In section 2 of these lecture notes (Gerard 't Hooft, 1998) an alternative interpretation of the weak interaction is presented, in which the weak force is confined, much like the strong force. As best I can understand, it works like this:

The fundamental vector bosons are the U(1) photon, SU(2) weak-gluons, and SU(3) strong-gluons.

The fundamental scalar boson is a higgs weak-parton (em charge $-{1\over 2}$, couples to weak force), $h$. This is not the usual Higgs boson $H$ and is not the same as its anti-particle, $\bar h$.

The fundamental fermions are left-handed quark weak-partons (em $+{1\over 6}$, weak, strong), $q$, left-handed lepton weak-partons (em $-{1\over 2}$, weak), $l$, right-handed up and down quarks (em $-{1\over 3}$ and $+{2\over 3}$, strong), and right-handed charged leptons (em $-1$).

Then the SU(2) interacting fields confine:

The usual weak vector bosons and the Higgs are bound states of higgs weak-partons. The Higgs boson $H$ is $\bar h h$ with no orbital angular momentum, and the $Z$ and $W^\pm$ are $\bar h h$, $\bar h\bar h$, and $hh$ with 1 quantum of orbital angular momentum. (This is something like the difference between the nucleons and the delta baryons, I gather.)

The usual left-handed quarks/leptons are bound states of higgs and quark/lepton weak-partons. Left-handed charged leptons are $hl$ and left-handed neutrinos are $\bar hl$, similarly the left-handed down and up quarks are $hq$ and $\bar hq$.

Presumably, the left-handed fermions then mix with the right-handed ones through a Yukawa interaction, and according to 't Hooft, everything after that is exactly the same as in the Standard Model - this SU(2) confinement picture is (apparently) just as valid a description of weak interaction as the usual electroweak symmetry breaking picture.

The question:

Literature on this model is pretty sparse - I haven't seen it anywhere else - and 't Hooft covers it very briefly, without expanding on the differences between it and the electroweak model. So, my questions are:

1) In this model, does SU(2) confinement happen before or after SU(3) confinement?

2) In this model, is the mass of fundamental particles derived from the energy of SU(2) confinement, the Yukawa interaction, or both? Is there still symmetry breaking, and a Higgs field with a non-zero VEV?

3) In the above notes 't Hooft asserts that the fermionic weak-partons could form bound states with each other, but only says that such states would be very unstable. Could this model be differentiated from the Standard Model by the detection of such particles?

EDIT: After looking into it more, it seems that it is intended for the SU(2) confinement to happen at a higher energy than SU(3) confinement (which makes sense, since otherwise we would have seen it). Thus, in this model, the names "weak force" and "strong force" are backwards, and the usual weak interaction is just a residual effect.

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    $\begingroup$ arxiv.org/abs/hep-ph/0206251 is similar $\endgroup$ Commented Jan 6, 2016 at 5:13
  • $\begingroup$ @MitchellPorter : he predicts the standard model Higgs boson at 129.6 geV/c² in 2002 ( LHC 2013 125.09±0.33 geV/c² ) ... $\endgroup$
    – user46925
    Commented Jan 14, 2016 at 6:34

1 Answer 1


I am going to take a stab at answering my own questions with what I have been able to find on the subject. (Still very sparse.)

1) In this model the SU(2) confinement occurs at much higher energies than SU(3) confinement, so that the weak-partons confine first (giving us quarks and leptons) and then quarks confine into hadrons second. This explains why quarks and leptons are observed to be point-like particles - higher energy is required to probe their internal structure.

3) Skipping my second question momentarily, it seems that the answer to my third question is yes - but only at higher energies, smaller distances, and shorter timescales than we can currently access, since the SU(2) confinement is very strong. Interactions with this strong SU(2) force would happen much more quickly than we could detect them.

The reason that the higgs-fermion and higgs-higgs bound states are more stable than the fermion-fermion bound states seems to have something to do with the higgs field acquiring a VEV or settling to a Bose-Einstein condensate state, making it abundantly more likely for higgs particles to interact with fermions than for the fermions to interact with each other. (But I am confused on this point, since 't Hooft also says that the SU(2) symmetry remains unbroken in this model. If the $F$ parameter in the notes is just an arbitrary choice of gauge about which to do a perturbative expansion, it is unclear to me why bound states with the higgs parton should be more stable than bound states with just the fermion partons.)

2) It seems to me that any bound state would have to acquire mass from the kinetic energy of its constituents, but the additional reference from Michael Porter's comment also includes a Yukawa coupling between the left-handed and right-handed fermions via the higgs-parton field, so mass seems to come from both mechanisms. How this would work is still very foggy to me.


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