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Five-particle phase-space integrals in QCD. (English) Zbl 1395.81285
Summary: We present analytical expressions for the 31 five-particle phase-space master integrals in massless QCD as an $$\epsilon$$-series with coefficients being multiple zeta values of weight up to 12. In addition, we provide computer code for the Monte-Carlo integration in higher dimensions, based on the RAMBO algorithm, that has been used to numerically cross-check the obtained results in 4, 6, and 8 dimensions.
##### MSC:
 81V05 Strong interaction, including quantum chromodynamics 81T17 Renormalization group methods applied to problems in quantum field theory 81U05 $$2$$-body potential quantum scattering theory
##### Software:
DREAM ; GSL; FIRE; Cuba; SummerTime; FIRE5; LiteRed; Axodraw; VEGAS; FORM
Full Text:
##### References:
 [1] A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four particle phase space integrals in massless QCD, Nucl. Phys.B 682 (2004) 265 [hep-ph/0311276] [INSPIRE]. · Zbl 1045.81558 [2] Gituliar, O., Master integrals for splitting functions from differential equations in QCD, JHEP, 02, 017, (2016) [3] Gituliar, O.; Moch, S., Towards three-loop QCD corrections to the time-like splitting functions, Acta Phys. Polon., B 46, 1279, (2015) · Zbl 1371.81048 [4] Almasy, AA; Moch, S.; Vogt, A., On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions, Nucl. Phys., B 854, 133, (2012) · Zbl 1229.81296 [5] Chetyrkin, KG; Tkachov, FV, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys., B 192, 159, (1981) [6] Tarasov, OV, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev., D 54, 6479, (1996) · Zbl 0925.81121 [7] R.N. Lee and K.T. Mingulov, DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions and its applications, arXiv:1712.05173 [INSPIRE]. · Zbl 1229.81296 [8] Lee, RN; Mingulov, KT, Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals, JHEP, 04, 061, (2018) [9] A.S. Schwarz, Gauge theories on noncommutative spaces, hep-th/0011261 [INSPIRE]. [10] Blumlein, J.; Broadhurst, DJ; Vermaseren, JAM, The multiple zeta value data mine, Comput. Phys. Commun., 181, 582, (2010) · Zbl 1221.11183 [11] Lee, RN; Mingulov, KT, Introducing summertime: a package for high-precision computation of sums appearing in DRA method, Comput. Phys. Commun., 203, 255, (2016) · Zbl 1375.81230 [12] Ferguson, H.; Bailey, D.; Arno, S., Analysis of PSLQ, an integer relation finding algorithm, Math. Comp., 68, 351, (1999) · Zbl 0927.11055 [13] Kleiss, R.; Stirling, WJ; Ellis, SD, A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun., 40, 359, (1986) [14] Baikov, PA; Chetyrkin, KG, Four loop massless propagators: an algebraic evaluation of all master integrals, Nucl. Phys., B 837, 186, (2010) · Zbl 1206.81087 [15] S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys.A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE]. · Zbl 0973.81082 [16] Laporta, S., High-precision calculation of the 4-loop contribution to the electron g-2 in QED, Phys. Lett., B 772, 232, (2017) [17] Smirnov, AV, FIRE5: a C++ implementation of Feynman integral reduction, Comput. Phys. Commun., 189, 182, (2015) · Zbl 1344.81030 [18] Nogueira, P., Automatic Feynman graph generation, J. Comput. Phys., 105, 279, (1993) · Zbl 0782.68091 [19] B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE]. · Zbl 0927.11055 [20] R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser.523 (2014) 012059 [arXiv:1310.1145] [INSPIRE]. [21] Lepage, GP, A new algorithm for adaptive multidimensional integration, J. Comput. Phys., 27, 192, (1978) · Zbl 0377.65010 [22] T. Hahn, CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun.168 (2005) 78 [hep-ph/0404043] [INSPIRE]. · Zbl 1196.65052 [23] B. Gough. GNU Scientific Library Reference Manual, 3rd edition, Network Theory Ltd. (2009). [24] J.C. Collins and J.A.M. Vermaseren, Axodraw Version 2, arXiv:1606.01177 [INSPIRE].
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