• [1]

    A. Gehrmann-De Ridder, T. Gehrmann, and E. W. N. Glover, JHEP 09, 056 (2005), arXiv:hep-ph/0505111

  • [2]

    J. Currie, E. Glover, and S. Wells, JHEP 04, 066 (2013), arXiv:1301.4693

  • [3]

    M. Czakon, Phys. Lett. B 693, 259-268 (2010), arXiv:1005.0274

  • [4]

    M. Czakon, Nucl. Phys. B 849, 250-295 (2011), arXiv:1101.0642

  • [5]

    R. Boughezal, K. Melnikov, and F. Petriello, Phys. Rev. D 85, 034025 (2012), arXiv:1111.7041

  • [6]

    S. Catani and M. H. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485, 291-419 (1997) [hep-ph/9605323] [InSPIRE], [Erratum: Nucl. Phys. B 510, 503 (1998)]

  • [7]

    V. Del Duca, C. Duhr, G. Somogyi et al., JHEP 04, 036 (2015), arXiv:1501.07226

  • [8]

    B. W. Harris and J. F. Owens, Phys. Rev. D 65, 094032 (2002), arXiv:hep-ph/0102128

  • [9]

    T. Binoth and G. Heinrich, Nucl. Phys. B 585, 741-759 (2000), arXiv:hep-ph/0004013

  • [10]

    S. Borowka, G. Heinrich, S. Jahn et al., Comput. Phys. Commun. 222, 313-326 (2018), arXiv:1703.09692

  • [11]

    M. Cacciari, F. A. Dreyer, A. Karlberg et al., Fully Differential Vector-Boson-Fusion Higgs Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett. 115, 082002 (2015), arXiv: 1506.02660 [InSPIRE], [Erratum: Phys. Rev. Lett. 120, 139901 (2018)]

  • [12]

    S. Catani and M. Grazzini, Phys. Rev. Lett. 98, 222002 (2007), arXiv:hep-ph/0703012

  • [13]

    R. Boughezal, X. Liu, and F. Petriello, Phys. Rev. D 91, 094035 (2015), arXiv:1504.02540

  • [14]

    R. Boughezal, C. Focke, X. Liu et al., Phys. Rev. Lett. 115, 062002 (2015), arXiv:1504.02131

  • [15]

    J. Gaunt, M. Stahlhofen, F. J. Tackmann et al., JHEP 09, 058 (2015), arXiv:1505.04794

  • [16]

    F. Caola, K. Melnikov, and R. Röntsch, Eur. Phys. J. C 77, 248 (2017), arXiv:1702.01352

  • [17]

    L. Magnea, E. Maina, G. Pelliccioli et al., 12, 107 (2018), arXiv: 1806.09570 [InSPIRE], [Erratum: JHEP 06, 013 (2019)]

  • [18]

    L. Magnea, E. Maina, G. Pelliccioli et al., JHEP 12, 062 (2018), arXiv:1809.05444

  • [19]

    C. Anastasiou and K. Melnikov, Nucl. Phys. B 646, 220-256 (2002), arXiv:hep-ph/0207004

  • [20]

    C. Anastasiou, L. J. Dixon, and K. Melnikov, Nucl. Phys. Proc. Suppl. 116, 193-197 (2003), arXiv:hep-ph/0211141

  • [21]

    C. Anastasiou, L. J. Dixon, K. Melnikov et al., Phys. Rev. Lett. 91, 182002 (2003), arXiv:hep-ph/0306192

  • [22]

    K. Chetyrkin and F. Tkachov, Nucl. Phys. B 192, 159-204 (1981)

  • [23]

    A. Kotikov, Phys. Lett. B 254, 158-164 (1991)

  • [24]

    T. Gehrmann and E. Remiddi, Nucl. Phys. B 580, 485-518 (2000), arXiv:hep-ph/9912329

  • [25]

    O. Tarasov, Phys. Rev. D 54, 6479-6490 (1996), arXiv:hep-th/9606018

  • [26]

    R. Lee, Nucl. Phys. B 830, 474-492 (2010), arXiv:0911.0252

  • [27]

    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]

  • [28]

    X. Liu, Y.-Q. Ma, and C.-Y. Wang, Phys. Lett. B 779, 353-357 (2018), arXiv:1711.09572

  • [29]

    X. Liu and Y.-Q. Ma, Phys. Rev. D 99, 071501 (2019), arXiv:1801.10523

  • [30]

    P. Zhang, C.-Y. Wang, X. Liu et al., JHEP 04, 116 (2019), arXiv:1810.07656

  • [31]

    Y. Wang, Z. Li, and N. Ul Basat, Phys. Rev. D 101, 076023 (2020), arXiv:1901.09390

  • [32]

    X. Guan, X. Liu, and Y.-Q. Ma, Complete reduction of two-loop five-light-parton scattering amplitudes, arXiv: 1912.09294 [InSPIRE]

  • [33]

    Q. Yang, R.-Y. Zhang, M.-M. Long et al., Chin. Phys. C 44, 093101 (2020), arXiv:2005.11010

  • [34]

    C. Brønnum-Hansen and C.-Y. Wang, Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion, arXiv: 2009.03742 [InSPIRE]

  • [35]

    V. A. Smirnov, Commun. Math. Phys. 134, 109-137 (1990)

  • [36]

    V. A. Smirnov, Mod. Phys. Lett. A 10, 1485-1500 (1995), arXiv:hep-th/9412063

  • [37]

    A. I. Davydychev and J. Tausk, Nucl. Phys. B 397, 123-142 (1993)

  • [38]

    D. J. Broadhurst, Eur. Phys. J. C 8, 311-333 (1999), arXiv:hep-th/9803091

  • [39]

    http://theor.jinr.ru/~kalmykov/three-loop/three.html#Master

  • [40]

    B. Kniehl, A. Pikelner, and O. Veretin, JHEP 08, 024 (2017), arXiv:1705.05136

  • [41]

    Y. Schroder and A. Vuorinen, JHEP 06, 051 (2005), arXiv:hep-ph/0503209

  • [42]

    T. Luthe, Fully massive vacuum integrals at 5 loops. PhD thesis, Bielefeld U., 2015 [InSPIRE]

  • [43]

    T. Luthe, A. Maier, P. Marquard et al., JHEP 03, 020 (2017), arXiv:1701.07068

  • [44]

    A. Smirnov and A. Petukhov, Lett. Math. Phys. 97, 37-44 (2011), arXiv:1004.4199

  • [45]

    S. Laporta, Int. J. Mod. Phys. A 15, 5087-5159 (2000), arXiv:hep-ph/0102033

  • [46]

    C. Anastasiou and A. Lazopoulos, JHEP 07, 046 (2004), arXiv:hep-ph/0404258

  • [47]

    A. V. Smirnov and F. S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic, arXiv: 1901.07808 [InSPIRE]

  • [48]

    P. Maierhöfer and J. Usovitsch, Kira 1.2 Release Notes, arXiv: 1812.01491 [InSPIRE]

  • [49]

    A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, arXiv: 1201.4330 [InSPIRE]

  • [50]

    R. N. Lee, J. Phys. Conf. Ser. 523, 012059 (2014), arXiv:1310.1145

  • [51]

    A. von Manteuffel and R. M. Schabinger, Phys. Lett. B 744, 101-104 (2015), arXiv:1406.4513

  • [52]

    T. Peraro, JHEP 12, 030 (2016), arXiv:1608.01902

  • [53]

    J. Klappert and F. Lange, Comput. Phys. Commun. 247, 106951 (2020), arXiv:1904.00009

  • [54]

    J. Klappert, S. Y. Klein, and F. Lange, Interpolation of Dense and Sparse Rational Functions and other Improvements in FireFly, arXiv: 2004.01463 [InSPIRE]

  • [55]

    J. Klappert, F. Lange, P. Maierhöfer et al., Integral Reduction with Kira 2.0 and Finite Field Methods, arXiv: 2008.06494 [InSPIRE]

  • [56]

    T. Peraro, JHEP 07, 031 (2019), arXiv:1905.08019

  • [57]

    J. Böhm, A. Georgoudis, K. J. Larsen et al., JHEP 09, 024 (2018), arXiv:1805.01873

  • [58]

    P. Mastrolia and S. Mizera, JHEP 02, 139 (2019), arXiv:1810.03818

  • [59]

    Z. Bern, L. J. Dixon, and D. A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett. B 302, 299-308 (1993) [hep-ph/9212308] [InSPIRE], [Erratum: Phys. Lett. B 318, 649 (1993)]

  • [60]

    E. Remiddi, Nuovo Cim. A 110, 1435-1452 (1997), arXiv:hep-th/9711188

  • [61]

    J. M. Henn, Phys. Rev. Lett. 110, 251601 (2013), arXiv:1304.1806

  • [62]

    R. N. Lee, JHEP 04, 108 (2015), arXiv:1411.0911

  • [63]

    W. Bernreuther, C. Bogner, and O. Dekkers, JHEP 06, 032 (2011), arXiv:1105.0530

  • [64]

    W. Bernreuther, C. Bogner, and O. Dekkers, JHEP 10, 161 (2013), arXiv:1309.6887

  • [65]

    O. Dekkers and W. Bernreuther, Phys. Lett. B 738, 325-333 (2014), arXiv:1409.3124

  • [66]

    V. Magerya and A. Pikelner, JHEP 12, 026 (2019), arXiv:1910.07522

  • [67]

    A. Gehrmann-De Ridder, T. Gehrmann, and G. Heinrich, Nucl. Phys. B 682, 265-288 (2004), arXiv:hep-ph/0311276

  • [68]

    A. Gehrmann-De Ridder, T. Gehrmann, and E. Glover, Nucl. Phys. B 691, 195-222 (2004), arXiv:hep-ph/0403057

  • [69]

    S. Groote, J. Korner, and A. Pivovarov, Annals Phys. 322, 2374-2445 (2007), arXiv:hep-ph/0506286

  • [70]

    T. Huber and D. Maitre, Comput. Phys. Commun. 178, 755-776 (2008), arXiv:0708.2443

  • [71]

    M. Y. Kalmykov and B. A. Kniehl, JHEP 07, 031 (2017), arXiv:1612.06637

  • [72]

    C. Anastasiou, C. Duhr, F. Dulat et al., JHEP 07, 003 (2013), arXiv:1302.4379

  • [73]

    A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series: More Special Functions, Taylor and Francis Ltd. vol.3 (1989) [InSPIRE]