Numerical evaluation of multi-loop integrals using subtraction terms

Journal of High Energy Physics

Volumn 2012, Issue 7, 2012, Pages

  Freitas, A ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

NLO computations

Indexed keywords

EID: 84864475159     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP07(2012)132     Document Type: Article

References (51)

1. Z interdependence, Phys. Lett. B 495 (2000) 338
2. [Erratum Phys. Lett. B 570 (2003) 260] [hep-ph/0007091].
3. M. Awramik, M. Czakon, A. Freitas and G. Weiglein, Precise prediction for the W boson mass in the standard model, Phys. Rev. D 69 (2004) 053006 [hep-ph/0311148].
4. eff and indirect determination of the Higgs boson mass, Phys. Rev. Lett. 93 (2004) 201805 [hep-ph/0407317].
5. 2), Phys. Lett. B 642 (2006) 563 [hep-ph/0605339].
6. effwith two-loop fermionic contributions, Nucl. Phys. B 731 (2005) 213 [hep-ph/0507158].
7. M. Awramik, M. Czakon and A. Freitas, Electroweak two-loop corrections to the effective weak mixing angle, JHEP 11 (2006) 048 [hep-ph/0608099].
8. eff with two-loop bosonic contributions, Nucl. Phys. B 765 (2007) 154 [hep-ph/0610312].
9. b using numerical Mellin-Barnes integrals, arXiv: 1205. 0299.
10. eff, Nucl. Phys. B 813 (2009) 174 [arXiv: 0811.1364].
11. 2 correction to the Drell-Yan K factor, Nucl. Phys. B 359 (1991) 343
12. [Erratum Nucl. Phys. B 644 (2002) 403].
13. 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].
14. s), Phys. Rev. D 74 (2006) 114017 [hep-ph/0609070].
15. M. Czakon, A. Mitov and S. Moch, Heavy-quark production in massless quark scattering at two loops in QCD, Phys. Lett. B 651 (2007) 147 [arXiv: 0705.1975].
16. M. Czakon, A. Mitov and S. Moch, Heavy-quark production in gluon fusion at two loops in QCD, Nucl. Phys. B 798 (2008) 210 [arXiv: 0707.4139].
17. M. Czakon, Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD, Phys. Lett. B 664 (2008) 307 [arXiv: 0803.1400].
18. R. Bonciani, A. Ferroglia, T. Gehrmann, D. Mâitre and C. Studerus, Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: The Quark-Antiquark Channel, JHEP 07 (2008) 129 [arXiv:0806.2301].
19. R. Bonciani, A. Ferroglia, T. Gehrmann and C. Studerus, Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel, JHEP 08 (2009) 067 [arXiv:0906.3671].
20. P. Baernreuther, M. Czakon and A. Mitov, Percent level precision physics at the Tevatron: first genuine NNLO QCD corrections to qq̄ → tt̄ + X, arXiv:1204.5201.
21. R. V. Harlander and W. B. Kilgore, Next-to-next-to-leading order Higgs production at hadron colliders, Phys. Rev. Lett. 88 (2002) 201801 [hep-ph/0201206].
22. C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004].
23. V. Ravindran, J. Smith and W. L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl. Phys. B 665 (2003) 325 [hep-ph/0302135].
24. C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: Differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett. 93 (2004) 262002 [hep-ph/0409088].
25. G. Davatz et al., Combining Monte Carlo generators with next-to-next-to-leading order calculations: Event reweighting for Higgs boson production at the LHC, JHEP 07 (2006) 037 [hep-ph/0604077].
26. S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012].
27. S. Actis, G. Passarino, C. Sturm and S. Uccirati, NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders, Phys. Lett. B 670 (2008) 12 [arXiv:0809.1301].
28. T. Binoth and G. Heinrich, An Automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013].
29. T. Binoth and G. Heinrich, Numerical evaluation of multiloop integrals by sector decomposition, Nucl. Phys. B 680 (2004) 375 [hep-ph/0305234].
30. J. Carter and G. Heinrich, SecDec: A general program for sector decomposition, Comput. Phys. Commun. 182 (2011) 1566 [arXiv:1011.5493].
31. Z. Nagy and D. E. Soper, Numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev. D 74 (2006) 093006 [hep-ph/0610028].
32. C. Anastasiou, S. Beerli and A. Daleo, Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically, JHEP 05 (2007) 071 [hep-ph/0703282].
33. S. Borowka, J. Carter and G. Heinrich, Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec. 2.0, arXiv:1204.4152.
34. C. Anastasiou and A. Daleo, Numerical evaluation of loop integrals, JHEP 10 (2006) 031 [hep-ph/0511176].
35. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [hep-ph/0511200].
36. A. Freitas and Y.-C. Huang, On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations, JHEP 04 (2010) 074 [arXiv:1001.3243].
37. Z. Nagy and D. E. Soper, General subtraction method for numerical calculation of one loop QCD matrix elements, JHEP 09 (2003) 055 [hep-ph/0308127].
38. S. Becker, C. Reuschle and S. Weinzierl, Numerical NLO QCD calculations, JHEP 12 (2010) 013 [arXiv:1010.4187].
39. S. Dittmaier, Separation of soft and collinear singularities from one loop N point integrals, Nucl. Phys. B 675 (2003) 447 [hep-ph/0308246].
40. R. Bonciani, P. Mastrolia and E. Remiddi, Vertex diagrams for the QED form-factors at the two loop level, Nucl. Phys. B 661 (2003) 289
41. [Erratum Nucl. Phys. B 702 (2004) 359] [hep-ph/0301170].
42. G. P. Lepage, Vegas: An Adaptive Multidimensional Integration Program, CLNS-80/447 (1980).
43. Wolfram Research Inc., Mathematica Version 6.0, http://www.wolfram.com/ products/mathematica/newin6/.
44. T. Hahn, CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78 [hep-ph/0404043].
45. - in the Weinberg Model, Nucl. Phys. B 160 (1979) 151.
46. W. Beenakker and A. Denner, Infrared divergent scalar box integrals with applications in the electroweak standard model, Nucl. Phys. B 338 (1990) 349.
47. R. K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851].
48. T. Binoth, E. N. Glover, P. Marquard and J. van der Bij, Two loop corrections to light by light scattering in supersymmetric QED, JHEP 05 (2002) 060 [hep-ph/0202266].
49. G. Weiglein, R. Scharf and M. Böhm, Reduction of general two loop selfenergies to standard scalar integrals, Nucl. Phys. B 416 (1994) 606 [hep-ph/9310358].
50. S. Bauberger, F. A. Berends, M. Böhm and M. Buza, Analytical and numerical methods for massive two loop selfenergy diagrams, Nucl. Phys. B 434 (1995) 383 [hep-ph/9409388].
51. A. I. Davydychev and J. Tausk, Two loop selfenergy diagrams with different masses and the momentum expansion, Nucl. Phys. B 397 (1993) 123.