Note: I refrain from using the concept of handedness and the terms left-handed and right-handed when referring to chirality since these usually refer to the helicity of charged fermions and their antiparticles and prefer to use instead the terms referring to their Lorentz invariant but not a constant of motion chirality, namely as Left-Chiral and Right-Chiral similar as looking statically at your two hands without any momentum involved. These handedness above terms sometimes used in common for either referring to helicity or chirality I find a big source of confusion even for the related WP pages references.

My question is:

It is stated in WP Chiral Theories,

"Particle physicists have only observed or inferred left-handed fermions and right-handed antifermions engaging in the charged weak interaction."

In the above quote WP uses the terms left-handed and right-handed referring to the chirality of these particles... ):

Since a right-chiral fermion would not carry any weak hypercharge thus it does not interact with the Higgs that would strongly imply that this electron does not gain any mass from the Higgs field. The same is also true for a left-chiral antifermion like a left-chiral positron (i.e. only right-chiral positrons carry a weak hypercharge).

But a massless electron cannot be described anymore as a physical electron.

Therefore I'm asking are there actually in nature any right-chiral isolated electrons or is this just a mathematical induced physics effective theory used in order to describe the Higgs mechanism?

  • $\begingroup$ Related question here. $\endgroup$
    – knzhou
    Mar 10, 2022 at 21:06

3 Answers 3


I would strongly disfavor your associating handedness with helicity instead of chirality, but no matter... Indeed, the WP usage of right-handed for right-chiral (annihilated by $1-\gamma_5$) is fine. It is a source of clarity, not confusion. In this issue, helicity stays out of the picture, regardless of language.

Since a right-chiral fermion would not carry any weak hypercharge thus it does not interact with the Higgs that would strongly imply that this electron does not gain any mass from the Higgs field....

Right-chiral fermion fields have a hypercharge proportional to their electric charge, by the (EWeak) Gell-Mann—Nishijima formula. They do interact with the Higgs field, in the Yukawa terms of vanishing total weak hypercharge. These terms couple right-chiral to left-chiral fermions and induce the fermion masses through the v.e.v. of the Higgs field, of course. (Charged current weak interactions refer to W couplings, and not Higgs couplings.)

Right-chiral electrons exist, and they are, on average, half the degrees of freedom my and your and the universe's electrons have.

They are never isolated, as the electron mass connects them to their left-chiral brothers. Chirality is not constant in time. They have little to do with the Higgs mechanism. (I hope you don't actually mean SSB, instead).

NB There is a pedagogical picture presenting this as a chirality oscillation controlled by the mass term in the hamiltonian. A stationary solution of the free Dirac equation dictates immediately, starting from the R state, $$ \langle \gamma_5 \rangle = \cos(2mt). $$

  • $\begingroup$ tinyurl.com/29amj6fs quote: "The helicity of a particle is right-handed if the direction of its spin is the same as the direction of its motion and left-handed if opposite." end quote. tinyurl.com/3mayhbfu quote: "Particle physicists have only observed or inferred left-handed fermions and right-handed antifermions engaging in the charged weak interaction." end quote. Two WP pages using the same terms, left-handed and right-handed for describing different concepts namely helicity and chirality. Someone should tell them to fix this. $\endgroup$
    – Markoul11
    Mar 10, 2022 at 22:22
  • $\begingroup$ Indeed, people using helicity sometimes slip into using the terminology of the chirality most associated with it at ultra-high energies; they would not be using helicity otherwise. This is taught and emphasized in all HEP courses. It is a convenient conflation, as long as it is not taken literally, as here. $\endgroup$ Mar 10, 2022 at 22:30
  • $\begingroup$ Also to which the term "handedness" is referring to? Helicity or chirality or direction of rotation clockwise or counterclockwise makes confusion even worse. The PSE answer for example says that handedness is the helicity, physics.stackexchange.com/a/356788/183646 . Also this WP page, en.wikipedia.org/wiki/Chirality#Physics adds even more to the confusion. Is there a clear terminology standard defined in the literature? Any reference to be shared? $\endgroup$
    – Markoul11
    Mar 10, 2022 at 22:41
  • $\begingroup$ Handedness is Chirality (from the Greek for hand, χείρ, as in "chiropractor"). For massless or almost infinitely energetic particles, positive helicity identifies with right-chirality, so people think of the two and refer to them interchangeably; for practical reasons. This happened and still happens for neutrinos, whose rest frame is hard to seriously contemplate. But a Lorentz boost can change helicity. It is a bit of a storm in a teacup, though... in the afternoon tea of pedantic theologians. You could ask a separate nomenclature question, but I hope you appreciate the facts. $\endgroup$ Mar 10, 2022 at 22:54
  • 2
    $\begingroup$ I'll answer the above comment myself: every interaction with the Higgs Field, not just the Higgs Boson, flips the chirality of the fermion, and the very same coupling with the Higgs field's v.e.v. is the mass term in the lagrangian. Helicity loses much of its import in the presence of mass. $\endgroup$ Mar 11, 2022 at 14:45

In its rest frame, an electron is an equal superposition of its left-chiral and right-chiral components. The two pieces transform differently under boosts, for reasons which occupy a chapter or two in textbooks on field theory. So if you are holding a polarized electron in your hand at rest, you’ll think it’s equal parts left- and right-chiral. But if I run past you relativistically, I’ll see your electron as one chirality or the other depending on whether I run at its “north pole” or its “south pole.”

The charged weak current only interacts with the left-chiral parts of the matter fields, and with the right-chiral parts of the antimatter fields. In the rest frame of the decay, electrons created by the charged current are purely left-chiral, and so the more energetic they are, the more strongly they are also left-polarized. But in the rest frame of the created electron, it is equal parts left- and right-chiral the whole time.

  • $\begingroup$ Does the left and right chiral phases for the electron at rest each lasts 2π of spin rotation? $\endgroup$
    – Markoul11
    Mar 10, 2022 at 21:58
  • $\begingroup$ Are you referring to the rotational frequency of the electron’s intrinsic spin? There is no such frequency. The electron’s spin angular momentum is intrinsic to the field. $\endgroup$
    – rob
    Mar 10, 2022 at 22:05
  • $\begingroup$ This whole right left flipping reminds me to the Dirac Belt 4π spinor characteristic of the electron. Where each 2π the electron changes phase. Any correlation? $\endgroup$
    – Markoul11
    Mar 10, 2022 at 23:02
  • $\begingroup$ A superposition between two states is different from “flipping back and forth,” even if there is some rotating phase associated with the superposition. Neither of these is related directly to the “double cover of the rotation group” that I think you are calling “Dirac’s Belt.” We rotate a lot of things in physics, in real space and in various kinds of phase space or configuration space. $\endgroup$
    – rob
    Mar 10, 2022 at 23:37

Left-chiral and right-chiral electrons don't exist as isolated long-lived objects.

Instead, what we call an electron (with rest mass $m$), is actually a particle constantly oscillating between being a left-chiral electron ($e_L$) and a right-chiral electron ($e_R$). The frequency of this oscillation is extremely high, $\nu=\frac{mc^2}{h}=1.2\cdot 10^{20}\text{ Hz}$. Every time the electron changes from $e_L$ to $e_R$ or vice versa, it emits/absorbs a boson to/from the ubiquitous Higgs field which permeates the whole world.

enter image description here

Here I have paraphrased what I understood from Leonard Susskind's lecture "Demystifying the Higgs Boson" (especially in time 42:30 - 51:40).

  • $\begingroup$ Are you sure it is not the helicity flipping sign but the chirality each time the electron collides with the Higgs Boson? Because I have seen the lecture from Susskind and I remember he was referring to the helicity and not the chirality, $\endgroup$
    – Markoul11
    Mar 10, 2022 at 22:04
  • $\begingroup$ @Markoul11 May be you are right. I always struggle telling the difference between helicity, chirality and handedness. $\endgroup$ Mar 10, 2022 at 22:09
  • $\begingroup$ Same also here. People use these terms interchangeable leaving the readers or audience guessing each time. This is very confusing. I suggest amending the terms left-handed and right handed always to which they are referring, helicity or chirality? For example, left-handed helicity or right-handed chirality or just right-chiral. Also avoid mixing the term "handedness" with helicity or chirality. It is my understanding that handedness refers to neither of these but instead to direction of spin rotation thus clockwise (left-handedness) or counterclockwise (right-handedness). $\endgroup$
    – Markoul11
    Mar 10, 2022 at 22:55
  • $\begingroup$ @Markoul11 It’s usually clear from context whether you are referring to helicity, chirality, or the energy regime where they overlap. This is annoying for people who are coming into the field without much context. I am reminded of a place in Griffiths’ introductory quantum textbook where he uses $m$ twice in the same equation, in one place as a mass and in another place as the azimuthal quantum number. In a footnote he writes something like “yes, this is annoying. Everybody does it. Sorry.” $\endgroup$
    – rob
    Mar 10, 2022 at 23:33
  • 1
    $\begingroup$ @Markoul11 At 43... Susskind clearly is referring to chirality, since flips imply non constancy in time, which chirality "suffers", but not helicity; but, indeed, he is beginning his discussion by helicity, replete with mass gestures, in case you thought of spin as a spinning top, instead of a bland formal arrow. The leap between the two occurs when he drops the crucial condition of moving with a speed close to that of light. L.S. is famous for neat intuitive pictures with such hidden leaps. $\endgroup$ Mar 11, 2022 at 15:09

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