Uniqueness of two-loop master contours

Journal of High Energy Physics

Volumn 2012, Issue 10, 2012, Pages

  Caron Huot, Simon ^a   Larsen, Kasper J ^b,c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

^c CEA SACLAY   (France)

Author keywords

Gauge symmetry; Scattering amplitudes

Indexed keywords

EID: 84868148506     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP10(2012)026     Document Type: Article

References (75)

1. R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
2. R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
3. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
4. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
5. Z. Bern, L.J. Dixon and D.A. Kosower, Progress in one loop QCD computations, Ann. Rev. Nucl. Part. Sci. 46 (1996) 109 [hep-ph/9602280] [INSPIRE].
6. Z. Bern and A. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336] [INSPIRE].
7. Z. Bern, L.J. Dixon and D.A. Kosower, One loop amplitudes for e+e- to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [INSPIRE].
8. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop selfdual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [INSPIRE].
9. R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
10. R. Britto, F. Cachazo and B. Feng, Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts, Phys. Rev. D 71 (2005) 025012 [hep-th/0410179] [INSPIRE].
11. S.J. Bidder, N. Bjerrum-Bohr, L.J. Dixon and D.C. Dunbar, N = 1 supersymmetric one-loop amplitudes and the holomorphic anomaly of unitarity cuts, Phys. Lett. B 606 (2005) 189 [hep-th/0410296] [INSPIRE].
12. S.J. Bidder, N. Bjerrum-Bohr, D.C. Dunbar and W.B. Perkins, One-loop gluon scattering amplitudes in theories with N < 4 supersymmetries, Phys. Lett. B 612 (2005) 75 [hep-th/0502028] [INSPIRE].
13. S.J. Bidder, D.C. Dunbar and W.B. Perkins, Supersymmetric Ward identities and NMHV amplitudes involving gluinos, JHEP 08 (2005) 055 [hep-th/0505249] [INSPIRE].
14. Z. Bern, N. Bjerrum-Bohr, D.C. Dunbar and H. Ita, Recursive calculation of one-loop QCD integral coefficients, JHEP 11 (2005) 027 [hep-ph/0507019] [INSPIRE].
15. N. Bjerrum-Bohr, D.C. Dunbar and W.B. Perkins, Analytic structure of three-mass triangle coefficients, JHEP 04 (2008) 038 [arXiv:0709.2086] [INSPIRE].
16. Z. Bern, L.J. Dixon and D.A. Kosower, Bootstrapping multi-parton loop amplitudes in QCD, Phys. Rev. D 73 (2006) 065013 [hep-ph/0507005] [INSPIRE].
17. 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].
18. R. Britto, B. Feng and P. Mastrolia, The Cut-constructible part of QCD amplitudes, Phys. Rev. D 73 (2006) 105004 [hep-ph/0602178] [INSPIRE].
19. P. Mastrolia, On Triple-cut of scattering amplitudes, Phys. Lett. B 644 (2007) 272 [hep-th/0611091] [INSPIRE].
20. A. Brandhuber, S. McNamara, B.J. Spence and G. Travaglini, Loop amplitudes in pure Yang-Mills from generalised unitarity, JHEP 10 (2005) 011 [hep-th/0506068] [INSPIRE].
21. G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].
22. Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
23. D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [INSPIRE].
24. S. Badger, Direct Extraction Of One Loop Rational Terms, JHEP 01 (2009) 049 [arXiv:0806.4600] [INSPIRE].
25. C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, D-dimensional unitarity cut method, Phys. Lett. B 645 (2007) 213 [hep-ph/0609191] [INSPIRE].
26. C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, Unitarity cuts and Reduction to master integrals in d dimensions for one-loop amplitudes, JHEP 03 (2007) 111 [hep-ph/0612277] [INSPIRE].
27. W.T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes, JHEP 04 (2008) 049 [arXiv:0801.2237] [INSPIRE].
28. R. Britto and B. Feng, Unitarity cuts with massive propagators and algebraic expressions for coefficients, Phys. Rev. D 75 (2007) 105006 [hep-ph/0612089] [INSPIRE].
29. R. Britto and B. Feng, Integral coefficients for one-loop amplitudes, JHEP 02 (2008) 095 [arXiv:0711.4284] [INSPIRE].
30. R. Britto, B. Feng and P. Mastrolia, Closed-Form Decomposition of One-Loop Massive Amplitudes, Phys. Rev. D 78 (2008) 025031 [arXiv:0803.1989] [INSPIRE].
31. R. Britto, B. Feng and G. Yang, Polynomial Structures in One-Loop Amplitudes, JHEP 09 (2008) 089 [arXiv:0803.3147] [INSPIRE].
32. C.F. Berger and D. Forde, Multi-Parton Scattering Amplitudes via On-Shell Methods, Ann. Rev. Nucl. Part. Sci. 60 (2010) 181 [arXiv:0912.3534] [INSPIRE].
33. Z. Bern, J.J. Carrasco, T. Dennen, Y.-t. Huang and H. Ita, Generalized Unitarity and Six-Dimensional Helicity, Phys. Rev. D 83 (2011) 085022 [arXiv:1010.0494] [INSPIRE].
34. D.A. Kosower and K.J. Larsen, Maximal Unitarity at Two Loops, Phys. Rev. D 85 (2012) 045017 [arXiv:1108.1180] [INSPIRE].
35. K.J. Larsen, Global Poles of the Two-Loop Six-Point N = 4 SYM integrand, arXiv:1205.0297 [INSPIRE].
36. A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Infrared structure of e+e- → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
37. S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [INSPIRE].
38. G. Dissertori et al., Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations, JHEP 08 (2009) 036 [arXiv:0906.3436] [INSPIRE].
39. G. Dissertori et al., Precise determination of the strong coupling constant at NNLO in QCD from the three-jet rate in electron-positron annihilation at LEP, Phys. Rev. Lett. 104 (2010) 072002 [arXiv:0910.4283] [INSPIRE].
40. P. Mastrolia and G. Ossola, On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes, JHEP 11 (2011) 014 [arXiv:1107.6041] [INSPIRE].
41. S. Badger, H. Frellesvig and Y. Zhang, Hepta-Cuts of Two-Loop Scattering Amplitudes, JHEP 04 (2012) 055 [arXiv:1202.2019] [INSPIRE].
42. E.I. Buchbinder and F. Cachazo, Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang-Mills, JHEP 11 (2005) 036 [hep-th/0506126] [INSPIRE].
43. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality For The S Matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].
44. E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
45. F. Cachazo and D. Skinner, On the structure of scattering amplitudes in N = 4 super Yang-Mills and N = 8 supergravity, arXiv:0801.4574 [INSPIRE].
46. F. Cachazo, Sharpening The Leading Singularity, arXiv:0803.1988 [INSPIRE].
47. J. Milne, Elliptic Curves, BookSurge Publishers (2006).
48. M.F. Paulos, M. Spradlin and A. Volovich, Mellin Amplitudes for Dual Conformal Integrals, JHEP 08 (2012) 072 [arXiv:1203.6362] [INSPIRE].
49. S. Caron-Huot, unpublished.
50. S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys. B 704 (2005) 349 [hep-ph/0406160] [INSPIRE].
51. S. Muller-Stach, S. Weinzierl and R. Zayadeh, A Second-Order Differential Equation for the Two-Loop Sunrise Graph with Arbitrary Masses, arXiv:1112.4360 [INSPIRE].
52. A. Hodges, The Box Integrals in Momentum-Twistor Geometry, arXiv:1004.3323 [INSPIRE].
53. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [INSPIRE].
54. J. Gluza, K. Kajda and D.A. Kosower, Towards a Basis for Planar Two-Loop Integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].
55. Z. Bern, L.J. Dixon and D. Kosower, A Two loop four gluon helicity amplitude in QCD, JHEP 01 (2000) 027 [hep-ph/0001001] [INSPIRE].
56. T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
57. T. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].
58. 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].
59. A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].
60. C. Duhr, H. Gangl and J.R. Rhodes, From polygons and symbols to polylogarithmic functions, arXiv:1110.0458 [INSPIRE].
61. S. Caron-Huot and S. He, Jumpstarting the All-Loop S-matrix of Planar N = 4 Super Yang-Mills, JHEP 07 (2012) 174 [arXiv:1112.1060] [INSPIRE].
62. E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
63. V.A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B 460 (1999) 397 [hep-ph/9905323] [INSPIRE].
64. 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].
65. Z. Bern, J. Carrasco, H. Ita, H. Johansson and R. Roiban, On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts, Phys. Rev. D 80 (2009) 065029 [arXiv:0903.5348] [INSPIRE].
66. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095] [INSPIRE].
67. L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrapping the three-loop hexagon, JHEP 11 (2011) 023 [arXiv:1108.4461] [INSPIRE].
68. L.J. Dixon, J.M. Drummond and J.M. Henn, Analytic result for the two-loop six-point NMHV amplitude in N = 4 super Yang-Mills theory, JHEP 01 (2012) 024 [arXiv:1111.1704] [INSPIRE].
69. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
70. G. Korchemsky, J. Drummond and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [INSPIRE].
71. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [INSPIRE].
72. Z. Bern, L. Dixon, D. Kosower, R. Roiban, M. Spradlin, C. Vergu and A. Volovich, The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [INSPIRE].
73. L. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].
74. S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [arXiv:1010.1167] [INSPIRE].
75. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand For Scattering Amplitudes in Planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].