The theoretical calculation underlying the cosmological constant problem

Question

The electroweak vacuum energy density is $10^{120}$ times larger than the currently observed value of the dark energy. I have two questions in regard to this statement.

$\bullet$ Firstly, what are the fields that contribute to the vacuum energy in the context of the Standard Model i.e., does this takes into account only the scalar field in the Standard Model (SM) (the Higgs field) or does it also take into account all gauge fields and fermions on the SM?

$\bullet$ How do physicists derive this $10^{120}$ order of magnitude discrepancy? How do theorists calculate the vacuum energy and come up with a value? I'm looking for a derivation.

IIRC the figure of $10^{120}$ is basically bogus, and a more realistic figure is smaller by $10^n$. It also seems to me that this particular example of the failure of semiclassical gravity has been blown out of proportion in the pop-sci consciousness compared to the other failures of semiclassical gravity. Semiclassical gravity makes some predictions that are widely believed to be correct (Hawking radiation) and some that are widely believed to be incorrect (divergences happening at an event horizon). Ad hoc renormalization procedures are proposed, but can't be tested against experiment. — , May 23 '18 at 21:09
Possible duplicate of What are the calculations for Vacuum Energy?. See also Is the cosmological constant the simplest candidate for dark energy?. — AccidentalFourierTransform, May 23 '18 at 23:27

The theoretical calculation underlying the cosmological constant problem

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