Abstract
Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of \(\delta m^{2}/m^{2}_{H}\) (where m H is the renormalized Higgs mass and δm 2 is the 1-loop Higgs mass correction). Whereas \(\delta m^{2}/m^{2}_{H}<1\) (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands \(\delta m^{2}/m^{2}_{H}\) arbitrarily large to reach that experimental value.
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Acknowledgements
Research supported by Fundação para a Ciêcia e Tecnologia, project CERN/FP/116334/2010, developed under the iniciative QREN, financed by UE/FEDER through COMPETE—Programa Operacional Factores de Competitividade. This research is part of the EU Research Infrastructure Integrating Activity Study of Strongly Interacting Matter (HadronPhysics3) under the 7th Framework Programme of EU: Grant Agreement No. 283286.
The authors thank CNPq and FAPEMIG for financial support and Dr. Luis Cabral for fruitful discussions.
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Vieira, A.R., Hiller, B., Nemes, M.C. et al. Naturalness and Theoretical Constraints on the Higgs Boson Mass. Int J Theor Phys 52, 3494–3503 (2013). https://doi.org/10.1007/s10773-013-1652-x
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DOI: https://doi.org/10.1007/s10773-013-1652-x