All possible models to explain the hierarchy problem?

[Suekdccia]

TL;DR

All possible models to explain the hierarchy problem?

There is an interesting paper by Arkani-Hamed and collaborators (https://arxiv.org/abs/1607.06821) to address the hierarchy problem.

There, they consider many possible models of fundamental particle physics where they all have an exact copy of the Standard Model but with different Higgs masses.

However, they indicate that this assumption is done for simplicity, but that we could relax these assumptions and consider models with greater differences

At the beginning, they say:

The first step is to introduce N sectors which are mutually non-interacting. The detailed particle content of these sectors is unimportant, with the exception that the Standard Model (SM) should not be atypical; many sectors should contain scalars, chiral fermions, unbroken gauge groups, etc. For simplicity, we imagine that they are exact copies of the SM, with the same gauge and Yukawa structure.

And at the end:

However, it is easy to imagine a broader class of theories that realizes the same mechanism. We can relax the assumption that the Higgs masses are uniformly spaced (or even pulled from a uniformly distribution) or that all the new sectors are exact copies of the SM. It is also possible to construct different models of reheating, with new physics near the weak scale to modify the UV behavior of the theory.All of this made me wonder: Are they saying that we could relax the assumptions of the model so that it would even include all possible UV theories (meaning all possible "microscopic" or "high-energy" physics, such as the different theories of quantum gravity and theories of everything proposed so far)?

 

[ChrisF]

TL;DR: All possible models to explain the hierarchy problem?

There is an interesting paper by Arkani-Hamed and collaborators (https://arxiv.org/abs/1607.06821) to address the hierarchy problem.

There, they consider many possible models of fundamental particle physics where they all have an exact copy of the Standard Model but with different Higgs masses.

However, they indicate that this assumption is done for simplicity, but that we could relax these assumptions and consider models with greater differences

At the beginning, they say:

The first step is to introduce N sectors which are mutually non-interacting. The detailed particle content of these sectors is unimportant, with the exception that the Standard Model (SM) should not be atypical; many sectors should contain scalars, chiral fermions, unbroken gauge groups, etc. For simplicity, we imagine that they are exact copies of the SM, with the same gauge and Yukawa structure.

And at the end:

However, it is easy to imagine a broader class of theories that realizes the same mechanism. We can relax the assumption that the Higgs masses are uniformly spaced (or even pulled from a uniformly distribution) or that all the new sectors are exact copies of the SM. It is also possible to construct different models of reheating, with new physics near the weak scale to modify the UV behavior of the theory.All of this made me wonder: Are they saying that we could relax the assumptions of the model so that it would even include all possible UV theories (meaning all possible "microscopic" or "high-energy" physics, such as the different theories of quantum gravity and theories of everything proposed so far)?

Re: All possible models to explain the hierarchy problem?

The short answer is: not quite, and the reason why is instructive.

Nnaturalness works because it imposes a specific constraint — the SM should not be atypical among the N sectors. This is doing real physical work. The reheaton selects the lightest sector precisely because the distribution of Higgs
masses is bounded and the SM sits at a predictable location within it. If you relax the assumptions all the way to "any possible UV theory," you lose that selection mechanism. The model becomes unfalsifiable — you can always invoke
some sector configuration that produces any observed output. That's not a solution to the hierarchy problem; it's a restatement of it in a larger space.

What Arkani-Hamed et al. mean by "relaxing assumptions" is more modest: you can vary the spacing of Higgs mass parameters, use non-uniform distributions, or modify the reheating mechanism — but the sectors still need to share enough
structure with the SM that the selection principle operates. It's not an invitation to include arbitrary UV completions.

On whether it encompasses all theories of quantum gravity / TOEs:
No — and deliberately so. Nnaturalness is agnostic about quantum gravity precisely because it doesn't need to solve that problem. It solves the weak-scale hierarchy problem without touching the Planck scale. String theory, LQG,
asymptotic safety — none of these are required or excluded by the mechanism. They live at a different energy scale and a different problem.

The broader question worth sitting with:
Every proposed solution to the hierarchy problem — SUSY, extra dimensions, composite Higgs, relaxion, Nnaturalness — assumes the Planck scale is the natural reference point and then asks why the Higgs is so much lighter. But that
assumption is never derived; it's inherited from dimensional analysis in QFT.

An alternative framing: what if the Higgs mass isn't unnaturally light relative to some UV scale, but is instead the natural output of the vacuum's geometric properties — the permittivity and permeability of empty space that determine
how fields propagate and where they stabilize? In that case there is no hierarchy problem to solve, because the Planck scale was never the right reference. The problem dissolves rather than gets explained.

That's a minority position, but it's worth noting that every solution to the hierarchy problem requires new physics that hasn't been observed, while the vacuum already has two directly measurable properties that set every
electromagnetic scale in nature.

Christian Fuccillo