# Left Handed / Right Handed Particles and the Weak Force

Good Afternoon,

I am a 50-year-old guy who was never a scientist or physics student. Just a person who loves to read books on particle physics.

I have a question on the Weak Force and particles. (I have read the existing answers here on the weak force, but would like a "dumbed down" answer to my question.)

In several books such as In Quest of the Quark by Dr. Linda Bartrom-Olsen and others that stated that only Left handed particles and Right Handed antiparticles are affected by the weak force.

$$d \to u + W^-$$ $$u \to d + W^+$$ etc

My questions are this:

1. What do right-handed particles feel?

2. Are there right-handed particles? If not why?

It's difficult to explain this without using Lagrangians. So I'll just do my best to explain what the terms in a lagrangian mean.

short answer: Left handed particles feel whatever force fields they couple to in the lagrangian.

For the sake of this discussion, we will define the lagrangian as a mathematical object that completely governs the laws of motion of the particles therein. It will take many definitions, but I will do my best to be clear.

Definitions:

force fields: You will often see these referred to as gauge fields. They are the fields that describe the mediators of a force (e.g. the photon field $$A_\mu$$ which mediates the EM force).

feel: We usually say that a given particle feels a force if it couples to the corresponding force field.

coupling: For the sake of this discussion (but is actually quite general), we say that particles couple to a field if they are multiplied together in the lagrangian.

Explanation

Now that the definitions are out of the way, lets get to the meat. The weak force is much harder to explain at a first pass, so what I will do is give the desired explanation first in terms of the electromagnetic force (often times called QED). The concepts will of course generalize.

QED

As I said before, the lagrangian governs everything so the first thing we must write down is this. Note: writing down the correct lagrangian for a given theory is not obvious and takes a tremendous amount of guesswork, so let's just say that we've done the guess work right.

We will represent an electron as $$\Psi$$ and an anti-electron as $$\bar{Psi}$$, and we will represent the EM field by $$A_\mu$$. The QED lagrangian is

$$L = \bar{\Psi}(i\gamma^\mu \partial_\mu - m)\Psi - ieA_\mu \bar{\Psi} \gamma^\mu \Psi$$

Looks intimidating. However, based on our few rules we can already see that there is a coupling given by

$$L_{cup} = - ieA_\mu \bar{\Psi} \gamma^\mu \Psi$$

What this means based on our above definitions is that electrons and anti electrons feel the electromagnetic force.

Handedness:

Now, it turns out all fermions (which we also represent by $$\Psi$$) can be written in the form

$$\Psi = \Psi_L + \Psi_R$$

I will not go into the how or why of this--we may just take it as a mathematical fact. So to find out if left handed and right handed fermions also feel the EM force, we plug this into our coupling lagrangian and find that

$$L_{cup} = - ieA_\mu \bar{\Psi}_R \gamma^\mu \Psi_R - ieA_\mu \bar{\Psi}_L \gamma^\mu \Psi_L - ieA_\mu \bar{\Psi}_L \gamma^\mu \Psi_R - ieA_\mu \bar{\Psi}_R \gamma^\mu \Psi_L$$

so we see that indeed both left handed and right handed $$\Psi$$ couple to the EM force (and hence feel it).

Relationship to Weak Force:

Now, I will not bother writing down the lagrangian for the electroweak force as it will only cause further confusion. But I will mention this. The electroweak lagrangian itself only contains couplings to fermions of the form

$$L \supset W_{\mu}\Psi_L \gamma^\mu \bar{\Psi}_L$$

where $$W_\mu$$ is the electroweak gauge field (force field).Again, this should not be obvious and coming up with the lagrangian is very difficult. However, if we take this as fact (as we did before) we observe that only the $$\Psi_L$$s feel the weak force and the $$\Psi_R$$s, which they do exist in the full lagrangian do not contain such a term. Hence they do not feel the weak force.

Are there right-handed particles?

What do right-handed particles feel?

That will take some explaining...

Our current understanding of particle physics is based on quantum fields, which can be manifest in a variety of ways. Particles are just one manifestation of the quantum fields. I mention this because the vocabulary "left-handed/right-handed" is used for two distinct concepts :

• One meaning of "left/right-handed" refers to the quantum fields (which are among the model's inputs), specifically to the matter fields (fermion fields). These are denoted $$\Psi$$ in the answer by Inertial Observer. The model also involves gauge fields, but the terms "left-/right-handed" do not apply to gauge fields. They apply only to the matter fields.

• The other meaning of "left/right-handed" refers to particles (which are among the model's predictions), and it has to do with the direction of a particle's spin compared to the direction of its momentum. Only massless particles are strictly restricted to be either left- or right-handed. Massive particles can be either (so yes, there are right-handed particles) but are typically neither; a massive particle's spin can be oriented arbitrarily, regardless of its momentum (and its momentum can even be zero, in which case the momentum doesn't have any direction at all).

The electromagnetic and weak interactions are sometimes said to be "unified," but that's a misnomer . A better way to say it is that they are two different mixtures of two more-fundamental gauge fields that are often denoted $$SU(2)_L$$ and $$U(1)_Y$$. What the names mean isn't important here; they're just names. Here are the important things:

• Only the left-handed matter fields couple directly to the $$SU(2)_L$$ gauge field. This is the reason for the subscript "$$L$$." The right-handed matter fields don't couple directly to (don't "feel") the $$SU(2)_L$$ gauge field.

• Both left- and right-handed fields couple directly to (directly "feel") the $$U(1)_Y$$ gauge field. Their charges with respect to this interaction are called hypercharges. However, the pattern of hypercharges is still asymmetric: the left-handed fields have different hypercharges than the right-handed fields.

• The electromagnetic field is one mixture of the $$SU(2)_L$$ and $$U(1)_Y$$ gauge fields. This mixture is special in two ways. First, it mediates a long-range force (which is related to the fact that photons are massless). Second, it is symmetric with respect to the left- and right-handed matter fields. This is why we don't need to use qualifiers like "left-handed" or "right-handed" when talking about the electromagnetic force.

• The weak interaction is the complementary mixture of the $$SU(2)_L$$ and $$U(1)_Y$$ gauge fields. It mediates an extremely short-range force (which is related to the fact that the $$W$$ and $$Z$$ bosons are very massive), and it does not couple symmetrically to the left- and right-handed matter fields.

• An individual particle with non-zero mass involves both left- and right-handed quantum fields. For example, an electron involves both left- and right-handed components of the fundamental matter fields. These $$L$$ and $$R$$ components of the electron couple symmetrically to electromagnetism but asymmetrically to the weak interaction. Describing the latter explicitly is messy, because the weak interaction is a messy mixture of $$SU(2)_L$$ and $$U(1)_Y$$.

In summary:

• The matter fields couple to the fundamental gauge fields $$SU(2)_L$$ and $$U(1)_Y$$. The left- and right-handed matter fields couple asymmetrically to $$U(1)_Y$$ with a simple (but asymmetric) pattern of hypercharges. The right-handed matter fields don't couple directly to $$SU(2)_L$$ at all.

• The picture is messier when described in terms of particles and in terms of the electromagnetic and weak interactions: the electromagnetic interaction doesn't distinguish between left- and right-handed at all (that part is clean), but the weak interaction treats them asymmetrically in a messy way. Physicists don't like messy, and that's why they regard the $$SU(2)_L$$ and $$U(1)_Y$$ gauge fields as more "fundamental" than the electromagnetic and weak fields.

References:

• "An individual particle with non-zero mass involves both left- and right-handed quantum fields. For example, an electron involves both left- and right-handed components of the fundamental matter fields. These L and R components of the electron couple symmetrically to electromagnetism but asymmetrically to the weak interaction. Describing the latter explicitly is messy, because the weak interaction is a messy mixture of SU(2)L and U(1)Y." So this keeps R handed particles (electrons, neutrino's and quarks) from mutating to another particle? – Rick Jan 1 at 2:15
• @Rick A particle like an electron or a quark can be regarded as a quantum superposition of left- and right-handed versions. Only the left-handed version feels the SU(2) interaction, so when (say) a down-quark in a neutron decays into an up-quark plus an electron plus a neutrino, it's the left-handed term in the superposition that is decaying. The right-handed term remains undecayed, but now we have a quantum superposition of "has decayed" and "has not decayed." As in any quantum measurement, we can only experience one or the other, with specific probabilities. (continued...) – Chiral Anomaly Jan 1 at 19:44
• @Rick As time passes, the odds that we're still experiencing the "not decayed yet" version gradually decrease. What I'm describing here is basically the usual "half-life" idea of an unstable particle. When we do experience the "has decayed" version, it's as though only the left-handed part of the down-quark were present right before the decay. But because quarks (and electrons, etc) have mass, a left-handed term quickly evolves into a superposition of left- and right-handed terms, so the resulting up-quark still ends up with both parts, as does the emitted electron. (continued again...) – Chiral Anomaly Jan 1 at 19:49
• @Rick Here's another way to say it: As in Inertial Observer's answer, the Lagrangian describing the behavior of all these quantum fields have different terms in which different combinations of fields are multiplied together, which is how they "interact." A mass term acts like an "interaction" between the left- and right-handed parts, so even though only the left-handed part interacts directly with the SU(2)L field, the left-handed part also interacts directly with the right-handed part, so they can change into each other. The more mass the particle has, the more quickly that happens. – Chiral Anomaly Jan 1 at 20:02

This answer is by an experimentalist, a particle physisicist:

My questions are this: 1. What do right-handed particles feel?

Here there be particles:

The straight lines are $$K^-$$ particles hitting protons in a hydrogen bubble chamber, the outlined particle is a $$π^+$$ generated with the strong interaction at the vertex. It decays with the weak interaction to a muon, which decays with the weak interaction to a positron. The charges are known because of the small knocked out electron by one of the straight tracks (electromagnetic interaction). The labels, strong, weak, electromagnetic were attached to the interactions because of the observed/measured strength, range,and characteristic time of the different interactions.

The accumulation of thousands of measurements for specific interactions was organized by a mathematical model beautifully, the standard model of particle physics. As a physics theory, it successfully predicts new set ups, thus the way the forces are organized in the model is considered fundamental, and it is described in the other answers based on the theory. BUT one has to understand that it is the data that demands the theory.

So right handed particles feel and behave as the mathematical model successfully describes, having separated for the weak interaction into left handed and right handed the particles with spin. . In the current mathematical model they feel nothing as they are not modeled to interact with the weak interaction. The charged ones have to be given enormous masses in the standard model to explain their non detection.

1. Are there right-handed particles?

As this is a mathematical concept, a label attached to the interacting particles by the well validated standard model, the only answer is "they have not been observed". Thus theories/models have to come up with mathematically sound reasons that they have not been observed. The simplest is to give them a mass so high that our laboratory experiments cannot detect them, and cosmic ray experiments, which have very high energies and started the whole particle physics game, do not have the accuracies needed for detecting rare events in their kilometer large experiments.

So it is an open question, both for theories and experiments.

If not why?

Because in order to keep the mathematical validity of the standard model right handed particles need enormous masses , and such particles have not been observed (yet?).

I want to emphasize that the need of assigning chirality to particles with spin , and thus splitting real ones to right and left handed, comes from the mathematical model. Maybe future mathematical models will not have such a need, naturally.