Thank you for your reply! I am still a bit confused. They are singlets, because they are constructed like that in the Lagrangian. My questions was more like, how do we know they don't interact (i.e. how do we know they are not needed in the SM)? Is this based on experimental data? Or does the theory somehow enforces them to be singlets (even without any experiment). I am a bit confused as in the Particle Physics book that I read, it is just said that right handed neutrino don't interact and hence they are singlets under SU(2). But I am not sure I know how do we know this.The reason there are no right-handed neutrinos in the standard model is that they are not needed and that they would not interact through any of the SM interactions, since they would be SM singlets.
There are several models of neutrino masses that do include right-handed neutrinos.
If they interacted they would not be right-handed neutrinos. They would be something else. A right-handed neutrino by definition is a standard model singlet.My questions was more like, how do we know they don't interact (i.e. how do we know they are not needed in the SM)?
My questions was more like, how do we know they don't interact (i.e. how do we know they are not needed in the SM)? Is this based on experimental data? ...
Right-handed fermions other than neutrinos interact via neutral currents due to their hypercharge and the admixture of hypercharge gauge boson in the Z.The weak interaction only acts on left-handed particles.
I understand this. My question is, is this fact known from experiments, or it follows from the theory directly?The weak interaction only acts on left-handed particles. All other particles have electric and/or color charge, so they can still interact via these interactions, but right-handed neutrinos have only gravity acting on then.
Oh I see! However I remember I read or heard several times a statement saying that any term that doesn't violate a symmetry/conservation law should be added to the Lagrangian. And if it doesn't appear in the real world we should find out why. For example the strong CP violating phase is part of the Lagrangian, but we try to explain why it is zero or very small (using axions, for example). We don't just define it equal to zero. I just feel that in the case of neutrinos the things are actually the other way around: We just don't add the term to the Lagrangian and assume it doesn't exist (i.e. we define the right handed neutrinos as singlets under SU(2)) instead of adding it to the Lagrangian (as doublets, the same as left handed neutrinos) and explaining why the nature ends up making them a singlet. Is there any (testable) model explaining why the right handed neutrinos are singlets under SU(2) (something similar to axions in the case of CP)? Thank you!Maybe the simplest way to answer this is to say that things are not added to the standard model if there is no evidence that they exist. I think your question, "How do we know they are not needed?", is asking it the wrong way around. A better question is, "Is there any evidence that they exist?", and I think the answer is no.
This is true, but it should be based on the actual field content in your theory. You should not add fields you do not need. In your example with the strong CP-phase, all of the fields that would be needed for that term are already in your theory and that term is a priori allowed, so why is it zero (or close to it)? The case of right-handed neutrinos is fundamentally different, we have no evidence of the existence of right-handed neutrinos so there is no a priori need to add it to the theory. If you did add it, you typically would also add all interactions including it that would be allowed by symmetry. Doing so leads to adding a Dirac mass term for neutrinos as well as a Majorana mass term for the right-handed neutrinos. This is part of the theoretical motivation behind the type-I seesaw mechanism: You add a right-handed neutrino to make neutrinos massive by creating a Yukawa coupling to the left-handed neutrinos just like for other fermions. The resulting Dirac mass term will be of the electroweak scale. However, due to right-handed neutrinos being standard model singlets they would also allow a right-right Majorana mass term. The scale of this term is in no way connected to the electroweak scale and if it is sufficiently large, this suppresses the masses of the left-handed neutrinos.Oh I see! However I remember I read or heard several times a statement saying that any term that doesn't violate a symmetry/conservation law should be added to the Lagrangian.
I see. So if a term is implied by the fields that you already have you must add it, but you don't need to add fields if they are not observed in nature. Thank you! So I guess I am still curious: do we know why the right handed particles are singlets under SU(2) (if I remember well, even in the seesaw mechanism they are added as singlets)? Like is there a theory from which this this emerges naturally, or we just defined it that way based on experimental evidence, without knowing why? I guess you can still argue that the field simply doesn't exist so asking why it doesn't exist is like coming up with any new field and asking why it doesn't exist (I agree it wouldn't make sense). But at the same time I find it a bit weird that the left and right handed parts of the same particles behave so differently, so I assume in this case it would make sense to ask why?This is true, but it should be based on the actual field content in your theory. You should not add fields you do not need. In your example with the strong CP-phase, all of the fields that would be needed for that term are already in your theory and that term is a priori allowed, so why is it zero (or close to it)? The case of right-handed neutrinos is fundamentally different, we have no evidence of the existence of right-handed neutrinos so there is no a priori need to add it to the theory. If you did add it, you typically would also add all interactions including it that would be allowed by symmetry. Doing so leads to adding a Dirac mass term for neutrinos as well as a Majorana mass term for the right-handed neutrinos. This is part of the theoretical motivation behind the type-I seesaw mechanism: You add a right-handed neutrino to make neutrinos massive by creating a Yukawa coupling to the left-handed neutrinos just like for other fermions. The resulting Dirac mass term will be of the electroweak scale. However, due to right-handed neutrinos being standard model singlets they would also allow a right-right Majorana mass term. The scale of this term is in no way connected to the electroweak scale and if it is sufficiently large, this suppresses the masses of the left-handed neutrinos.
If they were not then they would not be right-handed neutrinos. A right-handed neutrino by definition is a SM singlet. It is necessary to allow the Yukawa coupling to the right-handed neutrinos.So I guess I am still curious: do we know why the right handed particles are singlets under SU(2) (if I remember well, even in the seesaw mechanism they are added as singlets)?
It is known from experiment, the "Wu experiment".I understand this. My question is, is this fact known from experiments, or it follows from the theory directly?