Can a massless particle have both spin and charge?

Question

Can a hypothetical elementary particle, at least in theory (according to the current science), have 0 mass and yet also have both spin and electrical charge (at the same time)?

Answer 1

In the standard model, every massless particle transforms under representation of $U(1)_{EM}$ group. Therefore, every particle has an electric charge (some of them transform in the trivial representation and therefore have zero electric charge). On the other hand, spin is not well defined for a massless particle, since it's a quantity natural to the rest frame of the particle. Instead massless particles carry helicities, which are analogous to spin, although the word spin continues to be used colloquially. This is because massive particles transform in representations of their little group $SO(3)$ a.k.a spin, but massless particles transform in representations of $SO(2)$ a.k.a helicity.

So, to answer your question: massless particles carry can charge but not spin (in the strictest sense of the word).

A gentler, a less jargon filled explanation would be as follows: Technically there is nothing prohibiting a massless particle from carrying charge. The intuitive notion of a massless particle being affected by radiation continues to hold in the standard model. On the other hand, spin is subtler in that it requires you to think about what exactly is spin. One way to think about spin is to apply a magnetic field to the particle in its rest frame and ask how many possible configurations the particle has. However, for massless particles, relativity prohibits you from catching upto the particle and thinking of a rest frame for the particle. For massless particles the notion of spin is replaced by helicity.

Answer 2

Can a massless particle have both spin and charge?

Spin is the value assigned to measured elementary particles , including photons which are massless . Photons need to have spin 1 in order to have conservation of angular momentum in the electromagnetic interactions.

Charge also is a measured quantum number assigned to elementary particles and by conservation to their composites. Photons have zero charge, by observation.

The quantum field theoretical standard model is chosen because it fits the data and in its representations there are no states with 0 spin, massless, that have electric charges, by construction . The model is chosen to fit the data.

So, if we had observed a zero mass particle with electric charge, we would have found a different theoretical model as a standard one, in order to fit the data. As mentioned in the comments to the other answer, the gluons are zero mass, spin one , and are assigned a colored charge in the SM in order for the model to fit the data.

The answer to your question is that at the present level of observations there are no massless electrically charged particles observed and the theory has been chosen to fit the data, so the theory does not allow for a massless particle with spin to be electrically charged.