The Standard Model of Particle Physics has 26 experimentally measured parameters specific to the model (excluding physical constants like the speed of light that have applications outside the Standard Model).
One of the most common ways to enumerate them, although not unique (e.g. one could use Yukawas rather than masses and could replace one of the massive vector boson masses with an angle, and there is more than one way to parameterize the coupling constants), is as follows:
- Six quark masses.
- Three charged lepton masses.
- Three neutrino mass eigenstates.
- The W boson mass.
- The Z boson mass.
- The Higgs boson mass.
- One dimensionless coupling constant for each of the three Standard Model forces.
- Four CKM matrix parameters.
- Four PMNS matrix parameters.
Many of these constants "run" with energy scale as a consequence of the renormalization process pursuant to a beta function.
The terms of each beta function, in principle, can be calculated exactly from first principles without experimental input, although five loop approximations of beta functions are pretty much state of the art at the moment, a calculation which "required more than a year of computations on a decent number of multi-core workstations in a highly non-trivial theoretical framework.", under the watchful eyes of a team of five physicists and mathematicians.
My question is:
Which of the Standard Model constants run with energy scale pursuant to a beta function and which do not? Why is this the case?
The Part Of The Answer I Think That I Know
I know part of the answer (or at least I think I do based upon what I have read at the Particle Data Group and in physics journal articles):
Quark masses and charged lepton masses run with energy scale and have beta functions.
Each of the three coupling constants has a beta function.
I am fairly certain, but not completely certain, that the Higgs boson mass runs with energy scale and has a beta function.
I am not clear regarding whether the W boson mass and the Z boson mass have beta functions. I think they do, but I'm not sure.
I am not clear regarding whether the neutrino mass eigenstates have beta functions. All of the other fermion masses do, but the nature of neutrino mass is different from the nature of the other nine fermion masses. It isn't clear to me if the manner in which they are "glued" onto the original Standard Model puts those constants on the same footing as the other fermion masses for renormalization and beta function purposes.
I think, but I am not at all certain, that the four CKM matrix parameters and the four PMNS matrix parameters do not run with energy scale and do not have beta functions. But, I have difficulty articulating why I think that this is the case.
Indeed, in general, I have difficulty articulating what it is about a constant the causes it to run or not run with energy scale in a clear and concise manner that doesn't sound like I have diarrhea of the mouth.
Of course, if any premise of my question is inaccurate, I would also appreciate it if an answer could also address which of my assumptions is wrong and why.