Some steps towards improving IBP calculations and related topics. (English) Zbl 1478.81004
Bluemlein, Johannes (ed.) et al., Anti-differentiation and the calculation of Feynman amplitudes. Selected papers based on the presentations at the conference, Zeuthen, Germany, October 2020. Cham: Springer. Texts Monogr. Symb. Comput., 501-518 (2021).
Summary: A number of aspects of IBP reductions are discussed, indicating some of the major bottlenecks. Potential future developments are indicated, including some in the realm of mathematics and computer algebra.
For the entire collection see [Zbl 1475.81004].
For the entire collection see [Zbl 1475.81004].
MSC:
| 81-08 | Computational methods for problems pertaining to quantum theory |
References:
| [1] | B. Ruijl, T. Ueda, J.A.M. Vermaseren, Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams. Comput. Phys. Commun. 253, 107198 (2020) · Zbl 1535.81008 · doi:10.1016/j.cpc.2020.107198 |
| [2] | K.G. Chetyrkin, F.V. Tkachov, Integration by parts: The algorithm to calculate beta functions in 4 loops. Nucl. Phys. B192, 159 (1981) · doi:10.1016/0550-3213(81)90199-1 |
| [3] | S.G. Gorishny, A.L. Kataev, S.A. Larin, The \(\mathcal{O}(\alpha_S^3)\)-corrections to \(σ_{}\) tot \((e^+e^−\)→ hadrons) and Γ(τ → \(ν_{}\) τ + hadrons) in QCD. Phys. Lett. B212, 238 (1988); ibid. B259, 144 (1991) |
| [4] | J.A.M. Vermaseren, New features of FORM. arXiv:math-ph/0010025 |
| [5] | B.Ruijl, T. Ueda, J. Vermaseren, FORM version 4.2, e-print arXiv:1707.06453(hep-ph) |
| [6] | S.G. Gorishny, S.A. Larin, F.V. Tkachov, INR preprint P-0330 (Moscow, 1984) |
| [7] | S.G. Gorishny, S.A. Larin, L.R. Surguladze, F.V. Tkachov, Mincer: Program for multiloop calculations in quantum field theory for the schoonschip system. Comput. Phys. Commun. 55, 381 (1989) · doi:10.1016/0010-4655(89)90134-3 |
| [8] | S.A. Larin, F.V. Tkachov, J.A.M. Vermaseren, The FORM version of MINCER, Nikhef report NIKHEF-H-91-18 |
| [9] | S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations. Int. J. Mod. Phys. A 15, 5087-5159 (2000) · Zbl 0973.81082 |
| [10] | A.V. Smirnov, Algorithm FIRE - Feynman integral REduction. JHEP 10, 107 (2008) · Zbl 1245.81033 · doi:10.1088/1126-6708/2008/10/107 |
| [11] | A. von Manteuffel, C. Studerus, Reduze 2 - Distributed Feynman integral reduction. e-Print: arXiv:1201.4330 [hep-ph] |
| [12] | P. Maierher, J. Usovitsch, P. Uwer, Kira-A Feynman integral reduction program. Comput. Phys. Commun. 230, 99-112 (2018) · Zbl 1498.81004 · doi:10.1016/j.cpc.2018.04.012 |
| [13] | P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, Order alpha**4(s) QCD corrections to Z and tau decays. Phys. Rev. Lett. 101, 012002 (2008) · doi:10.1103/PhysRevLett.101.012002 |
| [14] | P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, Five-loop running of the QCD coupling constant. Phys. Rev. Lett. 118(8), 082002 (2017 |
| [15] | R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals. J. Phys. Conf. Ser. 523, 012059 (2014) |
| [16] | M. Veltman, An IBM-7090 Program for Symbolic Evaluation Of Algebraic Expressions, Especially Feynman Diagrams. CERN preprint (1965) |
| [17] | H. Strubbe, ‘Manual for schoonschip: A CDC 6000/7000 program for symbolic evaluation of algebraic expressions. Comput. Phys. Commun. 8, 1 (1974) · doi:10.1016/0010-4655(74)90081-2 |
| [18] | R.N. Lee, A.V. Smirnov, V.A. Smirnov, Master integrals for four-loop massless propagators up to transcendentality weight twelve. Nucl. Phys. B856, 95-110 (2012) · Zbl 1246.81057 · doi:10.1016/j.nuclphysb.2011.11.005 |
| [19] | T. Kaneko, A Feynman graph generator for any order of coupling constants. Comput. Phys. Commun. 92, 127-152 (1995) · doi:10.1016/0010-4655(95)00122-6 |
| [20] | F.V. Tkachov, An algorithm for calculating multiloop integrals. Teor. Mat. Fiz. 56, 350 (1983) |
| [21] | K.G. Chetyrkin, V.A. Smirnov, R* operation corrected. Phys. Lett. B144, 419 (1984) · doi:10.1016/0370-2693(84)91291-7 |
| [22] | V.A. Smirnov, K.G. Chetyrkin, R* operation in the minimal subtraction scheme. Theor. Math. Phys. 63, 462 (1985) · doi:10.1007/BF01017902 |
| [23] | K.G. Chetyrkin, Combinatorics of R-, R-1-, and R*-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses. arXiv:1701.08627 |
| [24] | F. Herzog, B. Ruijl, The R*-operation for Feynman graphs with generic numerators. JHEP 05, 037 (2017) · Zbl 1380.81133 · doi:10.1007/JHEP05(2017)037 |
| [25] | J. Blümlein, D. Broadhurst, J.A.M. Vermaseren, The multiple zeta value data mine. Comput. Phys. Commun. 181, 582-625 (2010). e-Print: arXiv:0907.2557 [math-ph] · Zbl 1221.11183 |
| [26] | D.J. Broadhurst, Massive three - loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity. Eur. Phys. J. C 8, 311-333 (1999). e-Print: arXiv:hep-th/9803091 [hep-th] |
| [27] | F. Brown, On the decomposition of motivic multiple zeta values. e-Print: arXiv:1102.1310 [math.NT] · Zbl 1321.11087 |
| [28] | J.M. Borwein, D.M. Bradley, D.J. Broadhurst, Special values of multiple polylogarithms. Trans. Am. Math. Soc. 353, 907-941 (2001). e-Print: arXiv:math/9910045 [math.CA] · Zbl 1002.11093 |
| [29] | O |
| [30] | K.G. Chetyrkin, F.V. Tkachov, Infrared R operation and ultraviolet counterterms in the MS scheme. Phys. Lett. B114, 340 (1982) · doi:10.1016/0370-2693(82)90358-6 |
| [31] | S.O. Moch, Talk in this workshop |
| [32] | R.N. Lee, Presenting LiteRed: a tool for the loop InTEgrals REDuction. e-Print: arXiv:1212.2685 [hep-ph] |
| [33] | C. Studerus, Reduze-Feynman integral reduction in C++. Comput. Phys. Commun. 181, 1293-1300 (2010) · Zbl 1219.81133 · doi:10.1016/j.cpc.2010.03.012 |
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.
