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all "spin-1" particles...but that's not their "isospin", right? can someone in the

know please straighten things out.

- Thread starter rntsai
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- #1

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all "spin-1" particles...but that's not their "isospin", right? can someone in the

know please straighten things out.

- #2

Vanadium 50

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Neither carries isospin.

- #3

malawi_glenn

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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

- #5

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So spin-1

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.

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

malawi_glenn

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

- #7

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It shouldn't matter what space we're in, an SU(3) octet is an SU(3) octet. It's weights

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

(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

should give the isospin of gluons

- #8

malawi_glenn

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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

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Things are beginning to clear up. What I was calling "isospin" looks like what you callYou 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).

"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

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

malawi_glenn

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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

Vanadium 50

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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.Gluons donothave zero "color isospin"; (actually 2 do, 6 don't,...).

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?

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malawi_glenn

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that is why we don't use "colour isospin", there is no need for it.

- #13

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

for the

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

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 :

(Y,I3)=

(-1,-1/2)

(-1, 1/2)

( 1,-1/2)

( 1, 1/2)

( 0, -1)

( 0, 0)

( 0, 1)

( 0, 0)

(Y,I3)=

(-2/3,0)

(1/3,-1/2)

(1/3, 1/2)

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