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I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an electroweak theory consistent with the observation of the non-conservation of the parity of the neutrino, the electron mass term could not be included and it also acquire mass due to the Higgs mechanism.

Are there some Standard Model particles having an explicit mass term, or all acquire mass as a result of spontaneous breaking of the gauge symmetry and its coupling with the Higgs field?

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Related physics.stackexchange.com/questions/3037/… –  twistor59 Dec 16 '12 at 14:39

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All the experimentally observed particles that are believed to be fundamental particles, but for neutrinos, in the Standard Model get a mass from the interaction with the Higgs boson. Please note that this aspect of the dynamics of the Standard Model is still under experimental investigation, despite there is data that clearly points towards this direction.

For neutrinos the situation has not yet been cleared by experiments.

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Hi, see my comments to Paganini that applies to your answer as well –  TwoBs Dec 25 '14 at 11:18
    
Still the mass of the object that you have integrated out does not come from the Higgs VEV. So, not all masses of fundamental particles might be originated by the Higgs. Not arguing about the light neutrinos, but the possible heavy ones that are integrated out ... –  Roberto Franceschini Dec 26 '14 at 11:57

First, a mass term for electron (or any fermion) does violate the gauge symmetry because, chiral right handed components (singlet) transform differently than chiral left handed components (doublet) under SU(2). So the Lagrangian cannot be invariant under the gauge transformation (transformation of doublet cannot compensate the transformation of singlet). Second, in the standard model, all fermions acquire their mass thanks to the Higgs mechanism (via Yukawa couplings). The case of the neutrinos is still an open question but in principle, if they are Dirac fermions (as all other fermions), they would be treated the same way.

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Why Dirac neutrinos would be different than Majorana neutrinos? Imagine integrating out the heavy right-handed neutrinos, they will generate operators like $(LH)^2$ which give mass to the neutrino via the Higgs mechanism from a non-renormalizable dimension-5 operator. –  TwoBs Dec 25 '14 at 11:17

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