Revisiting the Naturalness Problem -- Who is afraid of quadratic divergences? --

TL;DR

This paper reexamines the naturalness problem in particle physics, proposing that quadratic divergences can be subtracted via the Wilsonian renormalization group, which broadens the scope for constructing models beyond the Standard Model.

Contribution

It introduces a reinterpretation of quadratic divergences using Wilsonian RG, suggesting they should be subtracted, thus offering an alternative view on naturalness and model building.

Findings

Quadratic divergences can be absorbed into the critical surface.

Scale invariance of the SM offers an alternative solution to naturalness.

Model construction can focus on logarithmic divergences, simplifying the approach.

Abstract

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences, which can always be absorbed into a position of the critical surface, should be simply subtracted in model constructions. Such a picture gives another justification to the argument that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.