James Wells

The Hierarchy Problem of elementary particle physics can be divided into two separate problems: the Intrinsic and Extrinsic Hierarchy Problems. The Intrinsic Hierarchy Problem (IHP) arises when the Wilsonian renormalization group induces a large $$\Lambda _\textrm{UV}^2$$ cutoff dependence on a much lighter scalar mass, creating a large finetuning. The Extrinsic Hierarchy Problem (EHP) arises when the IR theory is augmented with generically assumed extra states and interactions in the UV, making the resulting IR effective theory appear highly finetuned. The IHP is straightforward to analyze within a theory, but has suspicious regulator dependence, which has been suggested by some to be indication of a faux problem. The EHP is less straightforward to analyze, but has strength of physical intuition. We analyze EHP as a formal paradox, spelling out its premises and reasoning. From this we classify solutions to the EHP in terms of premise violations, and we articulate why some purported solutions to the Hierarchy Problem only partially solve the IHP and leave the EHP unaddressed.

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.

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.