Or equally under “beyond the standard model”, depending on who you ask ;).both fall equally under the "standard model."
Was it not established above that what is produced when leptons decay preserves chirality? So neutrino beams preserve the chirality of the particles that created them, that much is clear. But on what basis does one claim that the fields that are produced are charge conjugations of each other, rather than chiral opposites? Does that not already assume something about the neutrino fields that has not been established experimentally?There is still one field that is produced when particles decay, and its charge conjugate is produced when antiparticles decay. Its natural to call these ”neutrino” and “anti-neutrino”.
Again that refers to the particles that have lepton number, such as the leptons that created the neutrino beam, and the leptons produced by the beam. But if antileptons produce a beam of neutrinos that turn out to be Majorana neutrinos, is that not a situation where the beam itself drastically violates lepton number conservation, even if the lepton number is recovered when the beam interacts in the detector and creates antileptons again? I thought that is what had been established above.Preference for lepton number conservation is not arbitrary, it is based on lepton number being conserved either exactly or to an extremely good approximation.
Well, they have opposite (weak hyper-) charges…But on what basis does one claim that the fields that are produced are charge conjugations of each othe
I don’t understand what this phrase is supposed to mean.the beam itself drastically violates lepton number conservation
It is often said that a Majorana neutrino cannot be distinguished as a particle or an antiparticle, are you saying that is not true?Well, they have opposite (weak hyper-) charges…
To my understanding, leptons have lepton number +1, while antileptons have lepton number -1. It is also my understanding that Majorana neutrinos would not have a lepton number (or would have lepton number zero, if there is any distinction there). Is that not correct? Because if it is correct, then when antileptons interact to create "antineutrinos" in a beam, we have particles with lepton number -1 creating no particles with lepton number -1. So that would be nothing close to lepton number conservation. However, when the "antineutrinos" are detected, they will create particles with lepton number -1, so the lepton number is in some sense recovered, even though it was not present in the beam itself. Is that not what would be happening if neutrinos are Majorana particles?I don’t understand what this phrase is supposed to mean.
Below the electroweak symmetry breaking scale, we no longer have weak hypercharge, we only have electric charge, and neutrinos are electrically neutral.they have opposite (weak hyper-) charges…
Majorana fermions can be written in terms of a Weyl field ##\chi## as (see post #167)It is often said that a Majorana neutrino cannot be distinguished as a particle or an antiparticle, are you saying that is not true?
Yes, ##\Psi## would have lepton number of 0, by virtue of ##\chi## and ##\chi^c## having opposite lepton numbers. The mass term is the only one that mixes ##\chi## and ##\chi^c##, and hence violates lepon number. In the interactions it is still conserved.It is also my understanding that Majorana neutrinos would not have a lepton number (or would have lepton number zero, if there is any distinction there).
I see, so that explains what you meant above, but what we are talking about is the concept of a "beam of antineutrinos." You are saying we can see, in that beam, neutrino fields and antineutrino fields that are superimposed, but we see nothing we could call a "beam of antineutrinos" if they are Majorana.Majorana fermions can be written in terms of a Weyl field ##\chi## as (see post #167)
## \Psi = \chi + \chi^c## .
Under charge conjugation it changes form ##\chi\to\chi^c##, so ##\Psi## stays the same. But ##\chi## and ##\chi^c## have opposite charges, and they are the things that appear in interaction terms. It does not matter if we are in the broken phase, they have a charge with which they couple to leptons and Ws and that is reversed between the two upon charge conjugation.
That language confuses me, because when I see a field being described as ##\chi + \chi^c##, I don't see something I am forced to say is mixed by a mass term, I see an equal superposition of a matterlike field and an antimatterlike field. In the viewgraphs I linked to above, the mass effect was that it made a definite chirality have a nondefinite helicity, saying the opposite helicity was present to order m/E since the neutrino isn't moving at the speed of light any more. But we've heard that Majorana neutrinos have zero lepton number, so that doesn't sound like the same thing. Also, when I see a supernova that neutronizes some ##10^{57}## electrons and protons, generating neutrinos in the process which we say might have zero lepton number, I do not see some tiny lepton number violation, I see ##10^{57}## leptons that might not be there any more had those neutrinos been able to escape into space (generally they don't, but that's a detail of supernovae).Yes, ##\Psi## would have lepton number of 0, by virtue of ##\chi## and ##\chi^c## having opposite lepton numbers. The mass term is the only one that mixes ##\chi## and ##\chi^c##, and hence violates lepon number. In the interactions it is still conserved.
Below the electroweak symmetry breaking energy, the only such coupling is the weak isospin coupling, and it only applies to the left-handed neutrino/right-handed antineutrino two-component spinor (which is a weak isospin doublet with the left-handed lepton/right-handed antilepton two-component spinor in each generation). This coupling has already been discussed in quite some detail in previous posts.It does not matter if we are in the broken phase, they have a charge with which they couple to leptons and Ws
As I have already described in a previous post, whether a given instance of this coupling involves a "neutrino" or "antineutrino" depends on the specific event and how it is oriented in spacetime. There is only one coupling; there aren't two, one for "neutrinos" and one for "antineutrinos". And all that is true whether or not neutrinos have Majorana masses or Dirac masses.and that is reversed between the two upon charge conjugation.
Ehm, sure. Are we disagreeing about anything?Below the electroweak symmetry breaking energy, the only such coupling is the weak isospin coupling, and it only applies to the left-handed neutrino/right-handed antineutrino two-component spinor (which is a weak isospin doublet with the left-handed lepton/right-handed antilepton two-component spinor in each generation). This coupling has already been discussed in quite some detail in previous posts.
As I have already described in a previous post, whether a given instance of this coupling involves a "neutrino" or "antineutrino" depends on the specific event and how it is oriented in spacetime. There is only one coupling; there aren't two, one for "neutrinos" and one for "antineutrinos". And all that is true whether or not neutrinos have Majorana masses or Dirac masses.
What the beam consists of will depend on what process procuded the neutrinos. For example if ##\pi^+## decays you will get positively charged leptons and neutrinos described by lets say ##\chi##, and if ##\pi^-## decays you get negatively charged ones and ##\chi^c##. There is no interaction that produce ##\Psi##.Then the question is, what controls the chirality of that beam? We still have to have a difference between a neutrino beam created by leptons vs. antileptons. If this was analogous to linearly polarized light seen as a superposition of circular polarizations, it would be the difference between χ+χc and χ−χc, what is the difference in the case of Majorana neutrinos?
I'm not sure. You appear to be saying that interactions producing ##\chi## and interactions producing ##\chi^c## are distinct interactions. They're not. They're the same term in the Lagrangian and the same vertex in Feynman diagrams; that term/vertex involves the two-component spinor whose two components are ##\chi## and ##\chi^c##. Whether we describe the neutrinos corresponding to external legs in the Feynman diagram as ##\chi## or ##\chi^c## depends on the specific details of the particular instance of the interaction.Are we disagreeing about anything?
That does indeed not sound right to me. ##\chi## is supposed to be a Weyl spinor, i.e. it has two components, its not a component of a spinor.that term/vertex involves the two-component spinor whose two components are χ and χc.
That depends somewhat on your counting. Are a term and its conjugate “the same term”?You appear to be saying that interactions producing χ and interactions producing χc are distinct interactions. They're not.
Well yes, and the beta decay produces anti-neutrinos while the beam that produces electrons should contain neutrinos, so that checks out.For example, in a previous post I described how beta decay, which produces an outgoing leg that you would describe with χc, is the same interaction (same term in the Lagrangian, same Feynman diagram vertex) as the interaction that produces electrons when neutrino beams hit a target containing neutrons; but in that interaction, the neutrino leg is ingoing and you would describe it with χ.
Ok, then I think we're just using different ordinary language to describe the same physics.These are of course in some sense “the same vertex”, I agree.
If neutrinos are Majorana particles, then you cannot get neutrinos described by only ##\chi## when ##\pi^+## decays, because Majorana particles are not described only by ##\chi##. There must be some other reason that a Majorana neutrino that comes from a ##\pi^+## decay is vastly more likely to make ##\pi^+## rather than ##\pi^-##, but it cannot be that it is described by only ##\chi## and not ##\chi^c## since that would not be a Majorana particle. So how does a Majorana particle favor making ##\pi^+## over ##\pi^-##?What the beam consists of will depend on what process procuded the neutrinos. For example if ##\pi^+## decays you will get positively charged leptons and neutrinos described by lets say ##\chi##, and if ##\pi^-## decays you get negatively charged ones and ##\chi^c##. There is no interaction that produce ##\Psi##.
Just to be clear, in the notation you are using, ##\bar{\nu}_R## is the CPT conjugate of ##\nu_L##, i.e., it is the same as what in another common notation would be called ##\nu_L^c##, correct?None of that is right,
Pion decay (how they make beams of neutrinos) proceeds via:
[tex] \pi^+ \rightarrow \mu^+ + \nu_L[/tex][tex] \pi^- \rightarrow \mu^- + \overline{\nu}_R[/tex]
One can detect neutrinos by the inverse reaction
[tex] \nu_L + N \rightarrow \mu^- + X[/tex][tex] \overline{\nu}_R+ N \rightarrow \mu^+ + X[/tex]
These are experimental facts, supported by the dozens of references in the PDG article I linked to. If you disagree, we need to address this going further.
Note that the fields [itex]\nu_R[/itex] and [itex]\overline{\nu}_L[/itex] do not participate. The whole question of Dirac vs. Majorana is whether I link together [itex]\nu_L[/itex] and [itex]\nu_R[/itex] to make a physical neutrino (Dirac) or [itex]\nu_L[/itex] and [itex]\overline{\nu}_R[/itex] (Majorana),
Of course. That's called "crossing symmetry" and "particle" and "antiparticle" (positive-frequencey/negative-frequency parts in the mode decomposition of the (asymptotic) free fields) always come together for all fields in a specific way such as to fulfill the microcausality constraint. Then the possible interaction terms are determined by Poincare invariance of the (variation of) the action.I'm not sure. You appear to be saying that interactions producing ##\chi## and interactions producing ##\chi^c## are distinct interactions. They're not. They're the same term in the Lagrangian and the same vertex in Feynman diagrams; that term/vertex involves the two-component spinor whose two components are ##\chi## and ##\chi^c##. Whether we describe the neutrinos corresponding to external legs in the Feynman diagram as ##\chi## or ##\chi^c## depends on the specific details of the particular instance of the interaction.
Due to the Majorana mass term the ##\chi^c## at the production vertex can interact with your neutron as a ##\chi##, i.e., you have lepton-number violation, and this is what enables neutrinoless double-##\beta## decay for Majorana neutrinos, which is forbidden for Dirac neutrinos. That's what all the hype is about!For example, in a previous post I described how beta decay, which produces an outgoing leg that you would describe with ##\chi^c##, is the same interaction (same term in the Lagrangian, same Feynman diagram vertex) as the interaction that produces electrons when neutrino beams hit a target containing neutrons; but in that interaction, the neutrino leg is ingoing and you would describe it with ##\chi##.