I often hear of hierarchy problem being used synonymous with Higgs fine tuning (
ID: 1381795 • Letter: I
Question
I often hear of hierarchy problem being used synonymous with Higgs fine tuning (esp with regards with motivations for SUSY). What exactly is the relationship between the two problems? As I understand it, the quadratic divergence from the Higgs self coupling means you need a lot of fine tuning to get a low Higgs mass.
However, the hierarchy problem is the following: Why is the electroweak scale (where W/Z physics is important, roughly 1 TeV) SO much less than the Planck scale.
So, why is this in effect, the same problem as the higgs fine tuning?
Explanation / Answer
It's the same problem because the low scale matches in both definitions; and the high scale matches in both definitions, too. Both problems are the puzzle why the two scales are so much different.
First, the low scale. In the Higgs fine-tuning, you define the low scale as the Higgs mass. But the Higgs mass can't be parameterically greater than the Z-boson or W-boson mass. If it were much greater