From my understanding of the standard model, I understand that there are 19 or 20 free parameters that we need to put in by hand as, and I'm guessing here, there is as yet no theoretical basis for calculating them. Examples that come to mind are the masses of the elementary particles, the electric charge on them...etc, all resulting from experimental results.

Two quick questions:

  1. Does anybody have a list of these free parameters?

  2. Does the Higgs boson also give us the freedom to choose a parameter value that allows agreement with experimental results?


Yes, wikipedia has a table which lists the 19 free parameters that need to be tuned by experiments. These include, as you already said, the masses of the elementary particles including the Higgs Boson, and some other notable ones are:

  • CKM Mixing angles and CP-violation phase.
  • Gauge coupling of the three symmetries (U(1), SU(2), SU(3)).
  • Higgs VEV
  • $\begingroup$ Thanks for that, I should have checked wiki first, just wasn't sure about the higgs in particular. Sorry for the unnecessary digging on your part. Regards $\endgroup$ – user74893 Mar 28 '15 at 17:11
  • $\begingroup$ i thought there were also the masses of particles. John Baez says there are 25 "fundamental constants" in the Standard Model (and 1 more for the Cosmological constant) $\endgroup$ – robert bristow-johnson Mar 28 '15 at 17:11
  • $\begingroup$ @No worries, and tbf the table was hidden. $\endgroup$ – Constandinos Damalas Mar 28 '15 at 17:11
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    $\begingroup$ Well, properly, Newton's constant and the cosmological constant are "free parameters of fundamental physics" and not of the standard model, since the standard model does not deal with gravity. And the particle masses (or at least the combination of yukawa couplings hand the higgs VeV that determine the masses) are most definitely amongst these parameters. $\endgroup$ – Jerry Schirmer Mar 28 '15 at 17:30
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    $\begingroup$ i took a look at comparing the table at Wikipedia to the Baez list. what about the "4 numbers for the Pontecorvo-Maki-Nakagawa-Sakata matrix"? is that in the list of free parameters of the Standard Model? $\endgroup$ – robert bristow-johnson Mar 28 '15 at 18:59

In the standard model, technically neutrinos are assumed to be massless. According to special relativity they would travel at the speed of light, so they would be timeless and could not oscillate. Hence, the 3 neutrino masses and 4 mixing angles are technically not parameters of the standard model. However, in simple extensions to the standard model, these parameters are free as well.

It is important to note that the 19 parameters in Wikipedia's table are not the only possible choice to describe the 19 degrees of freedom. i.e there are multiple choices of parameters that span this space.

  • $\begingroup$ Afaik the Higgs is part of the SM, wouldn't it mean that the SM has massive neutrinos and their Higgs coupling is part of the free parameters? $\endgroup$ – peterh May 13 '17 at 15:35

I would add to that list the masses and mixing angles of the three known neutrinos, which are just as arbitrary as the others within the confines of the standard model.

This adds seven parameters to the 19 listed in the Wikipedia article



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