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

In summary, the conversation discusses the possibility of an electron emitting a photon, which in turn splits into neutrino-antineutrino pairs. However, due to conservation laws such as electric charge and lepton number, this process is highly improbable and would require a very energetic electron. Discussions also mention the violation of lepton flavor and overall lepton number, but these are not as relevant as electric charge in this scenario. Additionally, the concept of sphaelerons and their potential role in violating baryon and lepton number is mentioned, but not confirmed or well-documented.
  • #1
zaybu
53
2
Are there laws forbidding that reaction? Which ones?

Thanks
 
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  • #2
Conservation of electric charge.
 
  • #3
Could an electron emit a photon, which in turn split into neutrino/anti-neutrino pairs?
 
  • #4
Photons don't have charge.
 
  • #5
zaybu said:
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.
 
  • #6
fzero said:
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.
 
  • #7
Parlyne said:
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.
 
  • #8
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.
 
  • #9
fzero said:
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.
 
  • #10
kloptok said:
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.
 
  • #11
Parlyne said:
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"?
 
  • #12
the_house said:
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.
 
  • #13
Sorry, I wasn't trying to derail the thread. I was actually just wondering if you could recommend a good reference.
 
  • #14
the_house said:
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.
 
  • #15
Parlyne said:
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.
 

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

Electrons are fundamental particles that have a specific mass and charge. They are not capable of spontaneously splitting into other particles, including neutrinos and anti-neutrinos, due to the laws of conservation of energy and charge.

2. Can electrons split into neutrino/anti-neutrino pairs under certain conditions?

No, electrons cannot spontaneously split into neutrino/anti-neutrino pairs under any known conditions. This process would violate the fundamental laws of physics.

3. What is the role of the weak nuclear force in preventing electron splitting?

The weak nuclear force is responsible for interactions between subatomic particles, including electrons and neutrinos. It ensures that electrons do not spontaneously split into neutrino/anti-neutrino pairs, as such a process would require a violation of the weak force's conservation laws.

4. Is there any evidence of electron splitting into neutrino/anti-neutrino pairs?

No, there is no evidence to support the idea of electrons spontaneously splitting into neutrino/anti-neutrino pairs. All observations and experiments in particle physics have consistently shown that electrons remain intact and do not split into other particles.

5. Can we artificially induce electron splitting into neutrino/anti-neutrino pairs?

While we cannot induce electrons to spontaneously split into neutrino/anti-neutrino pairs, scientists have been able to create neutrino/anti-neutrino pairs in high-energy particle collisions. This process requires a significant amount of energy and is not the same as spontaneous splitting of particles.

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