Are Dirac/Weyl/Majorana fermions exclusive? I think we can be pretty sure that fermions exist. We have several ways to describe them (Dirac, Weyl, Majorana, maybe someone I'm missing?), with different equations and number of components. My question is: are physical fermions
(1) either Dirac or Majorana or Weyl?
(2) just fermions, which we can describe in whatever way we find suitable for the theory we are currently studying?
If (1) is right, then what kind of fermions do we have in our universe?
 A: In the Standard Model, fermions are in left-handed doublets and right-handed singlets, all represented with left-handed Weyl spinors (the singlets are actually antiparticles), the representation being with respect to the SU(2) part of the electroweak interaction.  In the low energy theory, particles with left- and right-handed components in the SM pair off and look like they are either Dirac or Majorana.  As far as we know, all of the charged leptons and quarks are Dirac particles since Majorana particles allow violation of particle number by two units and baryon number seems to be conserved and lepton number seems to be conserved in the cases with charged leptons that we can readily observe.
Neutrinos could either be Dirac or Majorana but as far as we're aware not both and they can't be just Weyl as they are in the SM because that wouldn't allow them to have a mass.
A: All of the fermions in the Standard Model, with or without right-handed neutrinos, are Weyl fermions. Describing the post-EWSB, effectively massive fermions as Dirac fields is only an approximation. If there are right-handed neutrinos and a Majorana term in the Lagrangian, then there may be an exact description of the neutrinos as Majorana fields (I'm not sure), but there definitely is an exact description of them as Weyl fields even with that term. The fundamental laws (of the SM) are, or at least can be, formulated entirely in terms of Weyl fermions.
