Abstract
Improving the effective action by the renormalization group (RG) with several mass scales is an important problem in quantum field theories. A method based on the decoupling theorem was proposed in [1] and systematically improved [2] to take threshold effects into account. In this paper, we apply the method to the Higgs-Yukawa model, including wave-function renormalizations, and to a model with two real scalar fields (φ, h). In the Higgs-Yukawa model, even at one-loop level, Feynman diagrams contain propagators with different mass scales and decoupling scales must be chosen appropriately to absorb threshold corrections. On the other hand, in the two-scalar model, the mass matrix of the scalar fields is a function of their field values (φ, h) and the resultant running couplings obey different RGEs on a different point of the field space. By solving the RGEs, we can obtain the RG improved effective action in the whole region of the scalar fields.
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References
M. Bando, T. Kugo, N. Maekawa and H. Nakano, Improving the effective potential: multimass scale case, Prog. Theor. Phys. 90 (1993) 405 [hep-ph/9210229] [INSPIRE].
J.A. Casas, V. Di Clemente and M. Quirós, The effective potential in the presence of several mass scales, Nucl. Phys. B 553 (1999) 511 [hep-ph/9809275] [INSPIRE].
M. Holthausen, K.S. Lim and M. Lindner, Planck scale boundary conditions and the Higgs mass, JHEP 02 (2012) 037 [arXiv:1112.2415] [INSPIRE].
F. Bezrukov, M.Yu. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs boson mass and new physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the standard model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
S. Iso and Y. Orikasa, TeV Scale B-L model with a flat Higgs potential at the Planck scale — In view of the hierarchy problem, PTEP 2013 (2013) 023B08 [arXiv:1210.2848] [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
K. Kawana, Criticality and inflation of the gauged B-L model, PTEP 2015 (2015) 073B04 [arXiv:1501.04482] [INSPIRE].
Y. Hamada and K. Kawana, Vanishing Higgs potential in minimal dark matter models, Phys. Lett. B 751 (2015) 164 [arXiv:1506.06553] [INSPIRE].
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] [INSPIRE].
S. Moch et al., High precision fundamental constants at the TeV scale, arXiv:1405.4781 [INSPIRE].
G. Cortiana, Top-quark mass measurements: review and perspectives, Rev. Phys. 1 (2016) 60 [arXiv:1510.04483] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
M.B. Einhorn and D.R.T. Jones, A new renormalization group approach to multiscale problems, Nucl. Phys. B 230 (1984) 261 [INSPIRE].
C. Ford and C. Wiesendanger, Multiscale renormalization, Phys. Lett. B 398 (1997) 342 [hep-th/9612193] [INSPIRE].
T.G. Steele, Z.-W. Wang and D.G.C. McKeon, Multiscale renormalization group methods for effective potentials with multiple scalar fields, Phys. Rev. D 90 (2014) 105012 [arXiv:1409.3489] [INSPIRE].
M. Bando, T. Kugo, N. Maekawa and H. Nakano, Improving the effective potential, Phys. Lett. B 301 (1993) 83 [hep-ph/9210228] [INSPIRE].
T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].
K. Symanzik, Infrared singularities and small distance behavior analysis, Commun. Math. Phys. 34 (1973) 7 [INSPIRE].
S. Weinberg, Effective gauge theories, Phys. Lett. B 91 (1980) 51 [INSPIRE].
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Iso, S., Kawana, K. RG-improvement of the effective action with multiple mass scales. J. High Energ. Phys. 2018, 165 (2018). https://doi.org/10.1007/JHEP03(2018)165
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DOI: https://doi.org/10.1007/JHEP03(2018)165