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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?

Qmechanic
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3 Answers3

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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
PhotonBoom
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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.

Constantin Weisser
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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

https://en.wikipedia.org/wiki/Standard_Model#Construction_of_the_Standard_Model_Lagrangian

MikeV
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