Solution method: In [3] an effective reduction algorithm was provided for expressing a large class of triple-K integrals in terms of master integrals. The presented package implements this reduction scheme. As far as the multi-loop Feynman integrals are concerned, the conversion to multiple-K integrals proceeds by means of Schwinger parameterization. Additional comments including restrictions and unusual features: Despite extensive testing, this package is a one man job, therefore bugs are unavoidable. Please, report all issues at adam.bzowski@physics.uu.se or abzowski@gmail.com. [1] Wolfram Research Inc., Mathematica, Version 11.2, 12.0, Champaign, IL, 2020 [2] A. Bzowski, P. McFadden, K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111. http://arxiv.org/abs/1304.7760 arXiv:1304.7760, https://doi.org/10.1007/JHEP03(2014)111 doi: 10.1007/JHEP03(2014)111 [3] A. Bzowski, P. McFadden, K. Skenderis, Evaluation of conformal integrals, JHEP 02 (2016) 068. http://arxiv.org/abs/1511.0235/ arXiv:1511.02357, https://doi.org/10.1007/JHEP02(2016)068 doi: 10.1007/JHEP02(2016)068 (C) 2020 The Author(s). Published by Elsevier B.V.

Automated summary

The Mathematica package presented is tailored for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space, with additional tools for a wide range of 2- and 3-point massless multi-loop Feynman integrals. Detailed calculations for numerous conformal 3-point functions in momentum space are included in accompanying Mathematica notebooks.