Antenna subtraction at NNLO

Journal of High Energy Physics

Volumn , Issue 9, 2005, Pages

  Gehrmann de Ridder, Aude ^a   Gehrmann, Thomas ^b   Glover, E W Nigel ^c  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Jets; NLO Computations; QCD

Indexed keywords

EID: 26044435932     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2005/09/056     Document Type: Article

References (128)

1. R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and collider physics (Cambridge University Press, Cambridge), 1996
2. G. Dissertori, I.G. Knowles and M. Schmelling, Quantum chromodynamics: high energy experiments and theory (Oxford University Press) Oxford, 2003.
3. E.W.N. Glover, Progress in NNLO calculations for scattering processes 2003 Nucl. Phys. (Proc. Suppl.) 116 3 [hep-ph/0211412]
4. S. Moch, J.A.M. Vermaseren and A. Vogt, The three-loop splitting functions in QCD: the non-singlet case 2004 Nucl. Phys. B 688 101 [hep-ph/0403192]
5. A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: the singlet case 2004 Nucl. Phys. B 691 129 [hep-ph/0404111]
6. Z. Bern, L.J. Dixon and A. Ghinculov, Two-loop correction to Bhabha scattering 2001 Phys. Rev. D 63 053007 [hep-ph/0010075]
7. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to qq̄ → q′q̄′ 2001 Nucl. Phys. B 601 318 [hep-ph/0010212]
8. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two loop QCD corrections to massless identical quark scattering 2001 Nucl. Phys. B 601 341 [hep-ph/0011094]
9. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to massless quark gluon scattering 2001 Nucl. Phys. B 605 486 [hep-ph/0101304]
10. E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to gluon gluon scattering 2001 Nucl. Phys. B 605 467 [hep-ph/0102201]
11. C. Anastasiou, E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QED and QCD corrections to massless fermion boson scattering 2002 Nucl. Phys. B 629 255 [hep-ph/0201274]
12. E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QCD helicity amplitudes for massless quark massless gauge boson scattering 2003 J. High Energy Phys. JHEP06(2003)033 [hep-ph/0304169]
13. E.W.N. Glover, Two-loop QCD helicity amplitudes for massless quark quark scattering 2004 J. High Energy Phys. JHEP04(2004)021 [hep-ph/0401119]
14. Z. Bern, A. De Freitas and L.J. Dixon, Two-loop amplitudes for gluon fusion into two photons 2001 J. High Energy Phys. JHEP09(2001)037 [hep-ph/0109078]
15. Z. Bern, A. De Freitas and L.J. Dixon, Two-loop helicity amplitudes for gluon gluon scattering in QCD and supersymmetric Yang-Mills theory 2002 J. High Energy Phys. JHEP03(2002)018 [hep-ph/0201161]
16. 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 2003 J. High Energy Phys. JHEP06(2003)028 [hep-ph/0304168]
17. A. De Freitas and Z. Bern, Two-loop helicity amplitudes for quark-quark scattering in QCD and gluino gluino scattering in supersymmetric Yang-Mills theory 2004 J. High Energy Phys. JHEP09(2004)039 [hep-ph/0409007]
18. Z. Bern, A. De Freitas, L.J. Dixon, A. Ghinculov and H.L. Wong, QCD and QED corrections to light-by-light scattering 2001 J. High Energy Phys. JHEP11(2001)031 [hep-ph/0109079]
19. T. Binoth, E.W.N. Glover, P. Marquard and J.J. van der Bij, Two-loop corrections to light-by-light scattering in supersymmetric QED 2002 J. High Energy Phys. JHEP05(2002)060 [hep-ph/0202266]
20. T. Gehrmann and E. Remiddi, Analytic continuation of massless two-loop four-point functions 2002 Nucl. Phys. B 640 379 [hep-ph/0207020]
21. - → qq̄ g 2002 Phys. Rev. D 66 114001 [hep-ph/0207043]
22. - → 3jets 2002 Nucl. Phys. B 627 107 [hep-ph/0112081]
23. - → 3jets 2002 Nucl. Phys. B 642 227 [hep-ph/0206067]
24. F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions 1981 Phys. Lett. B 100 65
25. K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate beta functions in 4 loops 1981 Nucl. Phys. B 192 159
26. V.A. Smirnov, Analytical result for dimensionally regularized massless on-shell double box 1999 Phys. Lett. B 460 397 [hep-ph/9905323]
27. J.B. Tausk, Non-planar massless two-loop feynman diagrams with four on- shell legs 1999 Phys. Lett. B 469 225 [hep-ph/9909506]
28. T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multi-loop integrals 2000 Nucl. Phys. B 585 741 [hep-ph/0004013]
29. S. Laporta, High-precision calculation of multi-loop Feynman integrals by difference equations 2000 Int. J. Mod. Phys. A 15 5087 [hep-ph/0102033]
30. T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions 2000 Nucl. Phys. B 580 485 [hep-ph/9912329]
31. S. Moch, P. Uwer and S. Weinzierl, Nested sums, expansion of transcendental functions and multi-scale multi-loop integrals 2002 J. Math. Phys. 43 3363 [hep-ph/0110083]
32. S. Weinzierl, Symbolic expansion of transcendental functions 2002 Comput. Phys. Commun. 145 357 [math-ph/0201011]
33. C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD 2002 Nucl. Phys. B 646 220 [hep-ph/0207004]
34. V.A. Smirnov, Evaluating Feynman Integrals Springer Tracts of Modern Physics, Heidelberg, 2004
35. Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes 1993 Phys. Rev. Lett. 70 2677 [hep-ph/9302280]
36. Z. Kunszt, A. Signer and Z. Trócsányi, One loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon 1994 Phys. Lett. B 336 529 [hep-ph/9405386]
37. Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to two quark three gluon amplitudes 1995 Nucl. Phys. B 437 259 [hep-ph/9409393]
38. E.W.N. Glover and D.J. Miller, The one-loop QCD corrections for γ* → qq̄qq̄ 1997 Phys. Lett. B 396 257 [hep-ph/9609474]
39. - → q̄qq̄q 1997 Nucl. Phys. B 489 3 [hep-ph/9610370]
40. J.M. Campbell, E.W.N. Glover and D.J. Miller, The one-loop QCD corrections for γ* → qq̄gg 1997 Phys. Lett. B 409 503 [hep-ph/9706297]
41. - to four partons 1998 Nucl. Phys. B 513 3 [hep-ph/9708239]
42. s 1997 Phys. Rev. Lett. 78 811 [hep-ph/9609460]
43. - → (γ,Z) → four jets 1997 Phys. Rev. D 56 4031 [hep-ph/9706285]
44. Z. Nagy and Z. Trócsányi, Next-to-leading order calculation of four-jet shape variables 1997 Phys. Rev. Lett. 79 3604 [hep-ph/9707309]
45. - annihilation, 1999 Phys. Rev. D 60 054028 [hep-ph/9901277]
46. W.B. Kilgore and W.T. Giele, Next-to-leading order gluonic three jet production at hadron colliders 1997 Phys. Rev. D 55 7183 [hep-ph/9610433]
47. Z. Nagy and Z. Trócsányi, Multi-jet cross sections in deep inelastic scattering at next-to-leading order 2001 Phys. Rev. Lett. 87 082001 [hep-ph/0104315]
48. Z. Nagy, Three-jet cross sections in hadron hadron collisions at next-to-leading order 2002 Phys. Rev. Lett. 88 122003 [hep-ph/0110315]
49. Z. Nagy, Next-to-leading order calculation of three-jet observables in hadron hadron collision 2003 Phys. Rev. D 68 094002 [hep-ph/0307268]
50. J. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2jet and Z + 2jet production at hadron colliders 2002 Phys. Rev. D 65 113007 [hep-ph/0202176]
51. J.M. Campbell, M.A. Cullen and E.W.N. Glover, Four jet event shapes in electron positron annihilation 1999 Eur. Phys. J. C 9 245 [hep-ph/9809429]
52. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits 1994 Nucl. Phys. B 425 217 [hep-ph/9403226]
53. D.A. Kosower, All-order collinear behavior in gauge theories 1999 Nucl. Phys. B 552 319 [hep-ph/9901201]
54. D.A. Kosower and P. Uwer, One-loop splitting amplitudes in gauge theory 1999 Nucl. Phys. B 563 477 [hep-ph/9903515]
55. Z. Bern, V. Del Duca and C.R. Schmidt, The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order 1998 Phys. Lett. B 445 168 [hep-ph/9810409]
56. Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order, 1999 Phys. Rev. D 60 116001 [hep-ph/9903516]
57. S. Catani and M. Grazzini, The soft-gluon current at one-loop order 2000 Nucl. Phys. B 591 435 [hep-ph/0007142]
58. D.A. Kosower, All-orders singular emission in gauge theories 2003 Phys. Rev. Lett. 91 061602 [hep-ph/0301069]
59. S. Weinzierl, Subtraction terms for one-loop amplitudes with one unresolved parton 2003 J. High Energy Phys. JHEP07(2003)052 [hep-ph/0306248]
60. C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory 2003 Phys. Rev. Lett. 91 251602 [hep-th/0309040]
61. Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → g g splitting amplitudes in QCD 2004 J. High Energy Phys. JHEP08(2004)012 [hep-ph/0404293]
62. S.D. Badger and E.W.N. Glover, Two-loop splitting functions in QCD 2004 J. High Energy Phys. JHEP07(2004)040 [hep-ph/0405236]
63. C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD 2003 Phys. Rev. Lett. 91 182002 [hep-ph/0306192]
64. High-precision QCD at hadron colliders: electroweak gauge boson rapidity distributions at NNLO 2004 Phys. Rev. D 69 094008 [hep-ph/0312266]
65. - annihilation 1998 Nucl. Phys. B 517 269 [hep-ph/9707224]
66. J.M. Campbell and E.W.N. Glover, Double unresolved approximations to multiparton scattering amplitudes 1998 Nucl. Phys. B 527 264 [hep-ph/9710255]
67. S. Catani and M. Grazzini, Collinear factorization and splitting functions for next- to-next-to-leading order QCD calculations, 1999 Phys. Lett. B 446 143 [hep-ph/9810389]
68. S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond 2000 Nucl. Phys. B 570 287 [hep-ph/9908523]
69. F.A. Berends and W.T. Giele, Multiple soft gluon radiation in parton processes 1989 Nucl. Phys. B 313 595
70. V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit 2000 Nucl. Phys. B 568 211 [hep-ph/9909464]
71. T.G. Birthwright, E.W.N. Glover, V.V. Khoze and P. Marquard, Multi-gluon collinear limits from MHV diagrams 2005 J. High Energy Phys. JHEP05(2005)013 [hep-ph/0503063]
72. D.A. Kosower and P. Uwer, Evolution kernels from splitting amplitudes 2003 Nucl. Phys. B 674 365 [hep-ph/0307031]
73. D. de Florian and M. Grazzini, The structure of large logarithmic corrections at small transverse momentum in hadronic collisions 2001 Nucl. Phys. B 616 247 [hep-ph/0108273]
74. - energy energy correlation 2005 Nucl. Phys. B 704 387 [hep-ph/0407241]
75. 2 corrections to one-particle inclusive processes in dis 2003 Nucl. Phys. B 662 334 [hep-ph/0303199]
76. 2) QCD corrections to the electroproduction of hadrons with high transverse momentum 2005 Phys. Rev. D 71 034013 [hep-ph/0411212]
77. K.L. Adamson, D. de Florian and A. Signer, Gluon induced contributions to W Z and Wγ production at NNLO 2002 Phys. Rev. D 65 094041 [hep-ph/0202132]
78. , Gluon induced contributions to Zγ production at hadron colliders 2003 Phys. Rev. D 67 034016 [hep-ph/0211295]
79. D.A. Kosower, Multiple singular emission in gauge theories 2003 Phys. Rev. D 67 116003 [hep-ph/0212097]
80. S. Weinzierl, Subtraction terms at NNLO 2003 J. High Energy Phys. JHEP03(2003)062 [hep-ph/0302180]
81. W.B. Kilgore, Subtraction terms for hadronic production processes at next-to-next-to-leading order 2004 Phys. Rev. D 70 031501 [hep-ph/0403128]
82. S. Frixione and M. Grazzini, Subtraction at NNLO 2005 J. High Energy Phys. JHEP06(2005)010 [hep-ph/0411399]
83. G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements 2005 J. High Energy Phys. JHEP06(2005)024 [hep-ph/0502226]
84. G. Heinrich, A numerical method for NNLO calculations 2003 Nucl. Phys. (Proc. Suppl.) 116 368 [hep-ph/0211144]
85. C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO 2004 Phys. Rev. D 69 076010 [hep-ph/0311311]
86. T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition 2004 Nucl. Phys. B 693 134 [hep-ph/0402265]
87. G. Heinrich, A numerical approach to infrared divergent multi-parton phase space integrals 2004 Nucl. Phys. (Proc. Suppl.) 135 290 [hep-ph/0406332]
88. A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four-particle phase space integrals in massless QCD 2004 Nucl. Phys. B 682 265 [hep-ph/0311276]
89. 2) 2004 Phys. Rev. Lett. 93 032002 [hep-ph/0402280]
90. C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: differential cross sections through next-to-next-to-leading order 2004 Phys. Rev. Lett. 93 262002 [hep-ph/0409088]
91. C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order [hep-ph/0501130]
92. 2) [hep-ph/0505069]
93. - annihilation 1981 Nucl. Phys. B 178 421
94. - annihilation 1981 Zeit. Phys. C 11 315
95. Z. Kunszt and P. Nason, in, Z Physics at LEP 1 CERN Yellow Report 89-08, vol. 1, p. 373
96. - annihilation 1992 Phys. Rev. D 46 1980
97. 3 1992 Phys. Rev. D 46 192
98. S. Frixione, Z. Kunszt and A. Signer, Three-jet cross sections to next-to-leading order 1996 Nucl. Phys. B 467 399 [hep-ph/9512328]
99. G. Sterman and S. Weinberg, Jets from quantum chromodynamics 1977 Phys. Rev. Lett. 39 1436
100. G. Sterman, Mass divergences in annihilation processes, 1. Origin and nature of divergences in cut vacuum polarization diagrams 1978 Phys. Rev. D 17 2773
101. G. Sterman, Mass divergences in annihilation processes, 2. Cancellation Of divergences in cut vacuum polarization diagrams 1978 Phys. Rev. D 17 2789
102. S. Catani and M.H. Seymour, A general algorithm for calculating jet cross sections in NLO QCD 1997 Nucl. Phys. B 485 291 [hep-ph/9605323]
103. D.A. Kosower, Antenna factorization of gauge-theory amplitudes 1998 Phys. Rev. D 57 5410 [hep-ph/9710213]
104. D.A. Kosower, Antenna factorization in strongly-ordered limits 2005 Phys. Rev. D 71 045016 [hep-ph/0311272]
105. F.A. Berends and W. Giele, The six gluon process as an example of weyl-van der waerden spinor calculus 1987 Nucl. Phys. B 294 700
106. M.L. Mangano, S.J. Parke and Z. Xu, Duality and multi-gluon scattering 1988 Nucl. Phys. B 298 653
107. M.L. Mangano, S.J. Parke and Z. Xu, The color structure of gluon emission 1988 Nucl. Phys. B 309 461
108. L.J. Dixon, Calculating scattering amplitudes efficiently [hep-ph/9601359]
109. V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level 2000 Nucl. Phys. B 571 51 [hep-ph/9910563]
110. F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color-flow decomposition of QCD amplitudes 2003 Phys. Rev. D 67 014026 [hep-ph/0209271]
111. - → 2jets at NNLO 2004 Nucl. Phys. B 691 195 [hep-ph/0403057]
112. 2 contribution 2004 Nucl. Phys. (Proc. Suppl.) 135 97 [hep-ph/0407023]
113. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Quark-gluon antenna functions from neutralino decay 2005 Phys. Lett. B 612 36 [hep-ph/0501291]
114. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon gluon antenna functions from Higgs boson decay 2005 Phys. Lett. B 612 49 [hep-ph/0502110]
115. S. Catani, The singular behaviour of QCD amplitudes at two-loop order, 1998 Phys. Lett. B 427 161 [hep-ph/9802439]
116. G. Sterman and M.E. Tejeda-Yeomans, Multi-loop amplitudes and resummation 2003 Phys. Lett. B 552 48 [hep-ph/0210130]
117. T. Kinoshita, Mass singularities of feynman amplitudes 1962 J. Math. Phys. 3 650
118. T.D. Lee and M. Nauenberg, Degenerate systems and mass singularities 1964 Phys. Rev. 133 B1549
119. E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms 2000 Int. J. Mod. Phys. A 15 725 [hep-ph/9905237]
120. T. Gehrmann and E. Remiddi, Two-loop master integrals for γ* → 3jets: the planar topologies 2001 Nucl. Phys. B 601 248 [hep-ph/0008287]
121. T. Gehrmann and E. Remiddi, Two-loop master integrals for γ* → 3jets: the non- planar topologies 2001 Nucl. Phys. B 601 287 [hep-ph/0101124]
122. N. Nielsen, Der Eulersche Dilogarithmus und seine Verallgemeinerungen 1909 Nova Acta Leopoldiana (Halle) 90 123
123. K.S. Kölbig, J.A. Mignaco and E. Remiddi, On Nielsen's generalized polylogarithms and their numerical calculation 1970 BIT 10 38
124. T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms 2001 Comput. Phys. Commun. 141 296 [hep-ph/0107173]
125. T. Gehrmann and E. Remiddi, Numerical evaluation of two-dimensional harmonic polylogarithms 2002 Comput. Phys. Commun. 144 200 [hep-ph/0111255]
126. G.P. Lepage, A new algorithm for adaptive multidimensional integration 1978 J. Comput. Phys. 27 192
127. R. Kleiss, W.J. Stirling and S.D. Ellis, A new Monte Carlo treatment of multiparticle phase space at high-energies 1986 Comput. Phys. Commun. 40 359
128. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, work in progress