What are the eigenvalues of the color isospin for gluons and quarks?

In summary, it seems like a basic question and I'm sure many would answer that these are all "spin-1" particles...but that's not their "isospin", right? can someone in the know please straighten things out.
  • #1
rntsai
80
1
seems like a basic question and I'm sure many would answer that these are
all "spin-1" particles...but that's not their "isospin", right? can someone in the
know please straighten things out.
 
Physics news on Phys.org
  • #2
Neither carries isospin.
 
  • #3
They are both massless vector particles, they transform as vectors under rotations.

Thhis spin-1 does not refer to isospin, they have 0 isospin. When we refer to rotations is isospin space (isospin) we always denote this by adding iso. Isoscalar = spin 0 in isospin space (isopsin 0 particle), isovector = spin 1 in isopsin space (isospin 1 particle) etc.
 
  • #4
I have not read all the details, but wikipedia's article on isospin seems quite decent.
 
  • #5
malawi_glenn said:
They are both massless vector particles, they transform as vectors under rotations.

Thhis spin-1 does not refer to isospin, they have 0 isospin. When we refer to rotations is isospin space (isospin) we always denote this by adding iso. Isoscalar = spin 0 in isospin space (isopsin 0 particle), isovector = spin 1 in isopsin space (isospin 1 particle) etc.

So spin-1 doesn't refer to isospin which is what I suspected. It doesn't seem right
that all 8 gluons would have 0 isospin. Wouldn't you expect them to have the same
isospin distribution as any SU(3) octet? Something like the lower right picture in http://en.wikipedia.org/wiki/Isospin
even though that refers to a baryon octet...in the end they both refer to the same
adjoint rep of SU(3)
 
  • #6
isospin are the eigenvalues of the \lambda^3 Gell-Mann matrix, only quarks have isopsin. Isopsin is a concept which relates to the (approximate) same mass of the up- and down-quarks.

The gluons form an octet in SU(3) colour space, the meson octet is SU(3) flavour space.
 
  • #7
malawi_glenn said:
isospin are the eigenvalues of the \lambda^3 Gell-Mann matrix, only quarks have isopsin. Isopsin is a concept which relates to the (approximate) same mass of the up- and down-quarks.

The gluons form an octet in SU(3) colour space, the meson octet is SU(3) flavour space.

It shouldn't matter what space we're in, an SU(3) octet is an SU(3) octet. It's weights
(eigenvalues of certain elements) will follow a well defined combination. These elements
might well have completely different definitions, but that doesn't change the eigenvalues.

Are you saying that because gluons form an octet in SU(3) colour space, they all have isospin
0? As far as I know the only SU(3) involved here is the colour SU(3) of the standard model.
Its weights in the 3 rep give the isospins of quarks; its weights in the 8 rep
should give the isospin of gluons
 
  • #8
isospin has to do with flavour ... SU(3) flavour is an approximate symmetry of the three lightest quarks, used in hadron spectras.

isospin is that you say that the up-quark and the down-quark is the same particle, but with different z-components in isospin space. Also, the strong force, mediated by gluons, is isospin independent, since the gluons couple to the colour charge of the quarks, not their isospin or hypercharge.

You will of course have things like "colour isospin" and "colour hypercharge" since the representations used for SU(3)_colour is the same as for SU(3)_flavour, but we don't speak about this as isospin due the possible confusion of flavour-isospin (which we only call isospin).
 
  • #9
malawi_glenn said:
You will of course have things like "colour isospin" and "colour hypercharge" since the representations used for SU(3)_colour is the same as for SU(3)_flavour, but we don't speak about this as isospin due the possible confusion of flavour-isospin (which we only call isospin).

Things are beginning to clear up. What I was calling "isospin" looks like what you call
"colour isospin". SU(3)_color is the SU(3) in the standard model and the weights of it's
reps will give you "color isospin" and "color hypercharge". Gluons do not have
zero "color isospin"; (actually 2 do, 6 don't,...).

SU(3)_flavour is more of a mystery to me. I don't really know how it fits with the standrard
model; any reference suggestions?
 
  • #10
well in the standard model you only have the SU(2) weak isopsin-symmetry.

The flavour SU(3) symmetry is just used in hadron-physics, and is an approximate symmetry. You should not treat it as a symmetry of the standard model interactions. It has to do with composite systems, hadrons.

You can look in the Patrticle data group booklet, on quark model chapter of the hadrons. Particle data group booklet is an underestimated source for information on every aspect of particle physics, use it :-)
 
  • #11
rntsai said:
Gluons do not have zero "color isospin"; (actually 2 do, 6 don't,...).

I don't think you are using "color isospin" in a proper way. All 8 gluons carry the same quantum numbers, except for color, and even there, there is no unique definition of color. I could replace the red-green-blue basis by one rotated in this space and there would be no observable consequence.

What do you think this "color isospin" is and does? Can you give us an example of what it operates on and what the eigenvalues are?
 
  • #12
that is why we don't use "colour isospin", there is no need for it.
 
  • #13
Vanadium 50 said:
I don't think you are using "color isospin" in a proper way. All 8 gluons carry the same quantum numbers, except for color, and even there, there is no unique definition of color. I could replace the red-green-blue basis by one rotated in this space and there would be no observable consequence.

What do you think this "color isospin" is and does? Can you give us an example of what it operates on and what the eigenvalues are?

I think I do. Here's a list of the eigenvalues (any linear combination of these would also do)

for the 8 rep (gluons)

g^3,g^8

1 ,0
-1 ,0
1/2 ,sqrt(3)/2
-1/2 ,-sqrt(3)/2
1/2 ,-sqrt(3)/2
-1/2 ,sqrt(3)/2
0 ,0
0 ,0

for the 3 rep (quarks)

1/2 ,1/(2 sqrt(3))
-1/2 ,1/(2 sqrt(3))
0 ,-1/(sqrt(3))

colour isospin and hypercharge would be a combination of these
here are the eigenvalues for color hypercharge and color isospin :

8 rep
(Y,I3)=

(-1,-1/2)
(-1, 1/2)
( 1,-1/2)
( 1, 1/2)
( 0, -1)
( 0, 0)
( 0, 1)
( 0, 0)

3 rep
(Y,I3)=
(-2/3,0)
(1/3,-1/2)
(1/3, 1/2)
 
Last edited:

FAQ: What are the eigenvalues of the color isospin for gluons and quarks?

1. What is isospin in particle physics?

In particle physics, isospin is a quantum number that describes the strong nuclear force between subatomic particles. It is similar to the concept of electric charge, but instead describes the interactions between particles that are affected by the strong force.

2. How is isospin related to gluons and photons?

Gluons and photons are both fundamental particles that carry isospin. Gluons carry isospin related to the strong nuclear force, while photons carry isospin related to the electromagnetic force.

3. Can gluons and photons have different isospin values?

Yes, gluons and photons can have different isospin values. Gluons can have isospin values of 0, 1, or -1, while photons have an isospin value of 1.

4. How does isospin affect the behavior of gluons and photons?

Isospin affects the behavior of gluons and photons by determining how they interact with other particles. For example, gluons with different isospin values can interact differently with other particles, leading to different types of nuclear reactions.

5. Is isospin conserved in particle interactions?

Isospin is conserved in most particle interactions, similar to how electric charge is conserved. This means that the total isospin value before and after an interaction remains the same. However, there are some rare exceptions where isospin may not be conserved.

Similar threads

Replies
3
Views
2K
Replies
11
Views
2K
Replies
35
Views
8K
Replies
10
Views
1K
Replies
9
Views
3K
Replies
4
Views
3K
Replies
4
Views
2K
Back
Top