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Charged particles such as electrons and quarks are not allowed to have a hard Majorana mass (see here). With 'hard' I mean an explicit mass term in the Lagrangian which would break the corresponding symmetries. However, there are also mechanisms to effectively generate masses, for example, with instantons in the topologically non-trivial QCD vacuum ('t Hooft vertex / determinant). These mass terms do not explicitly arise in the Lagrangian, only occur due to the specific vacuum the Lagrangian 'chooses' and are thus not forbidden by symmetries.

Now my question is: are there any experimental bounds on Majorana masses for charged particles?

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Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

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