- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Three-loop Standard Model effective potential at leading order in strong and top Yukawa couplings

Stephen P. Martin1,2,3

  • 1Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
  • 2Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA
  • 3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 9310, USA

PDF

Phys. Rev. D 89, 013003 – Published 8 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.013003

Abstract

I find the three-loop contribution to the effective potential for the Standard Model Higgs field, in the approximation that the strong and top Yukawa couplings are large compared to all other couplings, using dimensional regularization with modified minimal subtraction. Checks follow from gauge invariance and renormalization group invariance. I also briefly comment on the special problems posed by Goldstone boson contributions to the effective potential, and on the numerical impact of the result on the relations between the Higgs vacuum expectation value, mass, and self-interaction coupling.

View figure in article

Article Text

References (53)

  1. G. Aad et al., (ATLAS Collaboration), Phys. Lett. B 716, 1 (2012).
  2. S. Chatrchyan et al. (CMS Collaboration), Phys. Lett. B 716, 30 (2012).
  3. G. Aad et al. (ATLAS Collaboration), Report No. ATLAS-CONF-2013-014, 2013.
  4. S. Chatrchyan et al. (CMS Collaboration), Report No. CMS-PAS-HIG-12-045, 2012.
  5. S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973).
  6. R. Jackiw, Phys. Rev. D 9, 1686 (1974).
  7. M. Sher, Phys. Rep. 179, 273 (1989), and references therein.
  8. C. Ford, I. Jack, and D. R. T. Jones, Nucl. Phys. B387, 373 (1992); B504, 551(E) (1997); See also C. Ford and D. R. T. Jones, Phys. Lett. B 274, 409 (1992); 285, 399(E) (1992).
  9. S. P. Martin, Phys. Rev. D 65, 116003 (2002).
  10. M. Lindner, M. Sher, and H. W. Zaglauer, Phys. Lett. B 228, 139 (1989).
  11. P. B. Arnold and S. Vokos, Phys. Rev. D 44, 3620 (1991).
  12. C. Ford, D. R. T. Jones, P. W. Stephenson, and M. B. Einhorn, Nucl. Phys. B395, 17 (1993).
  13. J. A. Casas, J. R. Espinosa, and M. Quirós, Phys. Lett. B 342, 171 (1995).
  14. J. R. Espinosa and M. Quiros, Phys. Lett. B 353, 257 (1995).
  15. J. A. Casas, J. R. Espinosa, and M. Quiros, Phys. Lett. B 382, 374 (1996).
  16. G. Isidori, G. Ridolfi, and A. Strumia, Nucl. Phys. B609, 387 (2001).
  17. J. R. Espinosa, G. F. Giudice, and A. Riotto, J. Cosmol. Astropart. Phys. 05 (2008) 002.
  18. N. Arkani-Hamed, S. Dubovsky, L. Senatore, and G. Villadoro, J. High Energy Phys. 03 (2008) 075.
  19. F. Bezrukov and M. Shaposhnikov, J. High Energy Phys. 07 (2009) 089.
  20. J. Ellis, J. R. Espinosa, G. F. Giudice, A. Hoecker, and A. Riotto, Phys. Lett. B 679, 369 (2009).
  21. J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, A. Riotto, and A. Strumia, Phys. Lett. B 709, 222 (2012).
  22. S. Alekhin, A. Djouadi, and S. Moch, Phys. Lett. B 716, 214 (2012).
  23. F. Bezrukov, M. Y. Kalmykov, B. A. Kniehl, and M. Shaposhnikov, J. High Energy Phys. 10 (2012) 140.
  24. G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, and A. Strumia, J. High Energy Phys. 08 (2012) 098.
  25. D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio, and A. Strumia, arXiv:1307.3536.
  26. F. Jegerlehner, M. Y. Kalmykov, and B. A. Kniehl, arXiv:1307.4226.
  27. A. V. Bednyakov, A. F. Pikelner, and V. N. Velizhanin, arXiv:1310.3806.
  28. C. G. Bollini and J. J. Giambiagi, Nuovo Cimento Soc. Ital. Fis. B 12, 20 (1972); Phys. Lett. 40B, 566 (1972).
  29. J. F. Ashmore, Lett. Nuovo Cimento 4, 289 (1972).
  30. G. M. Cicuta and E. Montaldi, Lett. Nuovo Cimento 4, 329 (1972).
  31. G.’t Hooft and M. J. G. Veltman, Nucl. Phys. B44, 189 (1972).
  32. G. ’t Hooft, Nucl. Phys. B61, 455 (1973).
  33. W. A. Bardeen, A. J. Buras, D. W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978).
  34. E. Braaten and J. P. Leveille, Phys. Rev. D 24, 1369 (1981).
  35. H. Yamagishi, Phys. Rev. D 23, 1880 (1981); Nucl. Phys. B216, 508 (1983).
  36. M. B. Einhorn and D. R. T. Jones, Nucl. Phys. B211, 29 (1983).
  37. B. M. Kastening, Phys. Lett. B 283, 287 (1992).
  38. M. Bando, T. Kugo, N. Maekawa, and H. Nakano, Phys. Lett. B 301, 83 (1993); Prog. Theor. Phys. 90, 405 (1993).
  39. K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B192, 159 (1981); F. V. Tkachov, Phys. Lett. 100B, 65 (1981).
  40. D. J. Broadhurst, Z. Phys. C 54, 599 (1992).
  41. L. V. Avdeev, Comput. Phys. Commun. 98, 15 (1996).
  42. D. J. Broadhurst, Eur. Phys. J. C 8, 311 (1999).
  43. Y. Schroder and A. Vuorinen, J. High Energy Phys. 06 (2005) 051. See also M. Steinhauser, Comput. Phys. Commun. 134, 335 (2001).
  44. N. I. Usyukina and A. I. Davydychev, Phys. Lett. B 332, 159 (1994); A. I. Davydychev and J. B. Tausk, Phys. Rev. D 53, 7381 (1996).
  45. M. Y. Kalmykov, Nucl. Phys. B718, 276 (2005).
  46. M. E. Machacek and M. T. Vaughn, Nucl. Phys. B222, 83 (1983).
  47. M. E. Machacek and M. T. Vaughn, Nucl. Phys. B236, 221 (1984).
  48. I. Jack and H. Osborn, Nucl. Phys. B249, 472 (1985).
  49. M. E. Machacek and M. T. Vaughn, Nucl. Phys. B249, 70 (1985).
  50. K. G. Chetyrkin and M. F. Zoller, J. High Energy Phys. 06 (2012) 033.
  51. K. G. Chetyrkin and M. F. Zoller, J. High Energy Phys. 04 (2013) 091.
  52. A. V. Bednyakov, A. F. Pikelner, and V. N. Velizhanin, Nucl. Phys. B875, 552 (2013).
  53. M. B. Einhorn and D. R. T. Jones, J. High Energy Phys. 04 (2007) 051.

Outline

Information

Phys. Rev. D 89, 013003– Published 8 January, 2014
  • Received 7 November 2013

© 2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation