For a scalar field on a sphere, the Fradkin-Vilkovisky measure combined with an on-shell cutoff identification converts the famous quadratic mass divergence into a logarithmic one.
Gauge hierarchy problem and scalegenesis
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We review the gauge hierarchy problem in the standard model. We discuss the meaning of the quadratic divergence in terms of the Wilsonian renormalization group. Classical scale symmetry, which prohibits dimensionful parameters in the bare action, could play a key role for the understanding of the origin of the electroweak scale. We discuss the scale-generation mechanism, i.e. scalegenesis in scale invariant theories. In this paper, we introduce a scale invariant extension of the SM based on a strongly interacting scalar-gauge theory. It is discussed that asymptotically safe quantum gravity provides a hint about solutions to the gauge hierarchy problem.
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Gravity and the Higgs boson mass
For a scalar field on a sphere, the Fradkin-Vilkovisky measure combined with an on-shell cutoff identification converts the famous quadratic mass divergence into a logarithmic one.