Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops

Journal of High Energy Physics

Volumn 2013, Issue 1, 2013, Pages

  Bednyakov, A V ^a   Pikelner, A F ^a   Velizhanin, V N ^b  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^b PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

Renormalization Group; Standard Model

Indexed keywords

EID: 84872292026     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2013)017     Document Type: Article

References (65)

1. ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [ arXiv:1207.7214 ].
2. CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [ arXiv:1207.7235 ].
3. N. Krasnikov, Restriction of the fermion mass in gauge theories of weak and electromagnetic interactions, Yad. Fiz. 28 (1978) 549.
4. P.Q. Hung, Vacuum instability and new constraints on fermion masses, Phys. Rev. Lett. 42 (1979) 873.
5. H.D. Politzer and S. Wolfram, Bounds on particle masses in the Weinberg-Salam model, Phys. Lett. B 82 (1979) 242 [Erratum ibid. 83B (1979) 421].
6. F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs boson mass and new physics, JHEP 10 (2012) 140 [ arXiv:1205.2893 ].
7. G. Degrassi et al., Higgs mass and vacuum stability in the standard model at NNLO, JHEP 08 (2012) 098 [ arXiv:1205.6497 ].
8. S. Alekhin, A. Djouadi and S. Moch, The top quark and Higgs boson masses and the stability of the electroweak vacuum, Phys. Lett. B 716 (2012) 214 [ arXiv:1207.0980 ].
9. J.C. Collins, Renormalization. An introduction to renormalization, the renormalization group, and the operator product expansion, Cambridge University Press, Cambridge U.K. (1984).
10. A. Vladimirov, Method for computing renormalization group functions in dimensional renormalization scheme, Theor. Math. Phys. 43 (1980) 417 [Teor. Mat. Fiz. 43 (1980) 210].
11. D. Gross and F. Wilczek, Ultraviolet behavior of nonabelian gauge theories, Phys. Rev. Lett. 30 (1973) 1343.
12. H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30 (1973) 1346.
13. D.R.T. Jones, Two loop diagrams in Yang-Mills theory, Nucl. Phys. B 75 (1974) 531.
14. O. Tarasov and A. Vladimirov, Two loop renormalization of the Yang-Mills theory in an arbitrary gauge, Sov. J. Nucl. Phys. 25 (1977) 585 [Yad. Fiz. 25 (1977) 1104].
15. W.E. Caswell, Asymptotic behavior of nonabelian gauge theories to two loop order, Phys. Rev. Lett. 33 (1974) 244.
16. E. Egorian and O. Tarasov, Two loop renormalization of the QCD in an arbitrary gauge, Theor. Math. Phys. 41 (1979) 863 [Teor. Mat. Fiz. 41 (1979) 26].
17. 2 gauge theory, Phys. Rev. D 25 (1982) 581.
18. w, Nucl. Phys. B 193 (1981) 53.
19. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83.
20. I. Jack and H. Osborn, General background field calculations with fermion fields, Nucl. Phys. B 249 (1985) 472.
21. S. Gorishnii, A. Kataev and S. Larin, Two loop renormalization group calculations in theories with scalar quarks, Theor. Math. Phys. 70 (1987) 262 [Teor. Mat. Fiz. 70 (1987) 372].
22. H. Arason et al., Renormalization group study of the standard model and its extensions. 1. The standard model, Phys. Rev. D 46 (1992) 3945.
23. T. Curtright, Three loop charge renormalization effects due to quartic scalar selfinteractions, Phys. Rev. D 21 (1980) 1543.
24. D.R.T. Jones, Comment on the charge renormalization effects of quartic scalar selfinteractions, Phys. Rev. D 22 (1980) 3140.
25. O.V. Tarasov, A.A. Vladimirov and A.Y. Zharkov, The Gell-Mann-Low function of QCD in the three loop approximation, Phys. Lett. B 93 (1980) 429.
26. S.A. Larin and J.A.M. Vermaseren, The three loop QCD β-function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [ hep-ph/9302208 ].
27. 2), Phys. Rev. D 59 (1999) 054005 [ hep-ph/9809507 ].
28. A.G.M. Pickering, J.A. Gracey and D.R.T. Jones, Three loop gauge β-function for the most general single gauge coupling theory, Phys. Lett. B 510 (2001) 347 [Phys. Lett. B 512 (2001) 230] [Erratum ibid. B 535 (2002) 377] [ hep-ph/0104247 ].
29. V.N. Velizhanin, Three-loop renormalization of the N = 1, N = 2, N = 4 supersymmetric Yang-Mills theories, Nucl. Phys. B 818 (2009) 95 [ arXiv:0809.2509 ].
30. V.N. Velizhanin, Three loop anomalous dimension of the non-singlet transversity operator in QCD, Nucl. Phys. B 864 (2012) 113 [ arXiv:1203.1022 ].
31. A.A. Bagaev, A.V. Bednyakov, A.F. Pikelner and V.N. Velizhanin, The 16th moment of the three loop anomalous dimension of the non-singlet transversity operator in QCD, Phys. Lett. B 714 (2012) 76 [ arXiv:1206.2890 ].
32. A.V. Bednyakov, Running mass of the b-quark in QCD and SUSY QCD, Int. J. Mod. Phys. A 22 (2007) 5245 [ arXiv:0707.0650 ].
33. A.V. Bednyakov, On the two-loop decoupling corrections to tau-lepton and b-quark running masses in the MSSM, Int. J. Mod. Phys. A 25 (2010) 2437 [ arXiv:0912.4652 ].
34. A.V. Bednyakov, Some two-loop threshold corrections and three-loop renormalization group analysis of the MSSM, arXiv:1009.5455.
35. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, Nucl. Phys. B 236 (1984) 221.
36. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, Nucl. Phys. B 249 (1985) 70.
37. L.F. Abbott, The background field method beyond one loop, Nucl. Phys. B 185 (1981) 189.
38. L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33.
39. L.N. Mihaila, J. Salomon and M. Steinhauser, Gauge coupling β-functions in the standard model to three loops, Phys. Rev. Lett. 108 (2012) 151602 [ arXiv:1201.5868 ].
40. L.N. Mihaila, J. Salomon and M. Steinhauser, Renormalization constants and β-functions for the gauge couplings of the Standard Model to three-loop order, arXiv:1208.3357.
41. K.G. Chetyrkin and M.F. Zoller, Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model, JHEP 06 (2012) 033 [ arXiv:1205.2892 ].
42. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [ hep-ph/0012260 ].
43. S. Gorishnii, S. Larin, L. Surguladze and F. Tkachov, MINCER: program for multiloop calculations in quantum field theory for the schoonschip system, Comput. Phys. Commun. 55 (1989) 381.
44. M. Tentyukov and J. Fleischer, A Feynman diagram analyzer DIANA, Comput. Phys. Commun. 132 (2000) 124 [ hep-ph/9904258 ].
45. S. Actis, A. Ferroglia, M. Passera and G. Passarino, Two-loop renormalization in the standard model. Part I: prolegomena, Nucl. Phys. B 777 (2007) 1 [ hep-ph/0612122 ].
46. S. Actis and G. Passarino, Two-loop renormalization in the standard model part II: renormalization procedures and computational techniques, Nucl. Phys. B 777 (2007) 35 [ hep-ph/0612123 ].
47. S. Actis and G. Passarino, Two-loop renormalization in the standard model part III: renormalization equations and their solutions, Nucl. Phys. B 777 (2007) 100 [ hep-ph/0612124 ].
48. N.D. Christensen and C. Duhr, FeynRules - Feynman rules made easy, Comput. Phys. Commun. 180 (2009) 1614 [ arXiv:0806.4194 ].
49. A. Semenov, LanHEP - A package for automatic generation of Feynman rules from the Lagrangian. Updated version 3.1, arXiv:1005.1909.
50. A. Denner, G. Weiglein and S. Dittmaier, Application of the background field method to the electroweak standard model, Nucl. Phys. B 440 (1995) 95 [ hep-ph/9410338 ].
51. O.V. Tarasov and A.A. Vladimirov, Three-loop calculations in non-Abelian gauge theories, JINR-E2-80-483 (1980).
52. G. 't Hooft and M. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189.
53. J. Vermaseren, New features of FORM, math-ph/0010025.
54. T. van Ritbergen, A.N. Schellekens and J.A.N. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [ hep-ph/9802376 ].
55. S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426.
56. 0 → γγ in the σ-model, Nuovo Cim. A 60 (1969) 47.
57. W.A. Bardeen, Anomalous Ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848.
58. C. Bouchiat, J. Iliopoulos and P. Meyer, An anomaly free version of Weinberg's model, Phys. Lett. B 38 (1972) 519.
59. D.J. Gross and R. Jackiw, Effect of anomalies on quasirenormalizable theories, Phys. Rev. D 6 (1972) 477.
60. F. Jegerlehner, Facts of life with γ(5), Eur. Phys. J. C 18 (2001) 673 [ hep-th/0005255 ].
61. P. Ferreira, I. Jack and D. Jones, The three loop SSM β-functions, Phys. Lett. B 387 (1996) 80 [ hep-ph/9605440 ].
62. I. Jack, D. Jones and A. Kord, Snowmass benchmark points and three-loop running, Annals Phys. 316 (2005) 213 [ hep-ph/0408128 ].
63. R.V. Harlander, L. Mihaila and M. Steinhauser, The SUSY-QCD β-function to three loops, Eur. Phys. J. C 63 (2009) 383 [ arXiv:0905.4807 ].
64. s and m(b) in the MSSM, Phys. Rev. D 76 (2007) 055002 [ arXiv:0706.2953 ].
65. 2) in the MSSM, JHEP 02 (2009) 037 [ arXiv:0810.5101 ].