User menu

Cuts from residues: the one-loop case

Bibliographic reference Abreu, Samuel ; Britto, Ruth ; Duhr, Claude ; Gardi, Einan. Cuts from residues: the one-loop case. In: Journal of High Energy Physics, (03/2017)
Permanent URL
  1. Cutkosky R. E., Singularities and Discontinuities of Feynman Amplitudes, 10.1063/1.1703676
  2. R. Eden, P. Landshoff, D. Olive and J. Polkinghorne, The Analytic S-Matrix, Cambridge University Press, Cambridge U.K. (1966).
  3. ’t Hooft G., Veltman M., Diagrammar, Particle Interactions at Very High Energies (1974) ISBN:9781468428285 p.177-322, 10.1007/978-1-4684-2826-1_5
  4. Landau L.D., On analytic properties of vertex parts in quantum field theory, 10.1016/0029-5582(59)90154-3
  5. Bern Zvi, Dixon Lance, Kosower David A., One-loop amplitudes for e+e− to four partons, 10.1016/s0550-3213(97)00703-7
  6. Britto Ruth, Cachazo Freddy, Feng Bo, Generalized unitarity and one-loop amplitudes in super-Yang–Mills, 10.1016/j.nuclphysb.2005.07.014
  7. D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [ arXiv:0704.1835 ] [ INSPIRE ].
  8. D.A. Kosower and K.J. Larsen, Maximal Unitarity at Two Loops, Phys. Rev. D 85 (2012) 045017 [ arXiv:1108.1180 ] [ INSPIRE ].
  9. Caron-Huot Simon, Larsen Kasper J., Uniqueness of two-loop master contours, 10.1007/jhep10(2012)026
  10. H. Johansson, D.A. Kosower and K.J. Larsen, Two-Loop Maximal Unitarity with External Masses, Phys. Rev. D 87 (2013) 025030 [ arXiv:1208.1754 ] [ INSPIRE ].
  11. H. Johansson, D.A. Kosower and K.J. Larsen, Maximal Unitarity for the Four-Mass Double Box, Phys. Rev. D 89 (2014) 125010 [ arXiv:1308.4632 ] [ INSPIRE ].
  12. M. Søgaard and Y. Zhang, Elliptic Functions and Maximal Unitarity, Phys. Rev. D 91 (2015) 081701 [ arXiv:1412.5577 ] [ INSPIRE ].
  13. K.J. Larsen and Y. Zhang, Integration-by-parts reductions from unitarity cuts and algebraic geometry, Phys. Rev. D 93 (2016) 041701 [ arXiv:1511.01071 ] [ INSPIRE ].
  14. H. Ita, Two-loop Integrand Decomposition into Master Integrals and Surface Terms, Phys. Rev. D 94 (2016) 116015 [ arXiv:1510.05626 ] [ INSPIRE ].
  15. Remiddi Ettore, Tancredi Lorenzo, Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral, 10.1016/j.nuclphysb.2016.04.013
  16. Primo Amedeo, Tancredi Lorenzo, On the maximal cut of Feynman integrals and the solution of their differential equations, 10.1016/j.nuclphysb.2016.12.021
  17. Frellesvig Hjalte, Papadopoulos Costas G., Cuts of Feynman Integrals in Baikov representation, 10.1007/jhep04(2017)083
  18. M. Zeng, Differential equations on unitarity cut surfaces, arXiv:1702.02355 [ INSPIRE ].
  19. Dennen Tristan, Spradlin Marcus, Volovich Anastasia, Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory, 10.1007/jhep03(2016)069
  20. T. Dennen, I. Prlina, M. Spradlin, S. Stanojevic and A. Volovich, Landau Singularities from the Amplituhedron, arXiv:1612.02708 [ INSPIRE ].
  21. M. Veltman, Cambridge Lecture Notes in Physics. Vol. 4: Diagrammatica: The Path to Feynman rules, Cambridge University Press, Cambridge U.K. (1994).
  22. E. Remiddi, Dispersion Relations for Feynman Graphs, Helv. Phys. Acta 54 (1982) 364 [ INSPIRE ].
  23. Mandelstam Stanley, Analytic Properties of Transition Amplitudes in Perturbation Theory, 10.1103/physrev.115.1741
  24. 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 ].
  25. Abreu Samuel, Britto Ruth, Duhr Claude, Gardi Einan, From multiple unitarity cuts to the coproduct of Feynman integrals, 10.1007/jhep10(2014)125
  26. Abreu Samuel, Britto Ruth, Grönqvist Hanna, Cuts and coproducts of massive triangle diagrams, 10.1007/jhep07(2015)111
  27. F. Cachazo, Sharpening The Leading Singularity, arXiv:0803.1988 [ INSPIRE ].
  28. Arkani-Hamed Nima, Cachazo Freddy, Kaplan Jared, What is the simplest quantum field theory?, 10.1007/jhep09(2010)016
  29. Fairlie D. B., Landshoff P. V., Nuttall J., Polkinghorne J. C., Singularities of the Second Type, 10.1063/1.1724262
  30. Fairlie D.B., Landshoff P.V., Nuttall J., Polkinghorne J.C., Physical sheet properties of second type singularities, 10.1016/0031-9163(62)90200-7
  31. Fotiadi Dimitri, Froissart Marcel, Lascoux Jean, Pham Frédéric, Applications of an isotopy theorem, 10.1016/0040-9383(65)90063-7
  32. R.C. Hwa and V.L. Teplitz, Homology and Feynman integrals, W.A. Benjamin Inc., San Francisco U.S.A. (1966).
  33. F. Pham eds., Singularities of Integrals, Springer, Berlin Germany (2005).
  34. Leray Jean, Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.), 10.24033/bsmf.1515
  35. Bern Zvi, Dixon Lance, Kosower David A., Dimensionally regulated one-loop integrals, 10.1016/0370-2693(93)90400-c
  36. O.V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54 (1996) 6479 [ hep-th/9606018 ] [ INSPIRE ].
  37. R.N. Lee, Space-time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D, Nucl. Phys. B 830 (2010) 474 [ arXiv:0911.0252 ] [ INSPIRE ].
  38. M. Spradlin and A. Volovich, Symbols of One-Loop Integrals From Mixed Tate Motives, JHEP 11 (2011) 084 [ arXiv:1105.2024 ] [ INSPIRE ].
  39. Baikov P.A, Explicit solutions of the multi-loop integral recurrence relations and its application, 10.1016/s0168-9002(97)00126-5
  40. Lee R.N., Calculating multiloop integrals using dimensional recurrence relation and D-analyticity, 10.1016/j.nuclphysbps.2010.08.032
  41. GROZIN A. G., INTEGRATION BY PARTS: AN INTRODUCTION, 10.1142/s0217751x11053687
  42. Ellis R. Keith, Zanderighi Giulia, Scalar one-loop integrals for QCD, 10.1088/1126-6708/2008/02/002
  43. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover Publications, Mineola U.S.A. (1972).
  44. Moch Sven, Uwer Peter, Weinzierl Stefan, Nested sums, expansion of transcendental functions, and multiscale multiloop integrals, 10.1063/1.1471366
  45. D. Fotiadi and F. Pham, Analytic Properties of Some Integrals over Complex Manifolds, in Homology and Feynman integrals, R.C. Hwa and V.L. Teplitz eds., W.A. Benjamin Inc., San Francisco U.S.A. (1966).
  46. Simmons-Duffin David, Projectors, shadows, and conformal blocks, 10.1007/jhep04(2014)146
  47. Caron-Huot Simon, Henn Johannes M., Iterative structure of finite loop integrals, 10.1007/jhep06(2014)114
  48. D. Fotiadi and F. Pham, Analytic study of Some Feynman Graphs by Homological Methods, in Homology and Feynman integrals, R.C. Hwa and V.L. Teplitz eds., W.A. Benjamin Inc., San Francisco U.S.A. (1966).
  49. E. Panzer, Feynman integrals and hyperlogarithms, arXiv:1506.07243 [ INSPIRE ].
  51. S. Bloch and D. Kreimer, Cutkosky Rules and Outer Space, arXiv:1512.01705 [ INSPIRE ].
  52. Boyling J. B., A homological approach to parametric Feynman integrals, 10.1007/bf02800115
  53. Landshoff P. V., Olive D. I., Polkinghorne J. C., The hierarchical principle in perturbation theory, 10.1007/bf02752870
  54. Tkachov F.V., A theorem on analytical calculability of 4-loop renormalization group functions, 10.1016/0370-2693(81)90288-4
  55. 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
  56. R.N. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, JHEP 07 (2008) 031 [ arXiv:0804.3008 ] [ INSPIRE ].
  57. Anastasiou Charalampos, Melnikov Kirill, Higgs boson production at hadron colliders in NNLO QCD, 10.1016/s0550-3213(02)00837-4
  58. Anastasiou Charalampos, Melnikov Kirill, Pseudoscalar Higgs boson production at hadron colliders in next-to-next-to-leading order QCD, 10.1103/physrevd.67.037501
  59. Anastasiou Charalampos, Dixon Lance, Melnikov Kirill, NLO Higgs boson rapidity distributions at hadron colliders, 10.1016/s0920-5632(03)80168-8
  60. Anastasiou Charalampos, Dixon Lance, Melnikov Kirill, Petriello Frank, Dilepton Rapidity Distribution in the Drell-Yan Process at Next-to-Next-to-Leading Order in QCD, 10.1103/physrevlett.91.182002
  61. C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [ hep-ph/0312266 ] [ INSPIRE ].
  62. Anastasiou Charalampos, Duhr Claude, Dulat Falko, Mistlberger Bernhard, Soft triple-real radiation for Higgs production at N3LO, 10.1007/jhep07(2013)003
  63. R.N. Lee and V.A. Smirnov, The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions, JHEP 12 (2012) 104 [ arXiv:1209.0339 ] [ INSPIRE ].
  64. H.P. Stapp, Inclusive cross-sections are discontinuities, Phys. Rev. D 3 (1971) 3177 [ INSPIRE ].
  65. Polkinghorne J. C., Inclusive cross-sections and discontinuities, 10.1007/bf02734212
  66. Caron-Huot Simon, Wilhelm Matthias, Renormalization group coefficients and the S-matrix, 10.1007/jhep12(2016)010
  67. Smirnov Alexander V., Petukhov Alexey V., The Number of Master Integrals is Finite, 10.1007/s11005-010-0450-0
  68. R.N. Lee and A.A. Pomeransky, Critical points and number of master integrals, JHEP 11 (2013) 165 [ arXiv:1308.6676 ] [ INSPIRE ].
  69. Kotikov A.V., Differential equations method. New technique for massive Feynman diagram calculation, 10.1016/0370-2693(91)90413-k
  70. Kotikov A.V., Differential equations method: the calculation of vertex-type Feynman diagrams, 10.1016/0370-2693(91)90834-d
  71. A.V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123 [Erratum ibid. B 295 (1992) 409] [ INSPIRE ].
  72. Gehrmann T., Remiddi E., Differential equations for two-loop four-point functions, 10.1016/s0550-3213(00)00223-6
  73. Henn Johannes M., Multiloop Integrals in Dimensional Regularization Made Simple, 10.1103/physrevlett.110.251601
  74. Federbush Paul, Calculation of Some Homology Groups Relevant to Sixth‐Order Feynman Diagrams, 10.1063/1.1704354
  75. A. Goncharov, Volumes of hyperbolic manifolds and mixed Tate motives, alg-geom/9601021 .