Feynman rules for the rational part of the standard model one-loop amplitudes in the 't Hooft-Veltman 5 scheme

Journal of High Energy Physics

Volumn 2011, Issue 9, 2011, Pages

  Shao, Hua Sheng ^a   Zhang, Yu Jie ^b   Chao, Kuang Ta ^a  

^a PEKING UNIVERSITY   (China)

^b BEIHANG UNIVERSITY   (China)

Author keywords

NLO computations; Standard model

Indexed keywords

EID: 80053166710     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP09(2011)048     Document Type: Article

References (70)

1. A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 1. quark-antiquark annihilation, JHEP 08 (2008) 108 [arXiv:0807.1248] [SPIRES].
2. A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [SPIRES].
3. G. Bevilacqua, M. Czakon, C.G. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO Wishlist: pp → tt̄bb̄, JHEP 09 (2009) 109 [arXiv:0907.4723] [SPIRES].
4. R.K. Ellis, K. Melnikov and G. Zanderighi, W + 3 jet production at the Tevatron, Phys. Rev. D 80 (2009) 094002 [arXiv:0906.1445] [SPIRES].
5. C.F. Berger et al., Next-to-leading order QCD predictions for W + 3-jet distributions at hadron colliders, Phys. Rev. D 80 (2009) 074036 [arXiv:0907.1984] [SPIRES].
6. C.F. Berger et al., Next-to-leading order QCD predictions for Z, γ* + 3-jet distributions at the Tevatron, Phys. Rev. D 82 (2010) 074002 [arXiv:1004.1659] [SPIRES].
7. C.F. Berger et al., Precise predictions for W + 4 jet production at the Large Hadron Collider, Phys. Rev. Lett. 106 (2011) 092001 [arXiv:1009.2338] [SPIRES].
8. T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, Next-to-leading order QCD predictions for W +W + jj production at the LHC, JHEP 12 (2010) 053 [arXiv:1007.5313] [SPIRES].
9. G. Bozzi, B. Jager, C. Oleari and D. Zeppenfeld, Next-to-leading order QCD corrections to W + Z and W - Z production via vector-boson fusion, Phys. Rev. D 75 (2007) 073004 [hep-ph/0701105] [SPIRES].
10. B. Jager, C. Oleari and D. Zeppenfeld, Next-to-leading order QCD corrections to Z boson pair production via vector-boson fusion, Phys. Rev. D 73 (2006) 113006 [hep-ph/0604200] [SPIRES].
11. B. Jager, C. Oleari and D. Zeppenfeld, Next-to-leading order QCD corrections to W+W- production via vector-boson fusion, JHEP 07 (2006) 015 [hep-ph/0603177] [SPIRES].
12. F. Campanario, Towards pp → V V jj at NLO QCD: bosonic contributions to triple vector boson production plus jet, arXiv:1105.0920 [SPIRES].
13. G. Bevilacqua, M. Czakon, C.G. Papadopoulos and M. Worek, Dominant QCD backgrounds in Higgs boson analyses at the LHC: a study of pp → tt̄ + 2 jets at next-to-leading order, Phys. Rev. Lett. 104 (2010) 162002 [arXiv:1002.4009] [SPIRES].
14. G. Bevilacqua et al., NLO QCD calculations with HELAC-NLO, Nucl. Phys. Proc. Suppl. 205-206 (2010) 211 [arXiv:1007.4918] [SPIRES].
15. M. Worek, Recent developments in NLO QCD calculations: the particular case of pp → tt̄ jj, arXiv:1012.4987 [SPIRES].
16. A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to WWbb̄ production at hadron colliders, Phys. Rev. Lett. 106 (2011) 052001 [arXiv:1012.3975] [SPIRES].
17. G. Bevilacqua, M. Czakon, A. van Hameren, C.G. Papadopoulos and M. Worek, Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order, JHEP 02 (2011) 083 [arXiv:1012.4230] [SPIRES].
18. T. Binoth et al., Next-to-leading order QCD corrections to pp → bb̄bb̄ + X at the LHC: the quark induced case, Phys. Lett. B 685 (2010) 293 [arXiv:0910.4379] [SPIRES].
19. N. Greiner, A. Guffanti, T. Reiter and J. Reuter, NLO QCD corrections to the production of two bottom-antibottom pairs at the LHC, arXiv:1105.3624 [SPIRES].
20. F. Campanario, C. Englert, M. Rauch and D. Zeppenfeld, Precise predictions for Wγγ+jet production at hadron colliders, arXiv:1106.4009 [SPIRES].
21. SM and NLO Multileg Working Group collaboration, J.R. Andersen et al., The SM and NLO multileg working group: summary report, arXiv:1003.1241 [SPIRES].
22. 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] [SPIRES].
23. 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] [SPIRES].
24. 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] [SPIRES].
25. 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] [SPIRES].
26. 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] [SPIRES].
27. F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals, JHEP 07 (2004) 017 [hep-ph/0404120] [SPIRES].
28. R. Pittau, Formulae for a numerical computation of one-loop tensor integrals, hep-ph/0406105 [SPIRES].
29. 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] [SPIRES].
30. G. Ossola, C.G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes, JHEP 07 (2007) 085 [arXiv:0704.1271] [SPIRES].
31. G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [SPIRES].
32. P. Mastrolia, G. Ossola, C.G. Papadopoulos and R. Pittau, Optimizing the reduction of one-loop amplitudes, JHEP 06 (2008) 030 [arXiv:0803.3964] [SPIRES].
33. G. Ossola, C.G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [SPIRES].
34. T. Binoth, J.P. Guillet and G. Heinrich, Algebraic evaluation of rational polynomials in one-loop amplitudes, JHEP 02 (2007) 013 [hep-ph/0609054] [SPIRES].
35. - in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [SPIRES].
36. A. Denner and S. Dittmaier, Reduction of one-loop tensor 5-point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [SPIRES].
37. A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [SPIRES].
38. P. Draggiotis, M.V. Garzelli, C.G. Papadopoulos and R. Pittau, Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [SPIRES].
39. M.V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the Electroweak 1-loop amplitudes, JHEP 01 (2010) 040 [arXiv:0910.3130]. [Erratum-ibid.1010:097,2010].
40. ξ gauge and in the unitary gauge, JHEP 01 (2011) 029 [arXiv:1009.4302] [SPIRES].
41. M.V. Garzelli and I. Malamos, R2SM: a package for the analytic computation of the R2 Rational terms in the standard model of the Electroweak interactions, Eur. Phys. J. C 71 (2011) 1605 [arXiv:1010.1248] [SPIRES].
42. W. Siegel, Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett. B 84 (1979) 193 [SPIRES].
43. Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451 [SPIRES].
44. 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] [SPIRES].
45. S. Catani, M.H. Seymour and Z. Trócsányi, Regularization scheme independence and unitarity in QCD cross sections, Phys. Rev. D 55 (1997) 6819 [hep-ph/9610553] [SPIRES].
46. 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] [SPIRES].
47. G. 't Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [SPIRES].
48. 5 in dimensional regularization, hep-ph/9401354 [SPIRES].
49. 5 scheme in dimensional regularization, Z. Phys. C 54 (1992) 503 [SPIRES].
50. 5 problem and anomalies: a Clifford algebra approach, Phys. Lett. B 237 (1990) 59 [SPIRES].
51. C.G. Bollini and J.J. Giambiagi, Lowest order divergent graphs in v-dimensional space, Phys. Lett. B 40 (1972) 566 [SPIRES].
52. G.M. Cicuta and E. Montaldi, Analytic renormalization via continuous space dimension, Nuovo Cim. Lett. 4 (1972) 329 [SPIRES].
53. J.F. Ashmore, A method of gauge invariant regularization, Lett. Nuovo Cim. 4 (1972) 289 [SPIRES].
54. P. Breitenlohner and D. Maison, Dimensional renormalization and the action principle, Commun. Math. Phys. 52 (1977) 11 [SPIRES].
55. P. Breitenlohner and D. Maison, Dimensionally renormalized Green's functions for theories with massless particles. 1, Commun. Math. Phys. 52 (1977) 39 [SPIRES].
56. P. Breitenlohner and D. Maison, Dimensionally renormalized Green's functions for theories with massless particles. 2, Commun. Math. Phys. 52 (1977) 55 [SPIRES].
57. 5, Phys. Lett. B 96 (1980) 147 [SPIRES].
58. 5, Nucl. Phys. B 177 (1981) 523 [SPIRES].
59. 5, Nucl. Phys. B 572 (2000) 387 [hep-th/9905076] [SPIRES].
60. C. Schubert, The Yukawa model as an example for dimensional renormalization with γ - 5, Nucl. Phys. B 323 (1989) 478 [SPIRES].
61. M. Pernici, M. Raciti and F. Riva, Dimensional renormalization of Yukawa theories via Wilsonian methods, Nucl. Phys. B 577 (2000) 293 [hep-th/9912248] [SPIRES].
62. M. Pernici, Semi-naive dimensional renormalization, Nucl. Phys. B 582 (2000) 733 [hep-th/9912278] [SPIRES].
63. M. Pernici and M. Raciti, Axial current in QED and semi-naive dimensional renormalization, Phys. Lett. B 513 (2001) 421 [hep-th/0003062] [SPIRES].
64. 5 in flavor changing neutral processes, Phys. Rev. D 52 (1995) 3036 [SPIRES].
65. 5, Eur. Phys. J. C 18 (2001) 673 [hep-th/0005255] [SPIRES].
66. J. Kublbeck, M. Böhm and A. Denner, Feyn arts: computer algebraic generation of Feynman graphs and amplitudes, Comput. Phys. Commun. 60 (1990) 165 [SPIRES].
67. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [SPIRES].
68. A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortschr. Phys. 41 (1993) 307 [arXiv:0709.1075] [SPIRES].
69. 5 scheme, Phys. Rev. D 41 (1990) 888 [SPIRES].
70. H.-S. Shao, Y.-J. Zhang and K.-T. Chao, Dijet invariant mass distribution in top quark hadronic decay with QCD corrections, arXiv:1106.5483 [SPIRES].