Can particles be weak force charge neutral?

In summary: Theories argue so much about "naturalness" of parameters, but if a particle doesn't start in the potential energy well of another, then if energy is conserved it cannot settle into that well. So the material can't clump. It needs some way to cool, and in this case it can only "cool" via gravitational interactions. Once the universe cools to gravity being weak, it would be very difficult for gravitational interactions to create new massive particles, so the only cooling would be via gravitational radiation, which is probably negligible. So in this scenario, the dark matter would likely remain completely thermally distributed -- settling into potential wells only as much as the thermal distribution would allow.So production at
  • #1
JustinLevy
895
1
can particles be "weak force" charge neutral?

In the standard model we have fermions of various electrical charges, including neutral. In some sense, we can consider right handed electrons as "weak force" neutral, however the mass term kind of "mixes" the left and right handed.

Is there something from representation theory that forbids us from getting a particle that is completely weak force neutral, strong force neutral, and electrically neutral?

While I see people choose representations in a theory to match the known particles, does this also work the other way ... the theory with a particular symmetry dictates for us which representations we _have_ to use for the particles?

I'm curious why dark matter is assumed to be something so mysterious. Is there some reason why we can't just add another particle to the standard mode which is neutral in all charges? Even when people discuss supersymmetric theories, there seems to be an assumption the particles have "weak force" charge.
 
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  • #2


You can add a completely uncharged particle to the model. Now, how do you produce it? And how do you detect it?
 
  • #3


Vanadium 50 said:
You can add a completely uncharged particle to the model. Now, how do you produce it? And how do you detect it?
So nothing constrains the fermion content? We can chose any representation we want? Does the symmetry chosen for the model at least constrain the boson content?

Answering your questions: Well I guess it would only interact gravitationally. So chances of seeing a production in a collider would be negligibly rare, but we already detect dark matter gravitationally.

If it only interacts gravitationally, it wouldn't be able to clump up, and so distributions of dark matter near galaxies I guess could give insight into whether this is possible. Actually, maybe this is already ruled out. Is there evidence that dark matter is not distributed perfectly thermally in the gravitational wells?
 
  • #4


JustinLevy said:
If it only interacts gravitationally, it wouldn't be able to clump up, and so distributions of dark matter near galaxies I guess could give insight into whether this is possible. Actually, maybe this is already ruled out. Is there evidence that dark matter is not distributed perfectly thermally in the gravitational wells?

But if it acts gravitationally, it WILL clump up as there are no scattering events that could create a negative pressure. So it would basically condensate, right?
 
  • #5


JustinLevy said:
We can chose any representation we want?

No, it's in a U(1) singlet, an SU(3) singlet and an SU(2) singlet.
 
  • #6


Hepth said:
But if it acts gravitationally, it WILL clump up as there are no scattering events that could create a negative pressure. So it would basically condensate, right?
I think this conclusion need not be correct. In order to become gravitatioally bound it must not be "hot". If the particles have high energy there is no way how they can be cooled in order to form lumps. I think there is a related discussion with hot and cold dark matter (CDM), but for dark matter in the context of SUSY at least you have a mechanism how it can be produced. Adding neutral matter to the SM w/o doing anything else there is no way to describe its production.
 
  • #7


Hepth said:
But if it acts gravitationally, it WILL clump up as there are no scattering events that could create a negative pressure. So it would basically condensate, right?
Classically, if a particle doesn't start in the potential energy well of another, then if energy is conserved it cannot settle into that well. So the material can't clump. It needs some way to cool, and in this case it can only "cool" via gravitational interactions. Once the universe cools to gravity being weak, it would be very difficult for gravitational interactions to create new massive particles, so the only cooling would be via gravitational radiation, which is probably negligible. So in this scenario, the dark matter would likely remain completely thermally distributed -- settling into potential wells only as much as the thermal distribution would allow.

tom.stoer said:
but for dark matter in the context of SUSY at least you have a mechanism how it can be produced. Adding neutral matter to the SM w/o doing anything else there is no way to describe its production.
Assuming the big bang hypothesis and unification at some energy, shouldn't production via gravitational interactions be just as likely as creation via electromagnetic or strong interactions at that energy scale? So production at the beginning shouldn't really be a problem, right?

Vanadium 50 said:
So nothing constrains the fermion content? We can chose any representation we want?
No, it's in a U(1) singlet, an SU(3) singlet and an SU(2) singlet.
Okay, yes, that was poorly worded. And this follow up will probably be too. My confusion is that theorists argue so much about "naturalness" of parameters, but if we have to choose by hand what representations we add in for matter content ... and purposely neglect others ... how is that not part of the naturalness discussions?

I guess from reading discussions on this board I somehow came to the incorrect conclusions that once the symmetry was chosen, that it somehow dictated what matter fell out. Examples of my confusions: string theorists seem to start with some symmetry and seem to claim it predicts what matter comes out, or another example is Garret's E8 theory and people knowing what matter can or cannot come out (somehow it predicts "mirror matter", and can only get one generation ... why aren't we free to add more matter using any representation of that symmetry we want?).

So my (probably still based in deep misunderstanding) question is: Once a symmetry is chosen, in what manner (if any) does it dictate or restrict what representations we use to include for matter?

So can we really just freely add in new matter if using the standard model symmetry?
 
  • #8


JustinLevy said:
So can we really just freely add in new matter if using the standard model symmetry?

Nearly.

One has to make sure that the theory stay renormalizable by power counting
Spin > 2 seems to be forbidden
Perhaps there are other problems I am not aware of

But besides that you can add what you like if you are able to "hide it" properly.
 
  • #9


"So my (probably still based in deep misunderstanding) question is: Once a symmetry is chosen, in what manner (if any) does it dictate or restrict what representations we use to include for matter?"

Well, force carriers need to be in the adjoint. Also, you need to ensure that your representation satisfies whatever chirality constraints that are appropriate.

But other than that, you either need experiment to tell you which rep to choose, or if you are a model builder, you choose the rep that makes the model simpler or fits together better. That last phrase can be involved. For instance if you are SuSY GUT model building, you need to pay attention to problems like doublet triplet splitting, which may force you to change the representation up a little (so eg the missing partner mechanism in SU(5)).

However, there aren't many other purely mathematical reasons, unless you go beyond Yang Mills theory.
 
  • #10


@Justin: Some of the more complicated models that use very high-dimensional algebras start with (nontrivial) irreps that are very large in the first place. Therefore, sometimes in those sorts of models, people try to fit all of the particle states into just one or two representations of the algebra. So, in su(5), for example, I don't know for sure, but I suspect one quark and one lepton family would somehow live in one 5 of the su(5), which could split down to quarks and leptons (i.e. behave differently) as you broke the su(5) down to the SM gauge algebra. Furthermore, all of the gauge bosons would live in the adjoint (the 24) of su(5). Of course, you still have the whole 3 families thing to deal with, so people build bigger models attempting to reduce the number of representations present even more, at the price of using larger and larger algebras which (usually) need to be broken more and more.

More generally, one could ask why nature chose groups like SU(3) and SU(2), and not SU(1000). I think that somewhere, deep down, there'll be some deep, fundamental reason for this. Furthermore, we seem to live in a universe where particle representations are restricted to the few smallest representations of each of these groups. I think that ultimately, that'll be something fundamental as well. I'm aware of some attempts way back when to argue that you could get small "gauge groups" out of string theory by associating them with the symmetry group of the compactified extra dimension. I'm unaware of the status of compactifying in such a way that we get the SM out of there. At that point, one might wonder if there's a physical reason why you can't have higher-dimensional reps, in much the same way that we can't have higher than spin 2 reps of the Lorentz algebra without breaking this and that. My two cents.
 
  • #11


afaik matter in the adjoint is possible theoretically; and I see no reason why not also in heigher reps
 
  • #12


It is true that string theory tends to favor smaller groups and group representations and it is tempting to speculate that that might be somewhat universal.

Normally that would be seen as a virtue but it can also be a bit of a problem for phenomenology in some ways. Some of the more attractive and realistic groups, like SO(10) or supersymmetric SU(5) will have a host of nice features, however there are some issues (like potential flavor problems, proton decay problems and doublet triplet splitting problems amongst many others) and some of the more attractive 'fixes' can sometimes lead to apparently large representations (for instance a symmetry breaking 'Higgs sector' in the 126 of SO(10)).

Now there are problems with large representations, independant of the friction with string theory. For instance, the fact that they typically lead to large threshold corrections, as well as couplings that run too fast and hence become strongly coupled before the Planck scale (this is undesirable, b/c it reintroduces potentially dangerous nonrenormalizable operators)

Long story short, this is very much an active research area and the full story is as yet not well understood but likely important and fundamental.
 
  • #13


Haelfix said:
"So my (probably still based in deep misunderstanding) question is: Once a symmetry is chosen, in what manner (if any) does it dictate or restrict what representations we use to include for matter?"

At least for gauge theories, the representation content does not change based on if (or in what manner) the symmetry is broken. An obvious example to demonstrate the point would be a quark or a lepton doublet under the Standard Model. This doublet remains the same before and after the symmetry breaking. One (or both) members may become massive as a result of the symmetry breaking, but the transformation properties of the the multiplet under Gauge transformations remains unaltered.

Deciding on the actual content of a Gauge model is a black art. But whatever multiplets of fermions you decide to chose add to your model, you also end up with the same multiplet after symmetry breaking. So your choice of multiplets better be good before you break the symmetry. You are not getting something different afterwards. The typical game played in model building with masses is a different story. Even though the multiplets remain the same, some components may become too massive to be observed (yet) giving the illusion that the multiplet may have changed.
 

1. Can particles be weak force charge neutral?

Yes, particles can be weak force charge neutral. The weak force is one of the four fundamental forces of nature and it acts on particles that have electric charge, such as electrons and protons. However, there are also particles that are neutral to the weak force, such as neutrinos and the Higgs boson.

2. What does it mean to be weak force charge neutral?

To be weak force charge neutral means that a particle does not interact with the weak force, and therefore does not have a weak charge. This is similar to how a particle can be electrically neutral and not interact with the electromagnetic force.

3. How is weak force charge neutrality determined?

Weak force charge neutrality is determined by measuring a particle's interaction with the weak force. If a particle does not experience any weak interactions, it is considered to be weak force charge neutral.

4. Are all particles weak force charge neutral?

No, not all particles are weak force charge neutral. As mentioned before, particles that have electric charge, such as electrons and protons, also have a weak charge. Additionally, some particles, like the W and Z bosons, are not neutral to the weak force and play a crucial role in its interactions.

5. What are the implications of a particle being weak force charge neutral?

The implications of a particle being weak force charge neutral depend on its role in interactions. For example, neutrinos, which are charge neutral to the weak force, are able to pass through matter without interacting, making them difficult to detect. On the other hand, particles with a weak charge, like the W and Z bosons, play a crucial role in the weak force's mechanism of particle interactions.

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