Asymptotic safety of gravity and the Higgs boson mass
Abstract
There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson m_{H} can be predicted. For a positive gravity induced anomalous dimension A_{λ} > 0 the running of the quartic scalar self interaction λ at scales beyond the Planck mass is determined by a fixed point at zero. This results in m_{H} =m_{min} = 126 GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For A_{λ} < 0 one finds m_{H} in the interval m_{min} <m_{H} <m_{max} ≃ 174 GeV, now sensitive to A_{λ} and other properties of the short distance running. The case A_{λ} > 0 is favored by explicit computations existing in the literature.
 Publication:

Physics Letters B
 Pub Date:
 January 2010
 DOI:
 10.1016/j.physletb.2009.12.022
 arXiv:
 arXiv:0912.0208
 Bibcode:
 2010PhLB..683..196S
 Keywords:

 Asymptotic safety;
 Gravity;
 Higgs field;
 Standard Model;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 8 pages, typos corrected, references added. Journal version