In the answer to this question on the origin of the hierarchy problem, it is stated that:
The low-energy parameters such as the LHC-measured Higgs mass 125 GeV are complicated functions of the more fundamental high-energy parameters governing the GUT-scale or Planck-scale theory. And if you figure out what condition is needed for the high-scale parameters to make the Higgs $10^{15}$ times lighter than the reduced Planck scale, you will see that they're unnaturally fine-tuned conditions requiring some dimensionful parameters to be in some precise ranges.
The answer to a similar question I asked distinguished between the five typically relevant mass scales, of which two are:
- $m$, the mass of the particle in question, e.g. the Higgs.
- $M$, the beyond-SM scale.
It is the scale $M \gg m$ which is the order of the high-energy parameters in the theory supposedly approximated at low energy by the Standard Model: the comment under the question I asked linked to this paper discussing the existence of finite "threshold corrections" of order $O\left({(M/m)^k}\right)$ in the renormalisation of the relevant parameters. This is shown on page 19 in the section on "decoupling" using the dimensional regularisation scheme, and on page 27 using the Wilsonian action.
Is this is a precise, albeit simplified, example of the source of the problem we have with the Higgs mass (and also potentially the cosmological constant)?
