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Old Oct 2nd 2019, 03:16 AM   #1
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Right-handed fermions in charged weak interactions

I've heard that it's not possible for right-chiral fermions to participate in charged weak interactions (those involving a W boson). Is that really true? Wouldn't that mean that a right-chiral electron couldn't undergo electron capture? And that a right-chiral muon or tau couldn't even decay? Because their decay to a neutrino (one which preserves lepton family number) would necessarily involve a W boson to conserve electric charge as the neutrino gets created (e.g. muon => W- and muon neutrino, W- => electron and electron antineutrino). So how can that be?
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Old Oct 2nd 2019, 04:01 PM   #2
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Originally Posted by muon View Post
I've heard that it's not possible for right-chiral fermions to participate in charged weak interactions (those involving a W boson). Is that really true? Wouldn't that mean that a right-chiral electron couldn't undergo electron capture? And that a right-chiral muon or tau couldn't even decay? Because their decay to a neutrino (one which preserves lepton family number) would necessarily involve a W boson to conserve electric charge as the neutrino gets created (e.g. muon => W- and muon neutrino, W- => electron and electron antineutrino). So how can that be?
You are correct that R chirality leptons (electrons, muons, taus) don't decay using a weak channel (W's or Z's.) However that doesn't mean the R leptons don't decay. It's possible that a tau (R or L) can decay via a strong channel. For instance both L and R taus can decay by emiting, say, a kaon (or a pion) as the intermediate.

I haven't considered electron capture before. Good question! So far as I know you are correct, in so far as an energy favorable channel (for an R lepton) would be able to be absorbed by a neutron using a weak channel. Again, though, it should be possible using a strong channel but I can't see that as a likely process as the lepton would have to have a fairly high energy to use, say, a kaon in the interaction and wouldn't be likely to form a stable particle.

-Dan
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Old Oct 2nd 2019, 04:50 PM   #3
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Correct me if I'm wrong, but all tau decays which involve mesons such as pions, also involve the emission of a tau neutrino. They have to to preserve lepton family number. To me that indicates that it's not a strong interaction, but a weak one. No neutrinos take part in any strong interactions. For that matter neither do leptons such as the tau, right? Because they're color-neutral. Muons also have no decays into hadrons such as pions anyway, because they're less massive than any hadron.

Maybe it's the case that right-chiral fermions become left-chiral after interacting with the Higgs field, and only then do they decay? Is that how that works? I don't understand the Higgs field but I've heard that it can flip chirality, is that true?
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Old Oct 4th 2019, 05:20 AM   #4
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Originally Posted by muon View Post
Correct me if I'm wrong, but all tau decays which involve mesons such as pions, also involve the emission of a tau neutrino. They have to to preserve lepton family number. To me that indicates that it's not a strong interaction, but a weak one. No neutrinos take part in any strong interactions. For that matter neither do leptons such as the tau, right? Because they're color-neutral. Muons also have no decays into hadrons such as pions anyway, because they're less massive than any hadron.

Maybe it's the case that right-chiral fermions become left-chiral after interacting with the Higgs field, and only then do they decay? Is that how that works? I don't understand the Higgs field but I've heard that it can flip chirality, is that true?
Bah! You caught me in a brain fart. I was considering a simpler problem where the tau simply ditches some energy, not that it ended up as a neutrino. My apologies.

I don't have time at the moment but answer to your question is in the interactions between right and left chiral states mediated by the Higgs. In a nutshell the right chiral state of a tau can emit a Higgs and end up in a left chiral state. Then it can decay further via the W-. (This is basically what you said in your last post.) I looked over the possible interactions this time, rather than just using the Particle Data Book. This is the only way that a R chiral tau can decay, barring electromagnetism.

You seem to have a knack for asking the "right" questions. Are you a student?

-Dan
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Last edited by topsquark; Oct 4th 2019 at 05:22 AM.
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Old Oct 4th 2019, 06:53 PM   #5
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Thanks, I think the Higgs interaction does make a little more sense now that I've read more about it. I've noticed that all left-chiral leptons and down/strange/bottom quarks have exactly 1 greater weak hyperchange and -1/2 less weak isospin than their right-chiral versions (for up/charm/top quarks it's flipped), while 1 weak hypercharge and -1/2 weak isospin are exactly the properties of the Higgs boson. Therefore those charges would be conserved through that interaction if the particle was to flip chirality through it. No I'm not a student, I've just been reading about particles out of interest
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Old Oct 4th 2019, 07:42 PM   #6
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Originally Posted by muon View Post
Thanks, I think the Higgs interaction does make a little more sense now that I've read more about it. I've noticed that all left-chiral leptons and down/strange/bottom quarks have exactly 1 greater weak hyperchange and -1/2 less weak isospin than their right-chiral versions (for up/charm/top quarks it's flipped), while 1 weak hypercharge and -1/2 weak isospin are exactly the properties of the Higgs boson. Therefore those charges would be conserved through that interaction if the particle was to flip chirality through it. No I'm not a student, I've just been reading about particles out of interest
Glad to see you are interested and it's nice to see someone working with this stuff. Someone around here has to keep me honest.

I'm currently not doing very well so my response time is down, but I'll get back to you on some of the details, if you like.

-Dan
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Old Oct 4th 2019, 08:51 PM   #7
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No problem, thanks!
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