User menu

From multiple unitarity cuts to the coproduct of Feynman integrals

Bibliographic reference Abreu, Samuel ; Britto, Ruth ; Duhr, Claude ; Gardi, Einan. From multiple unitarity cuts to the coproduct of Feynman integrals. In: Journal of High Energy Physics, Vol. 2014, no.10, p. 125 (2014)
Permanent URL
  1. Cutkosky R. E., Singularities and Discontinuities of Feynman Amplitudes, 10.1063/1.1703676
  2. G. ’t Hooft and M. Veltman, DIAGRAMMAR, NATO Adv. Study Inst. Ser. B Phys. 4 (1974) 177–322
  3. M. Veltman, Diagrammatica: The Path to Feynman rules, Cambridge Lect. Notes Phys. 4 (1994) 1.
  4. Landau L.D., On analytic properties of vertex parts in quantum field theory, 10.1016/0029-5582(59)90154-3
  5. E. Remiddi, Dispersion Relations for Feynman Graphs, Helv. Phys. Acta 54 (1982) 364 [ INSPIRE ].
  6. Bern Zvi, Dixon Lance, Dunbar David C., Kosower David A., One-loop n-point gauge theory amplitudes, unitarity and collinear limits, 10.1016/0550-3213(94)90179-1
  7. Bern Zvi, Dixon Lance, Dunbar David C., Kosower David A., Fusing gauge theory tree amplitudes into loop amplitudes, 10.1016/0550-3213(94)00488-z
  8. Britto Ruth, Cachazo Freddy, Feng Bo, Generalized unitarity and one-loop amplitudes in super-Yang–Mills, 10.1016/j.nuclphysb.2005.07.014
  9. R. Britto, E. Buchbinder, F. Cachazo and B. Feng, One-loop amplitudes of gluons in SQCD, Phys. Rev. D 72 (2005) 065012 [ hep-ph/0503132 ] [ INSPIRE ].
  10. Buchbinder Evgeny I, Cachazo Freddy, Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills, 10.1088/1126-6708/2005/11/036
  11. D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [ arXiv:0704.1835 ] [ INSPIRE ].
  12. Britto Ruth, Feng Bo, Integral coefficients for one-loop amplitudes, 10.1088/1126-6708/2008/02/095
  13. Mastrolia Pierpaolo, Double-cut of scattering amplitudes and Stokes' Theorem, 10.1016/j.physletb.2009.06.033
  14. D.A. Kosower and K.J. Larsen, Maximal Unitarity at Two Loops, Phys. Rev. D 85 (2012) 045017 [ arXiv:1108.1180 ] [ INSPIRE ].
  15. Goncharov A. B., Galois symmetries of fundamental groupoids and noncommutative geometry, 10.1215/s0012-7094-04-12822-2
  16. A.B. Goncharov, Multiple polylogarithms and mixed Tate motives, math/0103059 [ INSPIRE ].
  17. Gaiotto Davide, Maldacena Juan, Sever Amit, Vieira Pedro, Pulling the straps of polygons, 10.1007/jhep12(2011)011
  18. M. Caffo, H. Czyz, S. Laporta and E. Remiddi, The Master differential equations for the two loop sunrise selfmass amplitudes, Nuovo Cim. A 111 (1998) 365 [ hep-th/9805118 ] [ INSPIRE ].
  19. Müller-Stach Stefan, Weinzierl Stefan, Zayadeh Raphael, A second-order differential equation for the two-loop sunrise graph with arbitrary masses, 10.4310/cntp.2012.v6.n1.a5
  20. Caron-Huot Simon, Larsen Kasper J., Uniqueness of two-loop master contours, 10.1007/jhep10(2012)026
  21. L. Adams, C. Bogner and S. Weinzierl, The two-loop sunrise graph with arbitrary masses, arXiv:1302.7004 [ INSPIRE ].
  22. S. Bloch and P. Vanhove, The elliptic dilogarithm for the sunset graph, arXiv:1309.5865 [ INSPIRE ].
  23. Remiddi Ettore, Tancredi Lorenzo, Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph, 10.1016/j.nuclphysb.2014.01.009
  24. REMIDDI E., VERMASEREN J. A. M., HARMONIC POLYLOGARITHMS, 10.1142/s0217751x00000367
  25. Gehrmann T., Remiddi E., Two-loop master integrals for jets: the planar topologies, 10.1016/s0550-3213(01)00057-8
  26. Kalmykov M.Yu., Veretin O., Single-scale diagrams and multiple binomial sums, 10.1016/s0370-2693(00)00574-8
  27. Kalmykov Mikhail Yu, Ward Bennie F.L, Yost Scott A, Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter, 10.1088/1126-6708/2007/10/048
  28. Bonciani R., Degrassi G., Vicini A., On the generalized harmonic polylogarithms of one complex variable, 10.1016/j.cpc.2011.02.011
  29. Ablinger Jakob, Blümlein Johannes, Schneider Carsten, Harmonic sums and polylogarithms generated by cyclotomic polynomials, 10.1063/1.3629472
  30. Ablinger Jakob, Blümlein Johannes, Schneider Carsten, Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms, 10.1063/1.4811117
  31. Goncharov A. B., Multiple polylogarithms, cyclotomy and modular complexes, 10.4310/mrl.1998.v5.n4.a7
  32. Chen Kuo-Tsai, Iterated path integrals, 10.1090/s0002-9904-1977-14320-6
  33. Goncharov A. B., Spradlin M., Vergu C., Volovich A., Classical Polylogarithms for Amplitudes and Wilson Loops, 10.1103/physrevlett.105.151605
  34. A.B. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 [ INSPIRE ].
  35. Brown Francis C. S., Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$, 10.24033/asens.2099
  36. Duhr Claude, Gangl Herbert, Rhodes John R., From polygons and symbols to polylogarithmic functions, 10.1007/jhep10(2012)075
  37. F. Brown, On the decomposition of motivic multiple zeta values, arXiv:1102.1310 [ INSPIRE ].
  38. Duhr Claude, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, 10.1007/jhep08(2012)043
  39. Arkani-Hamed N., Bourjaily J., Cachazo F., Trnka J., Local integrals for planar scattering amplitudes, 10.1007/jhep06(2012)125
  40. F. Cachazo, Sharpening The Leading Singularity, arXiv:0803.1988 [ INSPIRE ].
  41. 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
  42. Henn Johannes M., Multiloop Integrals in Dimensional Regularization Made Simple, 10.1103/physrevlett.110.251601
  43. Henn Johannes M., Smirnov Alexander V., Smirnov Vladimir A., Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation, 10.1007/jhep07(2013)128
  44. Henn Johannes M., Smirnov Vladimir A., Analytic results for two-loop master integrals for Bhabha scattering I, 10.1007/jhep11(2013)041
  45. Henn Johannes M., Smirnov Alexander V., Smirnov Vladimir A., Evaluating single-scale and/or non-planar diagrams by differential equations, 10.1007/jhep03(2014)088
  46. Argeri Mario, Di Vita Stefano, Mastrolia Pierpaolo, Mirabella Edoardo, Schlenk Johannes, Schubert Ulrich, Tancredi Lorenzo, Magnus and Dyson series for Master Integrals, 10.1007/jhep03(2014)082
  47. Bogner Christian, Weinzierl Stefan, Periods and Feynman integrals, 10.1063/1.3106041
  48. Dixon Lance J., Drummond James M., Henn Johannes M., Bootstrapping the three-loop hexagon, 10.1007/jhep11(2011)023
  49. Dixon Lance J., Drummond James M., Henn Johannes M., Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory, 10.1007/jhep01(2012)024
  50. Drummond J. M., Generalised ladders and single-valued polylogs, 10.1007/jhep02(2013)092
  51. Chavez Federico, Duhr Claude, Three-mass triangle integrals and single-valued polylogarithms, 10.1007/jhep11(2012)114
  52. Dixon Lance J., Duhr Claude, Pennington Jeffrey, Single-valued harmonic polylogarithms and the multi-Regge limit, 10.1007/jhep10(2012)074
  53. Drummond James, Duhr Claude, Eden Burkhard, Heslop Paul, Pennington Jeffrey, Smirnov Vladimir A., Leading singularities and off-shell conformal integrals, 10.1007/jhep08(2013)133
  54. Dixon Lance J., Drummond James M., von Hippel Matt, Pennington Jeffrey, Hexagon functions and the three-loop remainder function, 10.1007/jhep12(2013)049
  55. Dixon Lance J., Drummond James M., Duhr Claude, Pennington Jeffrey, The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory, 10.1007/jhep06(2014)116
  56. Kotikov A.V., Differential equations method. New technique for massive Feynman diagram calculation, 10.1016/0370-2693(91)90413-k
  57. Kotikov A.V., Differential equations method: the calculation of vertex-type Feynman diagrams, 10.1016/0370-2693(91)90834-d
  58. Kotikov A.V., Differential equation method. The calculation of N-point Feynman diagrams, 10.1016/0370-2693(91)90536-y
  59. Gehrmann T., Remiddi E., Differential equations for two-loop four-point functions, 10.1016/s0550-3213(00)00223-6
  60. O. Steinmann, Über den Zusammenhang zwischen den Wightmanfunktionen und der retardierten Kommutatoren, Helv. Phys. Acta. 33 (1960) 257.
  61. O. Steinmann, Wightman-funktionen und retardierten kommutatoren, Helv. Phys. Acta. 33 (1960) 347.
  62. H.P. Stapp, Inclusive cross-sections are discontinuities, Phys. Rev. D 3 (1971) 3177 [ INSPIRE ].
  63. Ussyukina N.I., Davydychev A.I., Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs, 10.1016/0370-2693(93)91118-7
  64. Bern Zvi, Dixon Lance, Kosower David A., Dimensionally-regulated pentagon integrals, 10.1016/0550-3213(94)90398-0
  65. Anastasiou C., Glover E.W.N., Oleari C., Scalar one-loop integrals using the negative-dimension approach, 10.1016/s0550-3213(99)00637-9
  66. 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
  67. 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
  68. 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
  69. P. Ball, V.M. Braun and H.G. Dosch, Form-factors of semileptonic D decays from QCD sum rules, Phys. Rev. D 44 (1991) 3567 [ INSPIRE ].
  70. Mastrolia Pierpaolo, On triple-cut of scattering amplitudes, 10.1016/j.physletb.2006.11.037
  71. R.P. Feynman, Quantum theory of gravitation, Acta Phys. Polon. 24 (1963) 697 [ INSPIRE ].
  72. R. Feynman, Problems in quantizing the gravitational field, and the massless yang-mills field, in Magic without magic, J. Klauder ed., San Francisco (1972), pp. 355–375.
  73. R. Feynman, Closed loop and tree diagrams, in Magic without magic, J. Klauder ed., San Francisco (1972), pp. 377–408.
  74. Huber Tobias, Maître Daniel, HypExp 2, Expanding hypergeometric functions about half-integer parameters, 10.1016/j.cpc.2007.12.008
  75. R. Eden, P. Landshoff, D. Olive and J. Polkinghorne, The Analytic S-Matrix, Cambridge University Press, Cambridge U.K. (1966).
  76. Van Neerven W.L., Dimensional regularization of mass and infrared singularities in two-loop on-shell vertex functions, 10.1016/0550-3213(86)90165-3
  77. Brown Francis C.S., Polylogarithmes multiples uniformes en une variable, 10.1016/j.crma.2004.02.001