Why is there no massless spin 1/2 particles with charge? Is there any underlying theory? Whether any massless spin 1/2 particles cannot have charge? If so, why?
 A: The standard model of particle physics is the encapsulation of an enormous amount of data gathered in elementary particle experiments. The group structures of the model fit the symmetries observed in the data and the model predicts the behavior for future experiments, for example the existence of the top and the Higgs
The model starts before symmetry breaking, mediated by the Higgs field . At that time all the fermions of the theory are massless. It is symmetry breaking by the Higgs field that gives masses to the fermions. Since most fermions are charged, the original electrons, for example , are massless . Symmetry breaking occurs in cosmological models as the universe expands and cools so in the primordial energy there exist zero mass charged fermions. For a time line see here. .
The short answer is : the experimental data are consistent with a theory that has zero mass fermions only for very high energy concentrations.  None have been observed up to now, charged or neutral, considering that a small mass is assigned to neutrinos also by oscillation observations.
