Do any of the known laws of physics preclude the existance of an electrically charged particle with zero rest mass? I know there ain’t no such, but is the concept flat-out contradicted by anything?
This paper says that to have a massless charged particle of spin 1 or greater would violate Lorentz invarience. (Unfortunately, if you don’t have a subscription to the Physical Review Online Archive, you’ll have to pay to read the PDF).
The paper specifically says it doesn’t apply to spin 0 or spin 1/2 particles, but perhaps they’re forbidden to have both mass and charge for some other reason.
IANAPP but anyway my WAG:
Since massless particles travel at the speed of light I’d say that a charged massless particle would violate all sorts of laws, would require infinite energy, generate an infinitely strong magnetic field, that sort of thing.
As a hijack question for PWAPP***** I’ve always though of the neutrino as basically an electron minus the electric charge. Just how wrong is this idea?
*****People who are partical physicists.
IANAPP either, but I am a mathematician, which is almost the same thing these days. 
One thing wrong with it is that (afaik) neutrinos only spin one way, while electrons spin both. More accurately, it’s like there’s three particles: left-handed electron, right-handed electron, neutrino (I forget whether it’s left- or right-handed). There are also, of course, three antimatter counterparts.
Anyhow, there’s a symmetry group SU(2) hanging around – for every 2x2 unitary matrix with unit determinant there’s a 3x3 complex matrix that acts on the complex vector made up of the electron and neutrino states, and all states related by one of these actions are “really the same”. That is, left-handed electrons, right-handed electrons, and neutrinos are all really the same thing, but look different depending on what “direction” we look at them from. Similarly, the same symmetry exchanges neutrons and protons, so there’s only one nucleon that looks different depending on the “direction” in so-called “isospin space” we observe the particle from.
To cover my ass, I’ll just add that I haven’t really played with the standard model in a while, so I might have the exact details slightly off as to which particle sets SU(2) acts on. Corrections welcome.
Neutrinos produced by the weak interaction will only spin one way: Neutrinos are left-handed and antineutrinos are right-handed, which is to say that if a neutrino is moving away from you its spin will be counterclockwise. However, it’s now known that neutrinos (at least two of them, and probably all three) have a small but nonzero mass, and it’s impossible for a massive particle to have definite helicity, since they travel at less than the speed of light. So the handedness of neutrinos we observe is now generally considered to be a property of the weak interaction which produces them, rather than of the neutrinos themselves. But one could contrive (in principle, at least) an experiment which woud reverse the direction of travel of a neutrino and therefore its handedness, and neutrinos produced by means other than the weak interaction (e.g., by Hawking radiation) could have either handedness.
It is still an open question whether there is anything to distinguish neutrinos from antineutrinos other than their direction of spin. According to the mainstream Dirac model for the neutrino, there is also a conserved property called lepton number carried by neutrinos and electrons (and muons and tauons), which is equal to 1 for electrons and neutrinos and -1 for positrons and antineutrinos. Under this model, it’s not to far off to describe neutrinos as “electrons without the charge”. However, there is some controvertial recent work claiming to support the Majorana model for neutrinos. Under this model, the neutrino and antineutrino are distinguished only by spin (that is to say, the neutrino, like the photon, is its own antiparticle), and lepton number is not only not conserved, it’s not even well-defined. I will refrain from taking sides on this question.
Gluons carry color charge and are believed to be massless. They also have spin 1. tim314’s paper was written in 1961, before QCD (quantum chromo-dynamics) was formulated, so I don’t know if the points it makes are relevant to that arena.
OK, I’m a little confused. I understand (and to expand on what Chronos said) that (1) massive particles travel at speeds less than c, and (2) if a particle moves slower than c, there’s a frame of reference where it’s moving in the other direction. (e.g., the reference frame of someone chasing after the particle and catching up with it.) Thus, whether the particle is right handed or left handed depends on your frame of reference. So far so good.
What I don’t get is this: if the helicity of a particle depends on the reference frame from which it is viewed, how can one even make a statement like (to paraphrase) “weak interactions will only produce left-handed neutrinos and right-handed anti-neutrinos”? It seems even that statement depends on the observers frame of reference. In which case, what reference frame are we talking about?
Also: I’m about confused about “helicity” vs. “parity”. (Although I don’t think parity has been mentioned.) As I understand it, a particle has positive (negative) parity if the mathematical object that represents it in the theory gets a plus (minus) sign when the signs of all the coordinates are reversed. And I’ve heard weak interactions called “parity violating” because they act differently on particles of different helicity, but beyond that I’m not sure I understand the connection. Do particles of a certain parity always have a certain helicity? Can particles have definite parity without having definite helicity?
Actually, there’s a difference between “color charge” and electric charge. I don’t recall whether the gluon fields are complex and so couple nontrivially to the electromagnetic field. More directly on point, the W particles have charge +/-1 and are a priori massless. The (hypothetical) spontaneous gauge symmetry breaking gives them effective masses, though. Since gluons are color gauge bosons (like Ws are isospin gauge bosons), the same might hold for them to get effective masses.
Helicity is sort of like spin for massless fields. Basically, all fields are collections of complex functions which transform in certain ways under the lorentz group – they furnish “representations” of that group. As another example, the proton and neutron furnish a two-dimensional representation of the isospin group SU(2) – they form two-component vectors that transform in certain ways.
The complex representations (up to a phase) of SO(3,1) (rotations in 3+1-dimensional space) correspond to complex representations (exact) of SU(2). These are parametrized by a continuous parameter and a discrete one. The continuous parameter is interpreted as “mass”, while for positive mass the discrete parameter is interpreted as spin. For m=0, though, the discrete parameter behaves a little differently and is interpreted as “helicity” – basically, “spin in the direction of motion”. A right-handed massless particle coming towards you appears to be spinning around counterclockwise.
As for why this classification holds… that’s a lot more math than you’re likely interested in and that I’m interested in explaining in this thread.
The relevant reference frame is the zero-momentum frame (AKA center of mass frame) of the interaction. And since neutrinos are typically produced at energies so much greater than their mass, any experimentally-attainable reference frame will also typically show this helicity.
handedness != helicity
All particles have a specific handedness. The weak interaction couples only specific handednesses to other specific handednessess. For example, in the diagram:
in out
\ /
\ /
|
W
|
the “in” and “out” particles must have the same handedness (and the same lepton number.)
Let the subscripts “R” and “L” indicate handedness. Then, the valid “in” and “out” pairings are:
e[sub]L[/sub] --> [symbol]n[/symbol][sub]L[/sub]
anti-e[sub]R[/sub] --> anti-[symbol]n[/symbol][sub]R[/sub]
The right-handed electron and the left-handed positron do not participate (owing to the handedness and lepton number constraints.) They participate in the electromagnetic interaction, though, since they have electric charge. The right-handed neutrino and the left-handed anti-neutrino do not participate. Further, these two particles have no electric charge and no color charge, and thus they cannot participate in any Standard Model interaction. So, we just say they don’t exist. (The non-zero masses of the neutrinos make this existential simplification approximate. There are non-weak-interaction ways of getting these so-called “sterile” wrong-handedness states.)
As for helicity: it is nothing special – just the projection of the particle’s spin along its momentum direction in the frame of your choice. For massless or high-energy particles, helicity and handedness can be interchanged. This can be seen from the form of the handedness states written in terms of helicity states:
<e[sub]L[/sub]> = (constant) (<e[sub]neg[/sub]> + m/E <e[sub]pos[/sub]>)
<e[sub]R[/sub]> = (constant) (<e[sub]pos[/sub]> - m/E <e[sub]neg[/sub]>)
where “neg” and “pos” indicate negative and positive helicity eigenstates. m and E are the mass and energy of the particle. (m/E could be replaced by 1/[symbol]g[/symbol]). Even though helicity is nothing fundamental, it is useful since often m<<E. (Especially with neutrinos.)