Advertisement

Pitfalls of iterative pole mass calculation in electroweak multiplets

  • James McKayEmail author
  • Pat Scott
  • Peter Athron
Open Access
Regular Article

Abstract.

The radiatively induced mass splitting between components of an electroweak multiplet is typically of order 100 MeV. This is sufficient to endow the charged components with macroscopically observable lifetimes, and ensure an electrically neutral dark matter particle. We show that a commonly used iterative procedure to compute radiatively corrected pole masses can lead to very different mass splittings than a non-iterative calculation at the same loop order. By estimating the uncertainties of the two one-loop results, we show that the iterative procedure is significantly more sensitive to the choice of renormalisation scale and gauge parameter than the non-iterative method. This can cause the lifetime of the charged component to vary by up to 12 orders of magnitude if iteration is employed. We show that individual pole masses exhibit similar scale-dependence regardless of the procedure, but that the leading scale-dependent terms cancel when computing the mass splitting if and only if the non-iterative procedure is employed. We show that this behaviour persists at two-loop order: the precision of the mass splitting improves in the non-iterative approach, but our results suggest that higher-order corrections do not reduce the uncertainty in the iterative calculation enough to resolve the problem at two-loop order. We conclude that the iterative procedure should not be used for computing pole masses in situations where electroweak mass splittings are phenomenologically relevant.

References

  1. 1.
    J. Hisano, S. Matsumoto, M. Nagai, O. Saito, M. Senami, Phys. Lett. B 646, 34 (2007) hep-ph/0610249ADSCrossRefGoogle Scholar
  2. 2.
    A. Hryczuk, R. Iengo, P. Ullio, J. High Energy Phys. 3, 69 (2011) arXiv:1010.2172ADSCrossRefGoogle Scholar
  3. 3.
    H.-C. Cheng, B.A. Dobrescu, K.T. Matchev, Nucl. Phys. B 543, 47 (1999) hep-ph/9811316ADSCrossRefGoogle Scholar
  4. 4.
    J.L. Feng, T. Moroi, L. Randall, M. Strassler, S. Su, Phys. Rev. Lett. 83, 1731 (1999) hep-ph/9904250ADSCrossRefGoogle Scholar
  5. 5.
    M. Ibe, S. Matsumoto, R. Sato, Phys. Lett. B 721, 252 (2013) arXiv:1212.5989ADSCrossRefGoogle Scholar
  6. 6.
    M. Cirelli, N. Fornengo, A. Strumia, Nucl. Phys. B 753, 178 (2006) hep-ph/0512090ADSCrossRefGoogle Scholar
  7. 7.
    M. Cirelli, A. Strumia, New J. Phys. 11, 105005 (2009) arXiv:0903.3381ADSCrossRefGoogle Scholar
  8. 8.
    C. Cai, Z.-M. Huang, Z. Kang, Z.-H. Yu, H.-H. Zhang, Phys. Rev. D 92, 115004 (2015) arXiv:1510.01559ADSCrossRefGoogle Scholar
  9. 9.
    M. Cirelli, A. Strumia, M. Tamburini, Nucl. Phys. B 787, 152 (2007) arXiv:0706.4071ADSCrossRefGoogle Scholar
  10. 10.
    C.-S. Chen, Y. Tang, J. High Energy Phys. 4, 19 (2012) arXiv:1202.5717ADSCrossRefGoogle Scholar
  11. 11.
    L. Di Luzio, R. Gröber, J.F. Kamenik, M. Nardecchia, J. High Energy Phys. 7, 74 (2015) arXiv:1504.00359ADSCrossRefGoogle Scholar
  12. 12.
    A. Belyaev, G. Cacciapaglia, J. McKay, D. Marin, A.R. Zerwekh, arXiv:1808.10464 [hep-ph]Google Scholar
  13. 13.
    B. Ostdiek, Phys. Rev. D 92, 055008 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    W. Porod, F. Staub, Comput. Phys. Commun. 183, 2458 (2012) arXiv:1104.1573ADSCrossRefGoogle Scholar
  15. 15.
    F. Staub, Comput. Phys. Commun. 184, 1792 (2013) arXiv:1207.0906ADSCrossRefGoogle Scholar
  16. 16.
    F. Staub, Comput. Phys. Commun. 185, 1773 (2014) arXiv:1309.7223ADSCrossRefGoogle Scholar
  17. 17.
    P. Athron, J.-h. Park, D. Stöckinger, A. Voigt, Comput. Phys. Commun. 190, 139 (2015) arXiv:1406.2319ADSCrossRefGoogle Scholar
  18. 18.
    E. Del Nobile, R. Franceschini, D. Pappadopulo, A. Strumia, Nucl. Phys. B 826, 217 (2010) arXiv:0908.1567ADSCrossRefGoogle Scholar
  19. 19.
    Y. Yamada, Phys. Lett. B 682, 435 (2010) arXiv:0906.5207ADSCrossRefGoogle Scholar
  20. 20.
    J. McKay, P. Scott, Phys. Rev. D 97, 055049 (2018) arXiv:1712.00968ADSCrossRefGoogle Scholar
  21. 21.
    R. Mertig, M. Böhm, A. Denner, Comput. Phys. Commun. 64, 345 (1991)ADSCrossRefGoogle Scholar
  22. 22.
    V. Shtabovenko, R. Mertig, F. Orellana, Comput. Phys. Commun. 207, 432 (2016) arXiv:1601.01167ADSCrossRefGoogle Scholar
  23. 23.
    T. Hahn, Comput. Phys. Commun. 140, 418 (2001) hep-ph/0012260ADSCrossRefGoogle Scholar
  24. 24.
    A.V. Smirnov, Comput. Phys. Commun. 189, 182 (2015) arXiv:1408.2372ADSCrossRefGoogle Scholar
  25. 25.
    V. Shtabovenko, Comput. Phys. Commun. 218, 48 (2017) arXiv:1611.06793ADSCrossRefGoogle Scholar
  26. 26.
    R. Mertig, R. Scharf, Comput. Phys. Commun. 111, 265 (1998) hep-ph/9801383ADSCrossRefGoogle Scholar
  27. 27.
    S.P. Martin, D.G. Robertson, Comput. Phys. Commun. 174, 133 (2006) hep-ph/0501132ADSCrossRefGoogle Scholar
  28. 28.
    D.M. Pierce, J.A. Bagger, K.T. Matchev, R.-J. Zhang, Nucl. Phys. B 491, 3 (1997) hep-ph/9606211ADSCrossRefGoogle Scholar
  29. 29.
    F. Staub, Comput. Phys. Commun. 181, 1077 (2010) arXiv:0909.2863ADSCrossRefGoogle Scholar
  30. 30.
    F. Staub, Comput. Phys. Commun. 182, 808 (2011) arXiv:1002.0840ADSCrossRefGoogle Scholar
  31. 31.
    B.C. Allanach, Comput. Phys. Commun. 143, 305 (2002) hep-ph/0104145ADSCrossRefGoogle Scholar
  32. 32.
    B. Allanach, P. Athron, L.C. Tunstall, A. Voigt, A. Williams, Comput. Phys. Commun. 185, 2322 (2014) arXiv:1311.7659ADSCrossRefGoogle Scholar
  33. 33.
    J.C. Romao, Modern Techniques for One-Loop Calculations (2006)Google Scholar
  34. 34.
    G. ’t Hooft, M. Veltman, Nucl. Phys. B 153, 365 (1979)ADSCrossRefGoogle Scholar
  35. 35.
    G. Passarino, M. Veltman, Nucl. Phys. B 160, 151 (1979)ADSCrossRefGoogle Scholar
  36. 36.
    T. Cohen, M. Lisanti, A. Pierce, T.R. Slatyer, J. Cosmol. Astropart. Phys. 10, 61 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    Particle Data Group, Chin. Phys. C 40, 100001 (2016)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Physics, Imperial College LondonBlackett LaboratoryLondonUK
  2. 2.School of Physics and AstronomyMonash UniversityMelbourneAustralia
  3. 3.Australian Research Council Centre of Excellence for Particle Physics at the Tera-scale, Australia

Personalised recommendations