James Wells

The centrally recognized theoretical achievement that enabled the Higgs boson discovery in 2012 was the hypothesis of its existence, made by Peter Higgs in 1964. Nevertheless, there is a significant body of comparably important theoretical work prior to and after the Higgs boson hypothesis. In this article we present an additional perspective of how crucial theory work was to the genesis of the Higgs boson hypothesis, especially emphasizing its roots in Landau's theory of phase transitions and subsequent theoretical work on superconductivity. A detailed description is then given of the opposition to the Higgs boson hypothesis by many researchers, giving evidence to its speculative nature. And finally, it is discussed the importance of theory work in the decades after the hypothesis in order to make possible the experimental discovery of the Higgs boson.

It is argued that the \ cancellation model is a good proxy for discussions of finetuned cancellations in physical theories. XYCM is then analyzed from a statistical perspective, where it is argued that a finetuned point in the parameter space is not abnormal, with any such point being just as probable as any other point. However, landing inside a standardly defined finetuned region has a much lower probability than landing outside the region, and that probability is invariant under assumed ranges of parameters. This proposition requires asserting also that the finetuned target region is a priori established. Therefore, it is surmised that a highly finetuned theory is generally expected to be highly improbable. An actionable implication of this moderate naturalness position is that the search for a non-finetuned explanation to supplant an apparently finetuned theory is likely to be a valid pursuit, but not guaranteed to be. A statistical characterization of this moderate position is presented, as well as those of the extreme pro-naturalness and anti-naturalness positions.

Naturalness is an extra-empirical quality that aims to assess plausibility of a theory. Finetuning measures are often deputized to quantify the task. However, knowing statistical distributions on parameters appears necessary. Such meta-theories are not known yet. A critical discussion of these issues is presented, including their possible resolutions in fixed points. Both agreement to and skepticism of naturalness’s utility remains credible, as is skepticism to any extra-empirical theory assessment that claims to identify “more correct” theories that are equally empirically adequate. The severe implications of SEETA are set forward in some detail. We conclude with a summary and discussion of the viability of three main viewpoints toward naturalness and finetuning, where the “moderate naturalness position” is suggested to be most appealing, not suffering from the disquietudes of the extreme pro- and anti-naturalness positions.

Sensitivity to the square of the cutoff scale of quantum corrections of the Higgs boson mass self-energy has led many authors to conclude that the Higgs theory suffers from a naturalness or fine-tuning problem. However, speculative new physics ideas to solve this problem have not manifested themselves yet at high-energy colliders, such as the Large Hadron Collider at CERN. For this reason, the role of naturalness as a guide to theory model-building is being severely questioned. Most attacks suggest that one should not resort to arguments involving gravity, which is a much less understood quantum field theory. Another line of attack is against the assumption that there exists a multitude of additional heavy states specifically charged under the Standard Model gauge symmetries. Nevertheless, if we give ground on both of these assaults on naturalness, what remains is a naturalness concern over the prospect of numerous additional spin-zero scalar states in nature. The proliferation of heavy scalars generically destabilizes the Higgs boson mass, raising it to the highest and most remote scalar mass values in nature, thus straining the legitimacy of the Standard Model. The copious use of extra scalars in theory model building, from explaining flavor physics to providing an inflationary potential and more, and the generic expectation of extra scalar bosons in nature argues for the proliferation instability problem being the central concern for naturalness of the Standard Model. Some approaches to solving this problem are presented.