Two-loop helicity amplitudes for quark-quark scattering in QCD and gluino-gluino scattering in supersymmetric Yang-Mills theory

Journal of High Energy Physics

Volumn 8, Issue 9, 2004, Pages 887-956

  De Freitas, Abilio ^a   Bern, Zvi ^b  

^a DESY   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Hadronic Colliders; Jets; NLO Computations; QCD

Indexed keywords

EID: 23044432836     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (108)

1. F. Aversa, P. Chiappetta, M. Greco and J.P. Guillet, Higher order corrections to QCD jets, Phys. Lett. B 210 (1988) 225;
2. 3), Z. Physik C 46 (1990) 253.
3. 3) quarks and gluons, Phys. Rev. Lett. 64 (1990) 2121;
4. 3) in QCD, Phys. Rev. Lett. 69 (1992) 1496.
5. W.T. Giele, E.W.N. Glover and D.A. Kosower, Higher order corrections to jet cross-sections in hadron colliders, Nucl. Phys. B 403 (1993) 633 [hep-ph/9302225].
6. N. Kidonakis, Resummation for heavy quark and jet cross sections, Int. J. Mod. Phys. A 15 (2000) 1245 [hep-ph/9902484];
7. T jet production, Phys. Rev. D 63 (2001) 054019 [hep-ph/0007268].
8. s from DIS data within the bayesian treatment of systematic errors, Eur. Phys. J. C 10 (1999) 395;
9. W.T. Giele, S.A. Keller and D.A. Kosower, Parton distributions with errors, in La Thuile 1999, Results and perspectives in particle physics;
10. D. Stump et al., Uncertainties of predictions from parton distribution functions, I. The Lagrange multiplier method, Phys. Rev. D 65 (2002) 014012 [hep-ph/0101051];
11. J. Pumplin et al., Uncertainties of predictions from parton distribution functions II. The hessian method, Phys. Rev. D 65 (2002) 014013 [hep-ph/0101032];
12. W.T. Giele, S.A. Keller and D.A. Kosower, Parton distribution function uncertainties, hep-ph/0104052;
13. A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Uncertainties of predictions from parton distributions, I. Experimental errors, Eur. Phys. J. C 28 (2003) 455 [hep-ph/0211080].
14. S. Moch, J.A.M. Vermaseren and A. Vogt, The three-loop splitting functions in QCD: the non-singlet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192];
15. A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: the singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111].
16. S. Alekhin, Parton distributions from deep-inelastic scattering data, Phys. Rev. D 68 (2003) 014002 [hep-ph/0211096];
17. A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, NNLO global parton analysis, Phys. Lett. B 531 (2002) 216 [hep-ph/0201127].
18. W.L. van Neerven and A. Vogt, NNLO evolution of deep-inelastic structure functions: the non-singlet case, Nucl. Phys. B 568 (2000) 263 [hep-ph/9907472];
19. NNLO evolution of deep-inelastic structure functions: the singlet case, Nucl. Phys. B 588 (2000) 345 [hep-ph/0006154];
20. Improved approximations for the three-loop splitting functions in QCD, Phys. Lett. B 490 (2000) 111 [hep-ph/0007362];
21. S. Moch, J.A.M. Vermaseren and A. Vogt, Non-singlet structure functions at three loops: fermionic contributions, Nucl. Phys. B 646 (2002) 181 [hep-ph/0209100].
22. E.W.N. Glover, Progress in NNLO calculations for scattering processes, Nucl. Phys. 116 (Proc. Suppl.) (2003) 3 [hep-ph/0211412].
23. Z. Bern, J.S. Rozowsky and B. Yan, Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424];
24. Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162].
25. Z. Bern, L.J. Dixon and D.A. Kosower, A two-loop four-gluon helicity amplitude in QCD, J. High Energy Phys. 01 (2000) 027 [hep-ph/0001001].
26. Z. Bern, L.J. Dixon and A. Ghinculov, Two-loop correction to Bhabha scattering, Phys. Rev. D 63 (2001) 053007 [hep-ph/0010075].
27. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to qq̄ → q′q̄′, Nucl. Phys. B 601 (2001) 318 [hep-ph/0010212];
28. Two-loop QCD corrections to qq̄ → qq̄, Nucl. Phys. B 601 (2001) 341 [hep-ph/0011094].
29. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to massless quark gluon scattering, Nucl. Phys. B 605 (2001) 486 [hep-ph/0101304].
30. E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to gluon gluon scattering, Nucl. Phys. B 605 (2001) 467 [hep-ph/0102201].
31. Z. Bern, A. De Freitas and L.J. Dixon, Two-loop amplitudes for gluon fusion into two photons, J. High Energy Phys. 09 (2001) 037 [hep-ph/0109078].
32. Z. Bern, A. De Freitas, L.J. Dixon, A. Ghinculov and H.L. Wong, QCD and qed corrections to light-by-light scattering, J. High Energy Phys. 11 (2001) 031 [hep-ph/0109079].
33. Z. Bern, A. De Freitas and L.J. Dixon, Two-loop helicity amplitudes for gluon gluon scattering in QCD and supersymmetric Yang-Mills theory, J. High Energy Phys. 03 (2002) 018 [hep-ph/0201161].
34. - → 3jets, Nucl. Phys. B 627 (2002) 107 [hep-ph/0112081].
35. - → 3jets, Nucl. Phys. B 642 (2002) 227 [hep-ph/0206067];
36. f-contribution, Acta Phys. Polon. B33 (2002) 2921 [hep-ph/0207167].
37. Z. Bern, A. De Freitas and L.J. Dixon, Two-loop helicity amplitudes for quark gluon scattering in QCD and gluino gluon scattering in supersymmetric yang- mills theory, J. High Energy Phys. 06 (2003) 028 [hep-ph/0304168].
38. E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QCD helicity amplitudes for massless quark massless gauge boson scattering, J. High Energy Phys. 06 (2003) 033 [hep-ph/0304169].
39. E.W.N. Glover, Two-loop QCD helicity amplitudes for massless quark quark scattering, J. High Energy Phys. 04 (2004) 021 [hep-ph/0401119].
40. F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65;
41. K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate beta functions in 4 loops, Nucl. Phys. B 192 (1981) 159.
42. V.A. Smirnov, Analytical result for dimensionally regularized massless on-shell double box, Phys. Lett. B 460 (1999) 397 [hep-ph/9905323].
43. J.B. Tausk, Non-planar massless two-loop feynman diagrams with four on- shell legs, Phys. Lett. B 469 (1999) 225 [hep-ph/9909506].
44. T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329].
45. C. Anastasiou, T. Gehrmann, C. Oleari, E. Remiddi and J.B. Tausk, The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs, Nucl. Phys. B 580 (2000) 577 [hep-ph/0003261].
46. V.A. Smirnov and O.L. Veretin, Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators, Nucl. Phys. B 566 (2000) 469 [hep-ph/9907385].
47. C. Anastasiou, E.W.N. Glover and C. Oleari, Application of the negative-dimension approach to massless scalar box integrals, Nucl. Phys. B 565 (2000) 445 [hep-ph/9907523];
48. The two-loop scalar and tensor pentabox graph with light-like legs, Nucl. Phys. B 575 (2000) 416 [hep-ph/9912251].
49. S. Catani, The singular behaviour of QCD amplitudes at two-loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439].
50. F.A. Berends and W. Giele, The six gluon process as an example of Weyl-Van der Waerden spinor calculus, Nucl. Phys. B 294 (1987) 700;
51. M.L. Mangano, S.J. Parke and Z. Xu, Duality and multi-gluon scattering, Nucl. Phys. B 298 (1988) 653.
52. M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301.
53. Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett. 70 (1993) 2677 [hep-ph/9302280];
54. Z. Kunszt, A. Signer and Z. Trócsányi, One loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon, Phys. Lett. B 336 (1994) 529 [hep-ph/9405386];
55. Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to two quark three gluon amplitudes, Nucl. Phys. B 437 (1995) 259 [hep-ph/9409393].
56. J. Soffer and J.M. Virey, Testing various polarized parton distributions at RHIC, Nucl. Phys. B 509 (1998) 297 [hep-ph/9706229].
57. D. de Florian, S. Frixione, A. Signer and W. Vogelsang, Next-to-leading order jet cross sections in polarized hadronic collisions, Nucl. Phys. B 539 (1999) 455 [hep-ph/9808262].
58. E. Witten, Perturbative gauge theory as a string theory in twistor space, hep-th/0312171.
59. F. Cachazo, P. Svrcek and E. Witten, MHV vertices and tree amplitudes in gauge theory, J. High Energy Phys. 09 (2004) 006 [hep-th/0403047].
60. I. Bena, Z. Bern and D.A. Kosower, Twistor-space recursive formulation of gauge theory amplitudes, hep-th/0406133.
61. G. Georgiou and V.V. Khoze, Tree amplitudes in gauge theory as scalar MHV diagrams, J. High Energy Phys. 05 (2004) 070 [hep-th/0404072];
62. G. Georgiou, E.W.N. Glover and V.V. Khoze, Non-MHV tree amplitudes in gauge theory, J. High Energy Phys. 07 (2004) 048 [hep-th/0407027].
63. F. Cachazo, P. Svrcek and E. Witten, Twistor space structure of one-loop amplitudes in gauge theory, hep-th/0406177;
64. D.A. Kosower, Next-to-maximal helicity violating amplitudes in gauge theory, hep-th/0406175;
65. A. Brandhuber, B. Spence and G. Travaglini, One-loop gauge theory amplitudes in N = 4 super Yang-Mills from MHV vertices, hep-th/0407214.
66. M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev. D 15 (1977) 996;
67. Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B 124 (1977) 81;
68. S.J. Parke and T.R. Taylor, Perturbative QCD utilizing extended super symmetry, Phys. Lett. B 157 (1985) 81.
69. Z. Bern, A. De Freitas, L.J. Dixon and H.L. Wong, Supersymmetric regularization, two-loop QCD amplitudes and coupling shifts, Phys. Rev. D 66 (2002) 085002 [hep-ph/0202271].
70. 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].
71. Z. Bern, L.J. Dixon and D.A. Kosower, Progress in one-loop QCD computations, Ann. Rev. Nucl. Part. Sci. 46 (1996) 109-148 [hep-ph/9602280].
72. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-reggeon processes in the Yang-Mills theory, Sov. Phys. JETP 44 (1976) 443.
73. V. Del Duca and E.W.N. Glover, The high energy limit of QCD at two loops, J. High Energy Phys. 10 (2001) 035 [hep-ph/0109028];
74. A.V. Bogdan, V. Del Duca, V.S. Fadin and E.W.N. Glover, The quark Regge trajectory at two loops, J. High Energy Phys. 03 (2002) 032 [hep-ph/0201240].
75. G. Sterman and M.E. Tejeda-Yeomans, Multi-loop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130].
76. Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, J. High Energy Phys. 08 (2004) 012 [hep-ph/0404293].
77. J.C. Collins, Renormalization: an introduction to renormalization group, and the operator-product expansion, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1984.
78. R.K. Ellis and J.C. Sexton, QCD radiative corrections to parton parton scattering, Nucl. Phys. B 269 (1986) 445.
79. G. 't Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189.
80. Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451.
81. W. Siegel, Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett. B 84 (1979) 193;
82. D.M. Capper, D.R.T. Jones and P. van Nieuwenhuizen, Regularization by dimensional reduction of super symmetric and nonsupersymmetric gauge theories, Nucl. Phys. B 167 (1980) 479;
83. I. Jack, D.R.T. Jones and K.L. Roberts, Equivalence of dimensional reduction and dimensional regularization, Z. Physik C 63 (1994) 151 [hep-ph/9401349].
84. M.S. Chanowitz, M. Furman and I. Hinchliffe, The axial current in dimensional regularization, Nucl. Phys. B 159 (1979) 225.
85. H.F. Contopanagos and M.B. Einhorn, Theory of the asymptotic S matrix for massless particles, Phys. Rev. D 45 (1992) 1291.
86. F.A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T.T. Wu, Single bremsstrahlung processes in gauge theories, Phys. Lett. B 103 (1981) 124;
87. P. De Causmaecker, R. Gastmans, W. Troost and T.T. Wu, Helicity amplitudes for massless qed, Phys. Lett. B 105 (1981) 215;
88. Z. Xu, D.H. Zhang and L. Chang, Helicity amplitudes for multiple bremsstrahlung in massless nonabelian gauge theories, Nucl. Phys. B 291 (1987) 392.
89. Z. Kunszt, A. Signer and Z. Trócsányi, Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross-sections of multiparton processes, Nucl. Phys. B 420 (1994) 550 [hep-ph/9401294].
90. C. Anastasiou, E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QED and QCD corrections to massless fermion boson scattering, Nucl. Phys. B 629 (2002) 255 [hep-ph/0201274].
91. Z. Kunszt, A. Signer and Z. Trócsányi, One loop helicity amplitudes for all 2 → 2 processes in QCD and N =1 supersymmetric Yang-Mills theory, Nucl. Phys. B 411 (1994) 397 [hep-ph/9305239].
92. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279.
93. L. Lewin, Dilogarithms and associated functions, Macdonald, 1958.
94. K.S. Kölbig, J.A. Mignaco and E. Remiddi, On Nielsen's generalized poly logarithms and their numerical calculation, B.I.T. 10 (1970) 38.
95. E.I. Gates and K.L. Kowalski, Majorana Feynman rules, Phys. Rev. D 37 (1988) 938;
96. A. Denner, H. Eck, O. Hahn and J. Kublbeck, Compact Feynman rules for Majorana fermions, Phys. Lett. B 291 (1992) 278.
97. Z. Bern, L.J. Dixon and C. Schmidt, Isolating a light Higgs boson from the di-photon background at the LHC, Phys. Rev. D 66 (2002) 074018 [hep-ph/0206194];
98. L.J. Dixon and M.S. Siu, Resonance-continuum interference in the di-photon Higgs signal at the LHC, Phys. Rev. Lett. 90 (2003) 252001 [hep-ph/0302233].
99. G. Heinrich, A numerical method for NNLO calculations, Nucl. Phys. 116 (Proc. Suppl.) (2003) 368 [hep-ph/0211144];
100. D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D 67 (2003) 116003 [hep-ph/0212097];
101. S. Weinzierl, Subtraction terms at NNLO, J. High Energy Phys. 03 (2003) 062 [hep-ph/0302180];
102. A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four-particle phase space integrals in massless QCD, Nucl. Phys. B 682 (2004) 265 [hep-ph/0311276];
103. C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev. D 69 (2004) 076010 [hep-ph/0311311];
104. T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265];
105. 2), Phys. Rev. Lett. 93 (2004) 032002 [hep-ph/0402280];
106. - → 2 jets at NNLO, Nucl. Phys. B 691 (2004) 195 [hep-ph/0403057];
107. W.B. Kilgore, Subtraction terms for hadronic production processes at next-to-next-to-leading order, Phys. Rev. D 70 (2004) 031501 [hep-ph/0403128];
108. 2 contribution, hep-ph/0407023.