Gauge contribution to the 1/N F expansion of the Yukawa coupling beta function

Open Access
Regular Article - Theoretical Physics
  • 31 Downloads

Abstract

We provide a closed analytical form for the gauge contribution to the beta function of a generic Yukawa coupling in the limit of large N F , where N F is the number of heavy vector-like fermions charged under an abelian or non-abelian gauge group. The resummed expression is finite and for the abelian case presents a pole at the same location as for the corresponding gauge beta function. When applied to new physics scenarios characterized by large Yukawa couplings, the contribution calculated here can cure their pathological UV behavior and make the couplings asymptotically free.

Keywords

1/N Expansion Beyond Standard Model Renormalization Group 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    K.G. Wilson, Renormalization group and critical phenomena. 1. Renormalization group and the Kadanoff scaling picture, Phys. Rev. B 4 (1971) 3174 [INSPIRE].
  2. [2]
    S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: An Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge (1980), pp. 790-831 [INSPIRE].
  3. [3]
    D.F. Litim and F. Sannino, Asymptotic safety guaranteed, JHEP 12 (2014) 178 [arXiv:1406.2337] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R. Mann, J. Meffe, F. Sannino, T. Steele, Z.-W. Wang and C. Zhang, Asymptotically Safe Standard Model via Vectorlike Fermions, Phys. Rev. Lett. 119 (2017) 261802 [arXiv:1707.02942] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    S. Abel and F. Sannino, Framework for an asymptotically safe Standard Model via dynamical breaking, Phys. Rev. D 96 (2017) 055021 [arXiv:1707.06638] [INSPIRE].ADSGoogle Scholar
  6. [6]
    G.M. Pelaggi, A.D. Plascencia, A. Salvio, F. Sannino, J. Smirnov and A. Strumia, Asymptotically Safe Standard Model Extensions?, arXiv:1708.00437 [INSPIRE].
  7. [7]
    O. Antipin and F. Sannino, Conformal Window 2.0: The Large N f Safe Story, arXiv:1709.02354 [INSPIRE].
  8. [8]
    A. Palanques-Mestre and P. Pascual, The 1/N F Expansion of the γ and β-functions in QED, Commun. Math. Phys. 95 (1984) 277 [INSPIRE].
  9. [9]
    J.A. Gracey, The QCD β-function at O(1/N f ), Phys. Lett. B 373 (1996) 178 [hep-ph/9602214] [INSPIRE].
  10. [10]
    D. Espriu, A. Palanques-Mestre, P. Pascual and R. Tarrach, The γ Function in the 1/N F Expansion, Z. Phys. C 13 (1982) 153 [INSPIRE].ADSGoogle Scholar
  11. [11]
    B. Holdom, Large N flavor β-functions: a recap, Phys. Lett. B 694 (2011) 74 [arXiv:1006.2119] [INSPIRE].ADSGoogle Scholar
  12. [12]
    G. Bélanger, C. Delaunay and S. Westhoff, A Dark Matter Relic From Muon Anomalies, Phys. Rev. D 92 (2015) 055021 [arXiv:1507.06660] [INSPIRE].ADSGoogle Scholar
  13. [13]
    B. Gripaios, M. Nardecchia and S.A. Renner, Linear flavour violation and anomalies in B physics, JHEP 06 (2016) 083 [arXiv:1509.05020] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    P. Arnan, L. Hofer, F. Mescia and A. Crivellin, Loop effects of heavy new scalars and fermions in b + μ , JHEP 04 (2017) 043 [arXiv:1608.07832] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    G. D’Amico et al., Flavour anomalies after the \( {R}_{K^{\ast }} \) measurement, JHEP 09 (2017) 010 [arXiv:1704.05438] [INSPIRE].
  16. [16]
    J. Kawamura, S. Okawa and Y. Omura, Interplay between the bsℓℓ anomalies and dark matter physics, Phys. Rev. D 96 (2017) 075041 [arXiv:1706.04344] [INSPIRE].ADSGoogle Scholar
  17. [17]
    A. Freitas, J. Lykken, S. Kell and S. Westhoff, Testing the Muon g − 2 Anomaly at the LHC, JHEP 05 (2014) 145 [Erratum ibid. 09 (2014) 155] [arXiv:1402.7065] [INSPIRE].
  18. [18]
    K. Kowalska and E.M. Sessolo, Expectations for the muon g − 2 in simplified models with dark matter, JHEP 09 (2017) 112 [arXiv:1707.00753] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J.A. Gracey, Critical point analysis of various fermionic field theories in the large N expansion, J. Phys. A 25 (1992) L109 [INSPIRE].ADSGoogle Scholar
  20. [20]
    J.A. Gracey, Gauge independent critical exponents for QED coupled to a four Fermi interaction with and without a Chern-Simons term, Annals Phys. 224 (1993) 275 [hep-th/9301113] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  21. [21]
    J.A. Gracey, Analysis of Abelian gauge theory with four Fermi interaction at O(1/N 2) in arbitrary dimensions, J. Phys. A 26 (1993) 1431 [hep-th/9301117] [INSPIRE].ADSMATHGoogle Scholar
  22. [22]
    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 [INSPIRE].
  23. [23]
    M. Ozer, On the one loop Yukawa coupling beta function to order Y g 2 in a general α gauge and its gauge independence, Turk. J. Phys. 22 (1998) 351 [INSPIRE].Google Scholar
  24. [24]
    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005).Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.National Centre for Nuclear Research,WarsawPoland

Personalised recommendations