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

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!!

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.

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….

@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.

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?

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.”