User menu

Three-mass triangle integrals and single-valued polylogarithms

Bibliographic reference Chavez, Federico ; Duhr, Claude. Three-mass triangle integrals and single-valued polylogarithms. In: Journal of High Energy Physics, Vol. 2012, no.11, p. 114 (2012)
Permanent URL
  1. Chetyrkin K.G., Kataev A.L., Tkachov F.V., New approach to evaluation of multiloop Feynman integrals: The Gegenbauer polynomial x-space technique, 10.1016/0550-3213(80)90289-8
  2. Chetyrkin K.G., Tkachov F.V., Integration by parts: The algorithm to calculate β-functions in 4 loops, 10.1016/0550-3213(81)90199-1
  3. Gehrmann T., Remiddi E., Differential equations for two-loop four-point functions, 10.1016/s0550-3213(00)00223-6
  4. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [ hep-ph/0102033 ] [ INSPIRE ].
  5. Kotikov A.V., Differential equations method. New technique for massive Feynman diagram calculation, 10.1016/0370-2693(91)90413-k
  6. Kotikov A.V., Differential equations method: the calculation of vertex-type Feynman diagrams, 10.1016/0370-2693(91)90834-d
  7. Kotikov A.V., Differential equation method. The calculation of N-point Feynman diagrams, 10.1016/0370-2693(91)90536-y
  8. Boss �. �., Davydychev A. I., A method of calculating massive Feynman integrals, 10.1007/bf01016805
  9. Laporta S., Remiddi E., Analytic treatment of the two loop equal mass sunrise graph, 10.1016/j.nuclphysb.2004.10.044
  10. REMIDDI E., VERMASEREN J. A. M., HARMONIC POLYLOGARITHMS, 10.1142/s0217751x00000367
  11. Gehrmann T., Remiddi E., Two-loop master integrals for jets: the planar topologies, 10.1016/s0550-3213(01)00057-8
  12. A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, arXiv:1105.2076 .
  13. A.B. Goncharov, Multiple polylogarithms and mixed Tate motives, math/0103059 .
  14. Davydychev A.I., Kalmykov M.Yu., Massive Feynman diagrams and inverse binomial sums, 10.1016/j.nuclphysb.2004.08.020
  15. Davydychev A.I., Kalmykov M.Yu., New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams, 10.1016/s0550-3213(01)00095-5
  16. Ablinger Jakob, Blümlein Johannes, Schneider Carsten, Harmonic sums and polylogarithms generated by cyclotomic polynomials, 10.1063/1.3629472
  17. Smirnov V.A., Analytical result for dimensionally regularized massless on-shell double box, 10.1016/s0370-2693(99)00777-7
  18. Tausk J.B., Non-planar massless two-loop Feynman diagrams with four on-shell legs, 10.1016/s0370-2693(99)01277-0
  19. Smirnov V.A., Veretin O.L., Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators, 10.1016/s0550-3213(99)00686-0
  20. Anastasiou C., Gehrmann T., Oleari C., Remiddi E., Tausk J.B., The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs, 10.1016/s0550-3213(00)00251-0
  21. Anastasiou C., Tausk J.B., Tejeda-Yeomans M.E., The on-shell massless planar double box diagram with an irreducible numerator, 10.1016/s0920-5632(00)00853-7
  22. Gehrmann T., Remiddi E., Two-loop master integrals for jets: the non-planar topologies, 10.1016/s0550-3213(01)00074-8
  23. Bonciani R, Ferroglia A, Gehrmann T, Maître D, Studerus C, Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel, 10.1088/1126-6708/2008/07/129
  24. Bonciani R, Ferroglia A, Gehrmann T, Studerus C, Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel, 10.1088/1126-6708/2009/08/067
  25. Bonciani R., Ferroglia A., Gehrmann T., von Manteuffel A., Studerus C., Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel, 10.1007/jhep01(2011)102
  26. Birthwright T.G, Glover E.W.N, Marquard P, Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs, 10.1088/1126-6708/2004/09/042
  27. Ussyukina N.I., Davydychev A.I., An approach to the evaluation of three- and four-point ladder diagrams, 10.1016/0370-2693(93)91834-a
  28. Ussyukina Natalia I., Davydychev Andrei I., New results for two-loop off-shell three-point diagrams, 10.1016/0370-2693(94)90874-5
  29. A.I. Davydychev, Explicit results for all orders of the Q-expansion of certain massive and massless diagrams, Phys. Rev. D 61 (2000) 087701 [ hep-ph/9910224 ] [ INSPIRE ].
  30. F.C.S. Brown, Single-valued multiple polylogarithms in one variable, C. R. Acad. Sci. Paris Ser. I 338 (2004).
  31. Dixon Lance J., Duhr Claude, Pennington Jeffrey, Single-valued harmonic polylogarithms and the multi-Regge limit, 10.1007/jhep10(2012)074
  32. J. Drummond, Generalised ladders and single-valued polylogarithms, arXiv:1207.3824 [ INSPIRE ].
  33. Ree Rimhak, Lie Elements and an Algebra Associated With Shuffles, 10.2307/1970243
  34. A.B. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 .
  35. Chen Kuo-Tsai, Iterated path integrals, 10.1090/s0002-9904-1977-14320-6
  36. F.C.S. Brown, Multiple zeta values and periods of moduli spaces M 0,n , math/0606419 .
  37. Goncharov A. B., Spradlin M., Vergu C., Volovich A., Classical Polylogarithms for Amplitudes and Wilson Loops, 10.1103/physrevlett.105.151605
  38. Duhr Claude, Gangl Herbert, Rhodes John R., From polygons and symbols to polylogarithmic functions, 10.1007/jhep10(2012)075
  39. Duhr Claude, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, 10.1007/jhep08(2012)043
  40. Gaiotto Davide, Maldacena Juan, Sever Amit, Vieira Pedro, Pulling the straps of polygons, 10.1007/jhep12(2011)011
  41. J. Zhao, Variations of mixed Hodge structures of multiple polylogarithms, math/0302055 .
  42. H. Cheng and T.T. Wu, Expanding Protons: Scattering At High-energies, MIT Press, Cambridge U.S.A. (1987).
  43. Brown Francis, The Massless Higher-Loop Two-Point Function, 10.1007/s00220-009-0740-5
  44. Del Duca Vittorio, Duhr Claude, Nigel Glover E. W., Smirnov Vladimir A., The one-loop pentagon to higher orders in ϵ, 10.1007/jhep01(2010)042
  45. 't Hooft G., Veltman M., Scalar one-loop integrals, 10.1016/0550-3213(79)90605-9
  46. Smirnov A.V., Tentyukov M.N., Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA), 10.1016/j.cpc.2008.11.006
  47. Smirnov A.V., Smirnov V.A., Tentyukov M., FIESTA 2: Parallelizeable multiloop numerical calculations, 10.1016/j.cpc.2010.11.025
  48. C.W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, cs/0004015 .
  49. Vollinga Jens, Weinzierl Stefan, Numerical evaluation of multiple polylogarithms, 10.1016/j.cpc.2004.12.009
  50. T. Gehrmann and L. Tancredi, unpublished.
  52. A.B. Goncharov, Polylogarithms in arithmetic and geometry, in Proc. of the International Congress of Mathematicians, Vol. 1, 2 Zurich (1994), pg 374–387, Birkhauser, Basel Germany (1995).