Hi Flip, now with your changes your text has become impossible to understand because you change your names halfway trough. As pointed out by Ivan you start with defining the positron as right-chiral. This way you define the usual Dirac spinors as left-chiral electron and left-chiral anti-positron. In addition, you point out that the electron and the antipositron have the same charge and chirality. I think you noticed that this can't be correct, because during propagation something left-chiral mixes with something right-chiral. With your definitions from the beginning this is impossible, because everything right-chiral has positive charge and therefore we would have a mixing of charge during propagation. Therefore you use a new definition after the "important summary". Then, there you define the positron as left-chiral and we can have a mixing of the electron (=left-chiral) with the anti-positron (right-chiral) without violating charge conservation. Anyway, then it becomes unclear what we write conventionally into the Dirac spinor and call electron and positron. I'm pretty sure you're aware of all this, but rewriting would mean drawing lots of pictures again. Nevertheless a short remark may be in order, because things are really confusing right now.

How many times per second does an electron at rest interact with the Higgs field? Is the interaction rate proportional to the rest mass of the particle? As a particle is accelerated does it interact less frequently from an inertial observer's perspective? If so, is the change in interaction rate due just to time dialation or some other effect?

You say here the positron has right-chiral: "Electrons (left-chiral) and positrons (right-chiral) are two completely different particles, as evidenced by the positron's mustache."
And you say here that it has left-chiral: "Positron: left-chiral, charge +1, cannot interact with the W"

Excellent explanation . So my question now is what exactly is the empirical evidence for separating an electron into two chiralities...Is there experimental evidence that one chirality 'interacts" with the W ? Or is there some other evidence?
Thanks.

You wrote: "There is no “rest frame” in which a massless particle is at rest. The analogy for this is driving on the freeway: if you are driving at the same speed as the car in the lane next to you, then it appears as if the car next to you is not moving (relative to you)."

I did a double-take on this paragraph, but I believe you simply switched from talking about massless particles (that you cannot catch up with) to massive particles (that you can).

I don't believe I know a single fact about the weak force that isn't weird.

First of all, love this blog. I'm not a physics student, but I decided to try and understand the Higgs and the only thing I don't understand is how is the "neutral Higs" different than "The Higgs"...it's right chiral, as opposed to spinless? What then is the difference between H+ and H-? one of them got their weak charge from an electron and one of them got their weak charge from an anti-electron? But which is which?

Also, if I understand all of this correctly, when a fermion hits "the Higgs" the higs particle is converted into the H+ H- H0 bosoms which are then promptly asborbed by the weak force bosoms. And because of this there is really only one Higs ( the other three being unstable?)

The red and blue curved arrows you are using are indicating spin rotation and not the spin vector or just plain spin of the particle. The spin vector (i.e. direction of angular momentum, spin up +1/2 or spin down -1/2) is always obtained by using the right hand corkscrew rule. The velocity direction or else momentum for massive particles (gray arrow), is always aligned with the spin vector, pointing to the same direction, for right-handed (right helicity) particles and pointing to opposite directions for left-handed (left helicity) particles. A right helicity particle behaves always like a right threaded screw (i.e. when turned CCW with a screwdriver the screw is unscrewing and moves towards you) while a left helicity particle behaves always like a left threaded screw (i.e. when turned CCW with a screwdriver the screw is screwing and moves away from you).

In other words helicity under normal conditions shows you if the spin vectror is aligned to the momentum of the particle (right helicity) or not (left helicity). Chirality right or left is this normal intrinsic helicity of the particle when not influenced by external forces and relativistic effects. A moving massive particle being over-passed by an observer will appear as if this has flipped its helicity and momentum direction relative to the observer.

The magnetic moment N-S vector of a charged particle is pointing always in opposite direction from its spin vector for left chiral particles and in the same direction for right chiral particles. Nevertheless, with no external forces present or relativistic effects the magnetic moment of the particle prefers naturally to align with its momentum (i.e. direction of travel).

Normally, negative charged free particles like the electron, when not influenced by external forces and relativistic effects, have intrinsically a left helicity (left-handed and also left-chiral nature). Chirallity is the natural intrinsic helicity of a free particle when not influenced by external forces and relativistic effects). In this case the momentum velocity vector (gray vector) is dictated by the helicity of the particle. The same holds for the right helicity and chirality particles and which have usually positive charge.

A 1/2 spin fermion and left chiral viewed inside its inertial frame of reference above its North magnetic pole will have always a CW spin rotation resulting to a negative charge. On the other hand a 1/2 spin fermion and right chiral viewed inside its inertial frame of reference above its North magnetic pole will have always a CCW spin rotation resulting to a positive charge.

An Anti-particle is the same particle having the same charge polarity, minus or positive, which is forced under an external force or relativistic effect to change to the opposite its natural helicity (but not its chirality) and velocity direction. Therefore an Anti-positron is actually a free electron which is forced or made appear due a relativistic effect, to flip to the opposite velocity direction from what is dictated by its intrinsic helicity (i.e. helicity at inertial frame of reference thus chirality) and also appear due to relativistic effects that it has flipped helicity. (i..e. a fast moving observer overtaking the particle will switch view of the particle from its backside to its front side therefore a flip of its helicity.). Charge of the particle remains invariant at -e.

Similarly, an Anti-electron is actually a positron which is forced due relativistic effect to flip helicity. and momentum direction. Charge of the particle remains invariant at +e.

Hello, thanks for the usefull post. I have some questions:
Q1:

The conventional language in particle physics is to call these the left-handed (chirality) electron and the right-handed (chirality) electron. But I wanted to use a different notation to emphasize that these are not related to one another by parity (space inversion).

You are really telling here that the mirror image (P-symmetry) of a right-chiral particle is not the left-chiral counterpart? I am a little puzzled by that for two reasons 1) what I was able to aggregate from the web seems consistent with the contrary 2) at the massless limit (when chirality is helicity) it definitely IS the case.

Q2: It's related to the mass of neutrinos, as far as I can tell we consider neutrinos have mass. It is also stated that we've never observed one of the two chiralities for neutrinos. But if they have mass, they surely go into the mecanism you higlighted, in which Higgs field will mix both chirality of the particle. How can we reconciliate those two facts ? experimental: one of the chirality is never observed, theoretical: they have mass and their chirality should be mixed? (I have a little idea of the answer to this question, but I'd rather not influence your answer right now :))

https://uploads.disquscdn.c... what is a non chiral fermion .You have only commented on the experimental particles stuff. What is the theory of massive Planck mass non chiral fermions

Thank you for your nice explanation.
I believe I found a typo. In the section of Chiral theories, there are sentences as "The electron is a left-chiral particle while the positron is a right-chiral particle. Both have electric charge -1, but they are two completely different particles." I believe you ment to say the ani-positron (not positron).

I did understand your explanation, thanks. The only thing is that some times doble negatives make me a little confused. For instance "do not cause any charge non-conservation" I have to translate it into "do cause charge conservation" and hope it maintains its meaning. Thanks again for that wonderful explanation.

"https://disqus.Com/by/thadroberts/comments/
Wow, thanks for that. Guess some people will always take things negatively. As an author I greatly appreciated all the feedback I got from others, catching my typos, letting me know which sections needed to be made clearer, etc. I really liked this article and can only assume that with all the work that went into it the author might be seeking feedback. Please try not to exercise your attacks without thinking it through. "

Study Says People Who Continually Point Out Typos Are 'Jerks'

http://www.sciencealert.Com/people-who-constantly-pick-up-grammar-mistakes-are-kinda-jerks-scientists-find

Hi Flip,

I'm not sure where the best place is to post this question, but I thought here would be good. I'm wondering what the explanation is (if there is one) for how mass increases in terms of the Higgs mechanism. The mass of the leptons comes from how frequently they interact with particles from the Higgs condensate (is that correct?...). At speeds where relativity becomes relevant, mass increases, and so does that mean that at higher speeds it becomes more likely for a particle to interact with Higgs particles? Is the answer insightful in any way?

Hi Joseph,
A good place for reading more about the Higgs mechanism and how it relates to the mass of the fundamental particles would be this post:
http://www.quantumdiaries.o...
Or this post:
http://www.quantumdiaries.o...

So ... what is the chirality of the physical electron, at rest? It looks like it should be 0?

Hi.why no helicity=0 for massless particle?

Hello ,

The analogy of the chirality mixing mass term with another kind of mixing that takes place in the neutrino sector is interesting but raises a few questions for me:

Shouldnt we expect to be able to test (experimental evidence) a kind of disapearing effect if starting from a left chiral electron eigenstate of the weak interaction (emitted in a weak interaction for instance) then after some flight distance again a weak interaction only sensitive to the left chiral component of the mixing (mass mixing term due to propagation) should manifest giving only half of the interactions that would have resulted from an electron remaining pure left during its propagation. Is that the case?

Alternatively if the electron interacts electromagnetically is it possible to probe experimentally (for instance by studying the angular repartition of the tracks) wether the electron then interacted as a left or right chiral particle. The latter case would be an evidence for oscillation as for the neutrinos case.

In other words , is it possible to probe the existence of the chriral mixing term appart from the existence of mass itself? Does this question make sense at all?

best

F H-C

and i more question: In electron pairing, electron up and down mean left and right helicity or left and right chirality?

Hi Flip,

I want to clarify my doubt here. Isn't the physicsl electron the combination of left helicity left chiral electron component and right helicity left chiral anti-positron component?

left helicity left chiral electron will have left helicity right chiral positron in mirror (CPT). while left helicity left chiral electron would have right helicity right chiral anti-electron projection in morror. In case of positron, left helicity right chiral would have right helicity left chiral anti-positron.

in this scenario, left helicity left chiral electron should combine with righthelicity left chiral anti-positron and right helicity left chiral electron should combine with left helicity left chiral anti-positron.

Please think on it and resolve this doubt. I'm totally perplexed you can imigine this in writing that i can't even describe simply. many thanks!!

Hey Flip, I recently wrote a paper regarding chirality and the weak interaction, and thought you might be interested in looking at it. I'm not sure it's correct - you might have some insight. Let me know if you're interested and if so where to send it or if I can post it here, etc. Thanks.

Flip,
here is how I read your description:

The Standard Model is weird because "electrons" with different chirality behave differently, those with one chirality interact with W bosons, those with the other chirality do not.

here is my reaction to that:

just as photons are the bosons that allow electrically charged fermions to interact, so likewise W bosons are what allows "???"-charged fermions to interact.

therefore my question is where is the Right-Chiral "???"-charged "electron", it sure seems like it should exist even if we have not observed it.

-Peter A. Lawrence, San Jose, CA.

Hi Flip

For your convenience, I endeavor to correct and reformulate your section "Chiral Theories", providing your bloggers with a more easy reading. The following text is based on the asumption that the now published Table "Important Summary" related to the electron an positron is correct and that all particle icons are drawn correctly.
You may check the new text ocasionally and reply if you agree.

Kind greetings from Switzerland

Rene

Chiral theories

One of the funny features of the Standard Model is that it is a chiral theory, which means that left-chiral and right-chiral particles behave differently. In particular, the W bosons will only talk to "electrons" (left chiral electrons and right chiral anti-electrons) and refuses to talk to "positrons" (left chiral positrons and right chiral anti-positrons). You should stop and think about this for a moment: nature discriminates between left- and right-chiral particles! The weak force shows a selective behavior, violating Parity symmetry. (Of course, biologists are already familiar with this from 'chirality' of amino acids).
Note that Nature is still, in some sense, symmetric with respect to left- and right-helicity. In the case where everything is massless, the chirality and the helicity of a particle are the same. The W will couple to both left- and right-helicity particles: the electron and the anti-electron respectively. However, it still ignores the positron and anti-positron. In other words, the W will couple to an electric charge -1 left-handed particle (the electron), but does not couple to an electric charge -1 right-handed particle (the anti-positron). This is a very subtle point!

Technical Remark:
etc...

In order to really drive this point home, let me reintroduce two particles to you: the electron and the positron. You already know that the positron is the anti-partner of the electron... but for now, pretend you didn't know that. The electron shown below has left-handed helicity or spin, while the positron has right-handed helicity or spin. Both are chiral left-handed. They're two completely different particles.

Figure

The electron (with left-handed spin) and the positron (with right-handed spin) are two completely different particles, as evidenced by the positron's moustache. Both are left-chiral.

How different are these particles? Well, the electron has electric charge -1, while the positron has electric charge +1. Further the electron can couple to a neutrino through the W-boson, while the positron cannot. Why does the W only talk to the (left-chiral) electron? That's just the way the Standard Model is constructed; the left-chiral electron is charged under the weak force ("carries weak charge"), whereas the left-chiral positron is not. Note that at this stage, even the electron and the anti-positron are NOT the same particle! Even though they both have the same electric charge and the same helicity, the electron can talk to a W, whereas the antipositron cannot.

For now let us assume that all these particles are massless, so that these chirality states can be identified with their helicity states. Further, at this stage the electron has its own anti-particle (an "anti-electron") which has right-handed chirality which couples to the W-boson. The positron also has a different antiparticle (the "anti-positron") which also has right-handed chirality, but does NOT couple to the W-boson. We thus have a total of four particles (plus the four with opposite helicities):

Figure

The electron, anti-electron, positron and anti-positron. (Anti-particles are drawn with a slight green tint). It is crucially important that the electron and anti-positron are two different particles.

Technical Remark:
etc....

Hi everyone---I think some of the notation I use here is unnecessarily cumbersome, I apologize. For an overview using simpler notation, see my particle physics lecture notes here: http://www.lepp.cornell.edu...

@Richard: great question. The Higgs will interact with an eR and an eL. It cannot talk to two eRs at the same time, nor to two eLs at the same time. This is imposed by the "gauge" structure of the theory: the Higgs and eL are sensitive to the weak force, while the eR is not. The particular interaction of a Higgs-eR-eL is what is required to conserve weak charge (and also hypercharge, which is related to the weak and electric charges).

The particular combinations that have well defined masses are given by the Higgs interactions. You end up with three massive particles with well defined masses, after starting with six massless particles. (Recall one massive fermion is equivalent to two massless fermions.)

@Thomas: photons gauge bosons and have spin-1, the discussion here focused on fermions which are spin-1/2. But indeed, photons can be left- or right-handed---we know this more commonly as being left or right circularly polarized. It's the same photon, but just spinning in different directions---it both polarizations carry the same electromagnetic force.

"As we said above, for massless particles the chirality and helicity are the same. A massless left-chiral particle also has left-helicity". The photon is massless; can it be left-chiral/helicity and/or right-chiral/helicity. Are there then two form of the photon? If the photon carries the electro-magnetic force, does this mean both forms carry the electro-magnetic force or just one form? If just one form, then the other form carries...?

Hi - great post - I've got a question about this!

There seem to be two ways to take combinations of the e_L and e_R states, e.g. when the electrons interact with the Higgs field, what choses the relative phases of the e_R and e_L components?

e_S = (e_L + e_R) / sqrt(2)
e_A = (e_L + e-R) / sqrt(2)

Could I pick a symmetric and antisymmetric combination of these particles? etc. Do the different linear combinations have different masses? Does the full picture take the electron muon and tau chiral states, and mix them to produce real particles?

Just the resource I was looking for, and at an engaging level. Thanks!

thank you very much for this simple explanation of the basic concepts of spin and angular momentum , it was worth watching

Hi Flip. This is probably a silly question, but why can the electron only be spinning 'up' or 'down' ? Could it not be spinning sideways?

What happens if you drive in your car and match speeds with the electron, so it is not moving at all relative to you? Then which direction is its direction of motion? If you then moved perpendicular to how you were moving before, then have you caused the electron to change its spin direction? (it was previously spinning north, now it is spinning east, even though it didn't change its velocity, only you did) ?

You can never know the "true" direction of an electron's spin in quantum mechanics. This is similar to how you can't know the exact position and momentum of a particle. In QM parlance, the operators for spin around different axes don't commute.

What you can do is measure the spin around one particular axis. And when you do, you can get one of two values: spin up or spin down. If you later measure along a different axis, this new measurement is only statistically correlated to the previous one (and is uncorrelated if the new axis is 90 degrees from the old one). If you measure the z-axis spin, then later measure the y-axis spin, then go back and measure the z-axis spin again, the spin could be different! Measuring the y-axis spin destroyed any information about z-axis spin in the system (through "wavefunction collapse"). This is the uncertainty principle at work.

If you change your frame of reference relative to the particle, the spin you measure won't change along the same axis (the helicity might). If you measure along different axes you certainly could see how much the electron was spinning "sideways" -- but as above, you lose any information of how it was spinning "up" or "down."

Great post! But I'm a little confused about something. In the "CHIRAL THEORIES" section you say "the W bosons will only talk to electrons (left-chiral electrons and right-chiral anti-electrons) and refuses to talk to positrons (right-chiral positrons and left-chiral anti-positrons)" and a little later you say "The electron is left-chiral, while the positron is right-chiral. They’re two completely different particles."

But then this is the opposite of what's written in the "Summary Section":

Electron: left-chiral, charge -1, can interact with the W
Anti-electron: right-chiral, charge +1, can interact with the W
Positron: left-chiral, charge +1, cannot interact with the W
Anti-positron: right-chiral, charge -1, cannot interact with the W.

I think the summary section is correct while the earlier statements (regarding the positrons) is not. If the positron was right-chiral, the antipositron would have to be left-chiral. But then the electron mass term would have a left-chiral electron and a left-chiral antipositron, which is not correct.

Do you agree that there is a conflict between the statements or am I misinterpreting it somehow?

cheers,
D

Argh this was so confusing! The "summary" contradicts all the text and diagrams before it! I certainly hope the "summary" part was right, because that's what I'm gonna stick in my brain.

Hi DK, it's entirely possible that I was sloppy with conventions, I'll try to go over it again when I get a chance... but there's a possibility that I won't get the chance in the near future. -F

Hello Flip Tanedo,

Mu name is Manel Rosa Martins and I would like to ask for your kind permission to translate into Portuguese (European)and publish this excellent article of yours in the Astronomy Blog Astro PT. I am Particle Physics student and volunteer writer for the Astro Pt. We're aiming to enhance functional literacy amongst our readers and to try to reach them with accessible and accurate writing. I will respect attribution, publish your bio and send you a copy upon completion, if your authorization is granted , that is. Thanks
Manel R Martins

The MINOS experiment measures the two delta m squares. Whether or not theta_13 is greater than zero is a separate issue (maybe, that is).

All right then! So you are prepared to believe the MINOS results then, which clearly indicate that the so called antineutrino is NOT the antiparticle of the neutrino, so that CPT may be conserved. That is, the neutrino mixes a left and right Bilson-Thompson braid pair to form one (kind of Majorana) particle, while the antineutrino mixes the other pair, so that these two 'physical' particles may have distinct masses. As observed. No Lagrangians required. Who thought mass ever had anything to do with Lagrangians anyway?

Hi Kea, I do not know which MINOS results you are referring to, but to the best of my limited knowledge in that field, there has not been definitive evidence for any specific model of the right-handed neutrino sector other than the fact that neutrino indeed oscillate (and, most recently, that theta_13 >0).

A beutiful post. You really excel in making great concepts simple. We believe that world urgently needs people like you who make abstruce topics appear so appealing and inspiring. I had the same doubts raised about L and R chirality but now you have resolved these in the forgoing posts. Thanks.

Dear Flip,

I see no problem with quantum mechanics so long as its statistical foundation (and lack of explanation for its 100% certain predictions) is acknowledged. It is the "fundamental" particle-and-field model that seems contrived. Studying collision debris may be like breaking clocks and studying their parts, but it may also be like breaking billiard balls (rotating, that is) thinking them to be clocks. (And I seem to be having a hard time finding someone -- anyone -- to analyze that triaxial rotation "math problem". If I could do it I would, but I haven't a clue how to do it and my brain has a hard time learning new tricks.)

But I must thank you for your response -- I appreciate it, usually there is just silence.

David G.

Hello David G. I believe one quick answer is that the shell structure of molecules has been measured experimentally (I believe? You should cross check this with someone more knowledgeable), which provides a very non-trivial affirmation of quantum theory. -F

Ay there's the rub. I just learned that the W boson interacts with left handed particles and right handed anti particles. So if you call the LH particle state a electron and the right handed particle state a positron and do the same vice versa for the anti particles I get:

1. LH electron, W interaction, negative charge
2. RH positron, no W interaction, negative charge
3. RH anti-electron, W interaction, positive charge
4. LH anti-positron, no W interaction, positive charge

Which is the same as yours save for the names of the particles:

1. Electron: left-chiral, charge -1, can interact with the W
2. Anti-electron: right-chiral, charge +1, can interact with the W
3. Positron: left-chiral, charge +1, cannot interact with the W
4. Anti-positron: right-chiral, charge -1, cannot interact with the W.

Regards,

Lennart

Dear Flip,

Thank you for a fascinating introduction to helicity and chirality. However, I do not believe the process you describe represents the workings of nature. In other words, I have no faith in the particle model as a description of nature. I have no formal physics training and so you would probably class me as a crackpot. Knowing from my experience that physicists do not like to talk to me I must nevertheless propose an alternative process (based on an alternative atomic model). If this process does not provide a way to match exactly the quantum mechanical predictions, it should be easily demolished. My proposal is that an electron (and proton) is a rotating sphere occupying the entire atomic orbital (i.e. it resembles a 'smeared out' electric charge). There are three possible orthogonal axes, combinations of which can describe the sphere's rotation (i.e. the electron 'superposition' of two electron states may be resolved into a rotation on any two of the three axes). Firstly, as an expert on chirality and helicity, which are intimately related to rotation, I wonder if you have ever dealt with combinations of potentially triaxial rotations (say, two of three axes). Secondly, it appears that the electron-antipositron mixture is due to the measurement uncertainty principle +h/2 pi versus -h/2 pi. So in particle physics the up-versus-down becomes electron-versus-antipositron. Is that correct?
My belief in triaxial rotation is quite firm, since simple equations lead to a formula that gives the electron magnetic moment as 9.284 765 18 e-24 joules per tesla, without any spin-g factor (however, a combination of the spin-g factor and a factor which appeared in my calculations regains the conventional mass values of the electron and proton). In this model the system electron and proton have different radii than their free versions (which are the measured versions I believe).
I should note that a comment I made on the Physics 2.0 website -- to the effect that the q.m. probabilities for a measurement of entangled electrons (or from a superposition state) can be reproduced by manipulating the two-out-of-three possibilities for a triaxial rotation -- was deleted from the comment section altogether. I may be appear to be overly hostile sometimes (being a non-believer in the particle model) but there was no hostility in that post. The only reason I can come up with is that the comment was removed (rather than simply dismissed with a chuckle, etc.) because it posed some kind of threat to the original poster. So having found your very interesting post (and having been unaware of the four particle scenario) I wonder if you can comment on the possible outcomes of rotational combinations of spheres of rotating space, given the existence of three axes to choose from.
I am submitting this because you appear to be sincerely interested in revealing details of quantum mechanics as applied to fields. As I said earlier, I do not believe any such process as the electron zig-zag (with accompanying singularity, I think) exists in nature. It is an ingenious mathematical contrivance to deal with a measurement phenomenon but does not represent a natural process (and so also for the particle models which have grown out of it).

superposition exists you are correct, but not in this case. You're speaking of objects in an entirely quantum uncertain state.
but any electron/positron collision treats itself more or less in a classic sense so that the opposing chiral natures collapses the virtual particle.

I hope this analogy may help lol.
You have a box full of 100 shoes. (50=left), (50= right).. a box full of left and right shoes doesn't create a 3rd Z shoe.
superposition is the unmeasured uncertain state like with the infamous uncertainty principle. like a closed box without knowing what will emerge(dead cat or living cat). but while box is closed, its both.

a 3rd axis you believe in, would be the equal to saying you have a 3rd shoe in the mix, when that isn't what happens theoretically or in nature. Its always Left hand +/- or Right Hand +/-

lastly keep in mind that feynman diagrams are interactions which collapse superposition, and photon interaction creates engtanglement too. Its millions of times more complex than your statement of saying superposition is a new 3rd form. when it really truly isn't when you suss the field.

Hello Flip Tanedo,

Your last change has made things a bit foggy for me. In the summary you changed the chirality of the positron to left chiral while throughout the rest of the post it is still called right chiral.

Also the reason why the W boson doesn't talk with positrons is a bit unclear. The way I understand it RH chiral particles do not carry electroweak charge so W bosons only interact with LH chiral particles. Is this correct? If so shouldn't the summary become:

1. LH Chiral electron, W interaction, negative charge
2. LH Chiral positron, W interaction, positive charge
3. RH Chiral anti-electron, no W interaction, positive charge
4. RH Chiral anti-positron, no W interaction, negative charge

Your posts are wonderful and a true delight to read. If you would ever decide to write a book about physics I would love to buy it.

Regards,

Lennart

--[Sorry, the term “right chiral electron” is what particle physicists usually call what I am here calling the “anti-positron.”]--

Since I'm a physicist already happy with the e-_L e-_R convention, your "anti-positron isn't an electron" business made my head hurt!!

AWESOME explanation!!!!!... I really enjoy your blog, one of the best in Quantum Diaries!!!

Hi everyone, thanks for the comments over the past couple of days. My apologies for the delayed response.

@ Bjorn: Sorry, the term "right chiral electron" is what particle physicists usually call what I am here calling the "anti-positron."

I've updated the technical comment about this to help clarify.

@ Magneton: the way it is written now should be correct. Only the non-mustached particles interact with W bosons, i.e. only the electron and anti-electron.

@ Brian: yes! Excellent example!

Thanks!
F

Very nice post! I'm glad to see an explanation of chirality that's understandable to a non-specialist like myself.

There is a connection between this post and the branching ratios for charged pion decay, and reading this helps clarify things on that front. A negative (say) pion decays by the weak force into a (virtual) W-, and then into either an electron/neutrino pair, or a muon/neutrino pair. The first decay path is highly relativistic, but the second decay path is not (due to the muon's large rest mass, almost as large as the pion). As you say, the mixing angle between the electron and anti-positron is energy dependent, and for the highly relativistic "electron" decay of the pion, the emitted electron is almost all anti-positron, with barely any electron in its wave function to interact with the weak force. (The neutrino must be emitted with the correct chirality = helicity, which means the helicity of the emitted electron or muon is "wrong", so the "wrong"-chirality component dominates its wave function.) This strongly inhibits the electron decay, but not the muon decay, where the mixing angle is close to the 45 degree non-relativistic limit.

Electron: left-chiral, charge -1, cannot interact with the W
Anti-electron: right-chiral, charge +1, cannot interact with the W
Positron: right-chiral, charge +1, can interact with the W
Anti-positron: left-chiral, charge -1, can interact with the W this is right or not?

It seems that helicity is a property of motion and chirality a property of shape (where, in the case of an elementary particle, this might be represented by something like the shape of a level surface of its wave function). The language chosen by physicists is unfortunate as a helix is an object with fixed chirality but the chirality of the path of a "helical" motion depends on the relative motion of the medium in which it is traced.

Hi now is start making more and more sense,

But i wonder what the "right-chiral electron" is in your picture.

The “anti-positron” (does not interact with the W) is called eRc or eR-bar, is a left-chiral particle which is the anti-partner of right-chiral electron (eR) [6/21: corrected, thanks to ParoXoN.]

The positron is right-chiral and the anti-electron is right chiral, but i dont see any right chiral electron,