Why do electrons not spontaneously split into neutrino/anti-neutrino pairs?

[zaybu]

Are there laws forbidding that reaction? Which ones?

Thanks

 

[fzero]

Conservation of electric charge.

 

[zaybu]

Could an electron emit a photon, which in turn split into neutrino/anti-neutrino pairs?

 

[Pengwuino]

Photons don't have charge.

 

[fzero]

Could an electron emit a photon, which in turn split into neutrino/anti-neutrino pairs?

An electron could emit a photon, but the photon does not couple directly to neutrinos. A very energetic electron could emit a Z boson, which can decay to a neutrino and anti-neutrino. The electron would need an energy larger than the Z mass, so you'd typically only find these electrons in particle accelerators or cosmic rays, the electrons in atoms don't emit Z particles. Furthermore, around <20% of Z-bosons decay to neutrino pairs, while most of them would decay to hadron jets.

 

[Parlyne]

An electron could emit a photon, but the photon does not couple directly to neutrinos. A very energetic electron could emit a Z boson, which can decay to a neutrino and anti-neutrino. The electron would need an energy larger than the Z mass, so you'd typically only find these electrons in particle accelerators or cosmic rays, the electrons in atoms don't emit Z particles. Furthermore, around <20% of Z-bosons decay to neutrino pairs, while most of them would decay to hadron jets.

Even if the electron had enough energy, this would violate conservation of momentum unless the initial electron was way off its mass shell.

 

[fzero]

Even if the electron had enough energy, this would violate conservation of momentum unless the initial electron was way off its mass shell.

Typically the Z is off mass shell, in which case you don't strictly need energies above the Z mass, but the probability is low if you're too far below that scale. Spontaneous Z emission should be pretty kinematically unfavorable compared to production via annihilation anyway. Somehow I think these details aren't very useful to the OP.

 

[kloptok]

Another conservation law is the conservation of lepton (electron) number. This will be violated for any neutrino-antineutrino pair. To conserve electron number at least a neutrino-antineutrino pair as well as an additional (electron)-neutrino have to be produced.

 

[Parlyne]

Typically the Z is off mass shell, in which case you don't strictly need energies above the Z mass, but the probability is low if you're too far below that scale. Spontaneous Z emission should be pretty kinematically unfavorable compared to production via annihilation anyway. Somehow I think these details aren't very useful to the OP.

Actually, I meant that an electron can't just emit particles of any kind unless it's well off its mass shell. Any sort of emission by an on-shell electron would take the electron off-shell to lower mass; but, the electron is already the lightest charged particle, meaning that the off-shell electron would need to pick up extra momentum from somewhere else - either reabsorbing the emitted particle, in which case we're not really talking about an emission process anyway, or from an external source, in which case we're talking about a scattering process, not an emission.

Frankly, I don't think it's particularly useful to the OP to suggest that you can cause a stable particle to radiate just by adding energy.

 

[Parlyne]

Another conservation law is the conservation of lepton (electron) number. This will be violated for any neutrino-antineutrino pair. To conserve electron number at least a neutrino-antineutrino pair as well as an additional (electron)-neutrino have to be produced.

Lepton flavor number and overall lepton number are already known to be violated (the former by neutrino mixing, the later at least non-perturbatively by sphaelerons). Electric charge, on the other hand, has never been observed to fail to be conserved. And, given that the electron is the lightest charged particle, that is the more important effect here.

 

[the_house]

overall lepton number [...] known to be violated [...] at least non-perturbatively by sphaelerons

Out of curiosity, do you have a good source for this that I can read? A quick google search indicates that, contrary to my previous understanding, sphaleron processes could possibly cause a violation of baryon and lepton number, but the first papers I came across seem speculative about whether it actually happens (e.g., in the lifetime of the universe). It certainly hasn't been confirmed experimentally, so is it really "known to be violated"?

 

[Parlyne]

Out of curiosity, do you have a good source for this that I can read? A quick google search indicates that, contrary to my previous understanding, sphaleron processes could possibly cause a violation of baryon and lepton number, but the first papers I came across seem speculative about whether it actually happens (e.g., in the lifetime of the universe). It certainly hasn't been confirmed experimentally, so is it really "known to be violated"?

Sphaelerons are expected to be accessible around the time of the electroweak phase transition. But, whether or not they actually happen with any detectible frequency, it is the case that the Standard Model does not mathematically conserve lepton number (or baryon number). The only point I was trying to make here is that the symmetry that poses the more restrictive problem in the situation described above is also the more exact symmetry anyway. When the process you're talking about violates conservation of electric charge, you don't really need to look at whether or not it conserves electron flavor number.

 

[the_house]

Sorry, I wasn't trying to derail the thread. I was actually just wondering if you could recommend a good reference.

 

[Parlyne]

Sorry, I wasn't trying to derail the thread. I was actually just wondering if you could recommend a good reference.

I'm afraid I don't have a particularly good reference to recommend.

 

[kloptok]

Lepton flavor number and overall lepton number are already known to be violated (the former by neutrino mixing, the later at least non-perturbatively by sphaelerons). Electric charge, on the other hand, has never been observed to fail to be conserved. And, given that the electron is the lightest charged particle, that is the more important effect here.

I wouldn't really factor in neutrino oscillations here, since oscillation lengths typically are of order 100 km. Sphaelerons are beyond my knowledge, feel free to enlighten me as to what they are. I am aware that B/L-number conservation is not a fundamental gauge symmetry of the same kind as electric charge. However, as far as we know today, apart from neutrino oscillations and appearently these sphaelerons you mentioned, B/L-number is conserved at the energies we have been able to probe so far.

But sure, electric charge is the obvious thing not conserved in this case - in that I absolutely agree.