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:


*

*What do right-handed particles feel?

*Are there right-handed particles?  If not why?
 A: 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 do exist in the full Lagrangian, do not contain such a term. Hence they do not feel the weak force.
A: 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.


*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.
