×

pySecDec: a toolbox for the numerical evaluation of multi-scale integrals. (English) Zbl 07693053

Summary: We present pySecDec, a new version of the program SecDec, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.

MSC:

65-XX Numerical analysis
30-XX Functions of a complex variable

References:

[1] Henn, J. M., Phys. Rev. Lett., 110, 251601 (2013)
[2] Kotikov, A. V., Phys. Lett. B. Phys. Lett. B, Phys. Lett. B, 295, 409-127 (1992), (Erratum )
[3] Gehrmann, T.; Remiddi, E., Nuclear Phys. B, 580, 485-518 (2000) · Zbl 1071.81089
[4] Hepp, K., Comm. Math. Phys., 2, 301-326 (1966) · Zbl 1222.81219
[5] Roth, M.; Denner, A., Nuclear Phys. B, 479, 495-514 (1996)
[6] Binoth, T.; Heinrich, G., Nuclear Phys. B, 585, 741-759 (2000) · Zbl 1042.81565
[7] Heinrich, G., Internat. J. Modern Phys. A, 23, 1457-1486 (2008) · Zbl 1153.81522
[8] Carter, J.; Heinrich, G., Comput. Phys. Comm., 182, 1566-1581 (2011) · Zbl 1262.81119
[9] Borowka, S.; Carter, J.; Heinrich, G., Comput. Phys. Comm., 184, 396-408 (2013)
[10] Borowka, S.; Heinrich, G.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T., Comput. Phys. Comm., 196, 470-491 (2015) · Zbl 1360.81013
[11] Soper, D. E., Phys. Rev. D, 62, 014009 (2000)
[12] Beerli, S., A New Method for Evaluating Two-Loop Feynman Integrals and Its Application to Higgs Production (Ph.D. thesis), Zurich, ETH (2008)
[13] Bogner, C.; Weinzierl, S., Comput. Phys. Comm., 178, 596-610 (2008) · Zbl 1196.81010
[14] Gluza, J.; Kajda, K.; Riemann, T.; Yundin, V., Eur. Phys. J. C, 71, 1516 (2011)
[15] Ueda, T.; Fujimoto, J., PoS, ACAT08, 120 (2008)
[16] Kaneko, T.; Ueda, T., PoS, ACAT2010, 082 (2010)
[17] Smirnov, A.; Tentyukov, M., Comput. Phys. Comm., 180, 735-746 (2009) · Zbl 1198.81044
[18] Smirnov, A.; Smirnov, V.; Tentyukov, M., Comput. Phys. Comm., 182, 790-803 (2011) · Zbl 1214.81171
[19] Smirnov, A. V., Comput. Phys. Comm., 185, 2090-2100 (2014) · Zbl 1351.81078
[20] Smirnov, A. V., Comput. Phys. Comm., 204, 189-199 (2016) · Zbl 1378.65075
[21] J.A.M. Vermaseren, New features of FORM, 2000. arXiv:math-ph/0010025.
[22] Kuipers, J.; Ueda, T.; Vermaseren, J. A.M., Comput. Phys. Comm., 189, 1-19 (2015) · Zbl 1344.65050
[23] Hahn, T., Comput. Phys. Comm., 168, 78-95 (2005) · Zbl 1196.65052
[24] Hahn, T., J. Phys. Conf. Ser., 608, 1, 012066 (2015)
[25] J. Schlenk, T. Zirke, (2016) Proceedings, 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders): Los Angeles, CA, USA, June 15-19, 2015. arXiv:1601.03982.
[26] Schlenk, J., Techniques for Higher Order Corrections and Their Application to LHC Phenomenology (2016), Technical University Munich
[27] Kaneko, T.; Ueda, T., Comput. Phys. Comm., 181, 1352-1361 (2010) · Zbl 1219.65014
[28] B.D. McKay, A. Piperno, Practical graph isomorphism, II, 2013, ArXiv E-Prints arXiv:1301.1493. · Zbl 1394.05079
[29] http://www.graphviz.org.
[30] W. Bruns, B. Ichim, C. Söger, The power of pyramid decomposition in Normaliz, 2012, ArXiv E-Prints arXiv:1206.1916. · Zbl 1332.68298
[31] W. Bruns, B. Ichim, T. Römer, C. Söger, Normaliz. Algorithms for rational cones and affine monoids. Available from http://www.math.uos.de/normaliz.
[32] Fleischer, J.; Kotikov, A. V.; Veretin, O. L., Phys. Lett. B, 417, 163-172 (1998)
[33] Davydychev, A. I.; Kalmykov, M., Nuclear Phys. B, 699, 3-64 (2004) · Zbl 1123.81388
[34] Bonciani, R.; Mastrolia, P.; Remiddi, E., Nuclear Phys. B, 690, 138-176 (2004)
[35] Ferroglia, A.; Passera, M.; Passarino, G.; Uccirati, S., Nuclear Phys. B, 680, 199-270 (2004) · Zbl 1042.81060
[36] Heinrich, G.; Huber, T.; Maitre, D., Phys. Lett. B, 662, 344-352 (2008)
[37] von Manteuffel, A.; Panzer, E.; Schabinger, R. M., Phys. Rev. D, 93, 12, 125014 (2016)
[38] Bonciani, R.; Del Duca, V.; Frellesvig, H.; Henn, J. M.; Moriello, F.; Smirnov, V. A., J. High Energy Phys., 12, 096 (2016)
[39] Primo, A.; Tancredi, L., Nuclear Phys. B, 916, 94-116 (2017) · Zbl 1356.81136
[40] Fleischer, J.; Kotikov, A. V.; Veretin, O. L., Nuclear Phys. B, 547, 343-374 (1999)
[41] Dubovyk, I.; Freitas, A.; Gluza, J.; Riemann, T.; Usovitsch, J., Proceedings, 13th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory (LL2016): Leipzig, Germany, April 24-29, 2016. Proceedings, 13th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory (LL2016): Leipzig, Germany, April 24-29, 2016, PoS, LL2016, 075 (2016)
[42] Huber, T.; Maitre, D., Comput. Phys. Comm., 175, 122-144 (2006) · Zbl 1196.68326
[43] Binoth, T.; Glover, E. W.N.; Marquard, P.; van der Bij, J. J., J. High Energy Phys., 05, 060 (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.