Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation

Journal of High Energy Physics

Volumn 2013, Issue 7, 2013, Pages

  Henn, Johannes M ^a   Smirnov, Alexander V ^b,c   Smirnov, Vladimir A ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

Author keywords

Renormalization Regularization and Renormalons; Scattering Amplitudes

Indexed keywords

EID: 84881448242     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP07(2013)128     Document Type: Article

References (50)

1. A. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [ INSPIRE ].
2. A. Kotikov, Differential equation method: the calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123 [ INSPIRE ].
3. E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [ hep-th/9711188 ] [ INSPIRE ].
4. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [ hep-ph/9912329 ] [ INSPIRE ].
5. T. Gehrmann and E. Remiddi, Two loop master integrals for γ → 3 jets: the planar topologies, Nucl. Phys. B 601 (2001) 248 [ hep-ph/0008287 ] [ INSPIRE ]. (Pubitemid 33402603)
6. T. Gehrmann and E. Remiddi, Two loop master integrals for γ → 3 jets: the nonplanar topologies, Nucl. Phys. B 601 (2001) 287 [ hep-ph/0101124 ] [ INSPIRE ]. (Pubitemid 33402604)
7. A. Smirnov and A. Petukhov, The number of master integrals is finite, Lett. Math. Phys. 97 (2011) 37 [ arXiv:1004.4199 ] [ INSPIRE ].
8. K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [ INSPIRE ].
9. C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [ hep-ph/0404258 ] [ INSPIRE ].
10. A. Smirnov, Algorithm FIRE - Feynman Integral REduction, JHEP 10 (2008) 107 [ arXiv:0807.3243 ] [ INSPIRE ].
11. A. Smirnov and V. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, arXiv:1302.5885 [ INSPIRE ].
12. C. Studerus, Reduze-Feynman integral reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [ arXiv:0912.2546 ] [ INSPIRE ].
13. A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman integral reduction, arXiv:1201.4330 [ INSPIRE ].
14. R. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [ INSPIRE ].
15. M. Argeri and P. Mastrolia, Feynman diagrams and differential equations, Int. J. Mod. Phys. A 22 (2007) 4375 [ arXiv:0707.4037 ] [ INSPIRE ].
16. V.A. Smirnov, Analytic tools for Feynman integrals, Springer Tracts in Modern Physics volume 250, Springer U.S.A. (2012).
17. M. Czakon and A. Mitov, Inclusive heavy flavor hadroproduction in NLO QCD: the exact analytic result, Nucl. Phys. B 824 (2010) 111 [ arXiv:0811.4119 ] [ INSPIRE ].
18. A. von Manteuffel and C. Studerus, Top quark pairs at two loops and Reduze 2, PoS(LL2012)059 [ arXiv:1210.1436 ] [ INSPIRE ].
19. J.M. Henn, Multiloop integrals in dimensional regularization made simple, arXiv:1304.1806 [ INSPIRE ].
20. K.-T. Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1997) 831.
21. A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998) 497 [ arXiv:1105.2076 ] [ INSPIRE ].
22. V.A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B 460 (1999) 397 [ hep-ph/9905323 ] [ INSPIRE ].
23. V.A. Smirnov, Analytical result for dimensionally regularized massless on shell planar triple box, Phys. Lett. B 567 (2003) 193 [ hep-ph/0305142 ] [ INSPIRE ].
24. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [ hep-th/0505205 ] [ INSPIRE ].
25. G. Heinrich, T. Huber, D. Kosower and V. Smirnov, Nine-propagator master integrals for massless three-loop form factors, Phys. Lett. B 678 (2009) 359 [ arXiv:0902.3512 ] [ INSPIRE ].
26. T. Gehrmann, J.M. Henn and T. Huber, The three-loop form factor in N = 4 super Yang-Mills, JHEP 03 (2012) 101 [ arXiv:1112.4524 ] [ INSPIRE ].
27. J.M. Drummond and J.M. Henn, Simple loop integrals and amplitudes in N = 4 SYM, JHEP 05 (2011) 105 [ arXiv:1008.2965 ] [ INSPIRE ].
28. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, JHEP 06 (2012) 125 [ arXiv:1012.6032 ] [ INSPIRE ].
29. A. Kotikov, L. Lipatov, A. Onishchenko and V. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754-756] [ hep-th/0404092 ] [ INSPIRE ].
30. N. Arkani-Hamed et al., Scattering amplitudes and the positive Grassmannian, arXiv:1212.5605 [ INSPIRE ].
31. F. Brown and K. Yeats, Spanning forest polynomials and the transcendental weight of Feynman graphs, Commun. Math. Phys. 301 (2011) 357 [ arXiv:0910.5429 ] [ INSPIRE ].
32. C. Anastasiou, J. Tausk and M. Tejeda-Yeomans, The on-shell massless planar double box diagram with an irreducible numerator, Nucl. Phys. Proc. Suppl. 89 (2000) 262 [ hep-ph/0005328 ] [ INSPIRE ].
33. Z. Bern et al., Three-loop superfiniteness of N = 8 supergravity, Phys. Rev. Lett. 98 (2007) 161303 [ hep-th/0702112 ] [ INSPIRE ]. (Pubitemid 46633706)
34. V. Knizhnik and A. Zamolodchikov, Current algebra and Wess-Zumino model in two-dimensions, Nucl. Phys. B 247 (1984) 83 [ INSPIRE ].
35. T. Gehrmann, G. Heinrich, T. Huber and C. Studerus, Master integrals for massless three-loop form-factors: one-loop and two-loop insertions, Phys. Lett. B 640 (2006) 252 [ hep-ph/0607185 ] [ INSPIRE ].
36. G. Heinrich, T. Huber and D. MâItre, Master integrals for fermionic contributions to massless three-loop form-factors, Phys. Lett. B 662 (2008) 344 [ arXiv:0711.3590 ] [ INSPIRE ].
37. P. Baikov, K. Chetyrkin, A. Smirnov, V. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002 [ arXiv:0902.3519 ] [ INSPIRE ].
38. T. Gehrmann, E. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [ arXiv:1004.3653 ] [ INSPIRE ].
39. R. Lee and V. Smirnov, Analytic ε-expansions of master integrals corresponding to massless three-loop form factors and three-loop g - 2 up to four-loop transcendentality weight, JHEP 02 (2011) 102 [ arXiv:1010.1334 ] [ INSPIRE ].
40. J.M. Henn and T. Huber, The four-loop cusp anomalous dimension from iterated Wilson line integrals, arXiv:1304.6418 [ INSPIRE ].
41. E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [ hep-ph/9905237 ] [ INSPIRE ].
42. A. Smirnov and M. Tentyukov, Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA), Comput. Phys. Commun. 180 (2009) 735 [ arXiv:0807.4129 ] [ INSPIRE ].
43. A. Smirnov, V. Smirnov and M. Tentyukov, FIESTA 2: parallelizeable multiloop numerical calculations, Comput. Phys. Commun. 182 (2011) 790 [ arXiv:0912.0158 ] [ INSPIRE ].
44. 0,n, math/0606419.
45. G. A.B., A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 [ INSPIRE ].
46. M.Y. Kalmykov and B.A. Kniehl, Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations and polynomial solutions, Phys. Lett. B 714 (2012) 103 [ arXiv:1205.1697 ] [ INSPIRE ].
47. M.Y. Kalmykov and B.A. Kniehl, 'Sixth root of unity' and Feynman diagrams: hypergeometric function approach point of view, Nucl. Phys. Proc. Suppl. 205-206 (2010) 129 [ arXiv:1007.2373 ] [ INSPIRE ].
48. H.R.P. Ferguson, D.H. Bailey and S. Arno, Analysis of PSLQ, an integer relation finding algorithm, Math. Comput. 68 (1999) 351.
49. J. Fleischer, A. Kotikov and O. Veretin, Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass, Nucl. Phys. B 547 (1999) 343 [ hep-ph/9808242 ] [ INSPIRE ].
50. M. Marcolli, Feynman motives, World Scientific Publishing Company, Singapore (2009).