# Gluons and combinations

1. Jan 14, 2007

### JPC

hey , just wondering about gluons :

red - anti red
red - anti blue
red - anti green
blue - anti red
blue - anti blue
blue - anti green
green - anti red
green - anti blue
green - anti green

Our common sense tells us theres 9 , but in reality theres 8, how come ?

Is it that only 8 can exisits at the same time or something like that ?

2. Jan 14, 2007

### marlon

Good question which i answered https://www.physicsforums.com/blogs/viewblog.php?entry=131&userid=13790 [Broken]. I suggest you read the PHYSICAL EXPLANATION and skip the group theory stuff.

regards
marlon

Last edited by a moderator: May 2, 2017
3. Jan 14, 2007

### JPC

whoo still a bit confusing, but now i have a clearer idea

but what doesnt seem logic, is that if u say theres 8 , u should be able to give a list of the 8. The lists changes all the time ?

4. Jan 14, 2007

### CarlB

It's a matter of counting degrees of freedom. "Linear superposition" implies that you can describe those degrees of freedom in a bunch of different ways.

There is one less degree of freedom than the natural way of describing the particles, so one of them must not exist. But you have a fairly wide choice of which one it is.

I have a suspicion that there is a more natural way of describing the gluons that doesn't end up with the difference in the number of natural particles. The reason for putting things into irreducible representations is because if you didn't so reduce them, you'd end up with more than one undetermined parameter anyway. Hence the search for an irrep that unifies the particles. So the weird situation in the gluons could be because there is an underlying reality that is related to all 9 gluon concepts, it's just that the group theory has two degrees of freedom. One of the degrrees of freedom covers the 8 gluons, the second degree of freedom covers the "scalar" left over.

Last edited: Jan 14, 2007
5. Jan 14, 2007

### Haelfix

The fact that you can describe 8 gluons in different but equivalent ways arises b/c we are dealing with a nonbroken gauge symmetry (a redundancy of description). Indeed it was somewhat embarrasing to people in the early days, b/c all this group theory seemed to put some constraints on a system, but not specify it exactly or uniquely.

That changed when people realized it was ultimately just the same physics and had no experimental importance. So the choice of labeling is just a manmade choice of how you choose your representation basis, so typically we just pick the most calculationally easy one and go with that. Over time, the coloring convention became standard, and thats how people do it.

6. Jan 15, 2007

### humanino

Let me just add that, if the "scalar" ("white", "color singlet") gluon existed, it would NOT be confined. As Zee put it, this scalar gluon would couple to hadronic matter uniformly, creating an attractive force proportional to (approximately) mass, thus giving rise to a gravitational-like interaction.

This of course cannot work to unify gravity in the SM : for one thing, the graviton is spin-2. There are many other caveats.

7. Jan 15, 2007

### mjsd

Since this discussion reminds me of my earlier post about doublet, singlet and how things are juggled et al, let me gate-crash this discussion. Sorry if I say something stupid or wrong.

Marlon, reading your previous thread on Why 8 gluons?, there isn't seem to be any real explanations on why there are 8 except it is a group theory thing. You then went on explaining what is a color singlet and I guess you are trying to say that there are really only 8 independent ways in juggling colored quarks via SU(3) transformation (just like in 3D rotation you have 3 different axes to choose from). Hence 8 gluons effectively. Anyway, that's just elaborating the group theory argument with examples, not explaining why 8 in the first place. CarlB mentioned degrees of freedom....again different way of saying the same thing.

I guess to put it simply, there are 8 gluons, because we make it so (with good reasons of course, like agreeing with experiments). We choose the SU(3) gauge group as an axiom because observations are hinting that quarks transform very much like the symmetry group SU(3), and it turned out that SU(3) has 8 generators only. So there is ought to be 8 gluons only.

JPC: if you still can't understand why there is only 8 when it is "apparently 9". Try looking at this example (no group theory required)
Think about the symmetries of an equilateral triangle (label all corners uniquely so you can see which transformations are equivalent to which, eg. rotation by 120 deg clockwise is equivalent to rotation by 240 deg anti-clockwise). If you just blindly write down all symmetries you can think of, there are infinitely many of them! but many are actually equivalent. In fact there are only 6 independent ways (including the identity the "do nothing" symmetry) NB: I can choose any set of 6 independent ways from the infinitely many.
eg. {do-nothing, rotate by 120 anti-clockwise, rotate by 240 anti-clockwise, reflection through vertical, reflection through vertical then rotate by 120 anti-clockwise, reflection through vertical then rotate by 240 anti-clockwise}

8. Jan 15, 2007

### Severian

The symmetry that QCD is based on is basically a symmetry in relabelling the colors red, green and blue. (More exactly, if you consider red green and blue as directions in the color space, QCD is symmetric under rotations.)

Now, obviously swapping the colors will change all of your proposed 'gluon' you list. So swapping green <-> blue will change "blue - anti red" into "green - anti red" for example.

However, there is one (and only one) combination of the states you list that maps onto itself under any swap of colors, namely the sum of "blue - anti blue", "red - anti red", and "green - anti green" (usually written $$\frac{1}{\sqrt{3}} ( B \bar B + R \bar R + G \bar G)$$).

Now, since we want the physics to be symmetric under 'swapping colors' then every gluon that is related to another gluon by a swap must have the same couplings to quarks as its 'swapped friends'. So eight of the gluons must have the same coupling (the strong coupling).

But the last one - the combination I wrote down above - maps onto itself, so it can have any coupling it likes and the physics will still be symmetric under 'color swaps'. I can, in principle, give it an arbitrary coupling to quarks.

However, as humanino pointed out (and Zee before him!) this would look like a new force which we don't see. And in QCD, this extra coupling is actually set to zero (technically QCD is based on the group SU(3) rather than U(3)).

Edit: cross-posted with mjsd there

9. Jan 15, 2007

I have a question. In your answer you imply (with the if) that a "color singlet gluon" does not exist--but do not these papers show that is does exist, and that its existence may be linked to coupling of matter and antimatter (for example to help explain how a quark + antiquark form union in a pion)
http://zhang.bioinformatics.ku.edu/papers/1999_2.pdf [Broken]
http://xxx.lanl.gov/PS_cache/hep-ex/pdf/9809/9809016.pdf
http://il.arxiv.org/PS_cache/hep-ph/pdf/9807/9807314.pdf

Last edited by a moderator: May 2, 2017
10. Jan 16, 2007

### humanino

Indeed, I can understand that you are confused ! Actually, in those papers, they are refering to "gluon clusters", or "gluon ladders" correponding to the diagram at the following link :

I will try to keep it simple, so I will be schematic (problem is that I am not familiar with ultarelativistic diffration, which is what you are refering in those papers). There are objects called "Pomerons" which appear when you scatter hadrons at very high energy. At first, Pomerons are just pseudo-particles which you "find in your data" when you describe them with models using only very general principles (principles such as "all functions are analytical", "causality", "conservation of probability"... This leads to Regge phenomenology of hadronic scattering). The very peculiar thing about Pomerons is that they carry the quantum numbers of the vacuum, that is no charge at all (including no color charge, color singlets, or "scalars"). Then latter, they were derived from QCD as gluons ladders (and then called "perturbative" or "hard" Pomerons), but there are unresolved technical issues and this interpretation is still speculative.

See for instance : http://en.wikipedia.org/wiki/Pomeron
For an excellent technical introduction, see An introduction to Pomerons

What we were discussing here is more fundamental. It is about group representation theory. Of course, those questions are linked, but you can read in the previous paper that it is in a very non-trivial manner !

This I do not understand. Why do you make this statement ?

Image credit : Probing the pomeron

11. Jan 16, 2007

### marlon

Err, seems to me you are saying the exact same thing. Besides, the stuff on degrees of freedom directly comes from group theory ! I really don't see what other explanation you can give us ?

Besides, i also CLEARLY stated why only 8 and NOT 9. I gave the physical interpretation as well.

marlon

12. Jan 16, 2007

### mjsd

We are all saying the same thing alright. We probably just have a slightly different definition as to what constitutes a real explanation. Mine is of course no better or worse than yours.

13. Jan 16, 2007

### JPC

Hum

i didnts get all your explanations (reason : lack of quantic knowledge + vocab)
but hopefully mjsd helped me out with a figurative explanation

But, hey , thank you all for your explanations

14. Jan 16, 2007

First, thank you for your information on pomerons.

The statement you mention derived from this previous comment you made:
Let me just add that, if the "scalar" ("white", "color singlet") gluon existed, it would NOT be confined. As Zee put it, this scalar gluon would couple to hadronic matter uniformly, creating an attractive force proportional to (approximately) mass, thus giving rise to a gravitational-like interaction.

Some type of gluon mechanism has to hold together the quark+antiquark in a pion--I was only thinking perhaps this is the role of the "color singlet gluon" ? I have no idea the mechanism of how quark+antiquark form pion.

15. Jan 17, 2007

### humanino

We understand fairly well heavy quark confinement. Heavy quarks are almost classical objects, their "quantumness" is sufficiently well behaved so that most classical pictures do not fail grossly. For instance in :
Quark-antiquark potential with retardation and radiative contributions and the heavy quarkonium mass spectra
D. Ebert, R. N. Faustov, and V. O. Galkin
(appeared also in Phys. Rev. D 62, 034014 (2000) )
you can see how succesfully we can model heavy quark bound states.

The case of the pion however is much more difficult. The problem of confinement is not solved by a linearly rising potential (which would be trivial, and we know that it does not keep rising), it is the problem of binding very light quarks in structures whose spatial extent is much less than the Compton wavelength. One needs to employ heavy artillery here, typically Dyson-Schwinger equations. The subject is vast. If you want to see what sort of things are done, take a look for instance at :
Mesons as Bound States of Confined Quarks: Zero and Finite Temperature
P. Maris, P. C. Tandy

16. Jan 17, 2007

### CarlB

While I believe this to be the case, I thought that the standard belief is that the quark potential energy rises linearly with distance and that this explains confinement. I've seen the graphs from the lattice QCD people showing this comes out in simulation, for example. Can you explain further?

I've found papers on arXiv which approximate the linear potential energy with a very flat / straight Yukawa potential, so that is one explanation. For example:
http://arxiv.org/abs/nucl-th/0610001 [/edit]

Do you recall the old theory that supposed that the bare quarks were heavier than the nucleons, but that their binding energy was comparable to their rest masses?

Last edited: Jan 17, 2007
17. Jan 17, 2007

### humanino

In lattice calculations, you take two static quarks and calculate the gluon field created by these sources. In the real world, when one "tries to take two quarks appart", at some point the glue tube breaks into meson/antimeson pair in the real world. First, let me remind two scales :

Size of hardons : 1 fm
Compton wavelength of light quarks : 40 fm

Now at which scale does the string break ? At first, one can evaluate it from the static quark/antiquark potential. If you take the string breaking to occur when the potential energy exceeds twice the pion mass, you'll get something around 0.5 fm ! I also wanted to quote lattice simulations of the string breaking, but they must use heavy quarks. Even when you overcome difficulties with light quarks, they'll give you something around 1.2 fm (see for instance Observation of String Breaking in QCD). In any case, we are very far from the quark Compton wavelength. The conclusion one can draw from this is that confinement must be quantum mechanical. We cannot use classical pictures.

This argument might appear weak. There are more sound ones. Very convining to me is the following paper :
Instantons and baryon dynamics
Once one-gluon exchange and linear "confining" potential are smoothed out, u and d correlations in the nucleon are still calculable by the instanton contribution only. Instantons are intrinsically quantum mechanical. Although they are calculated as classical solitons in the euclidean gluon field, they correspond to quatum tunneling in the minkovskian gluon field (like a WKB approximation).

Yet other arguments exist. I will not try to sum up agruments from "Is the proton really bound ?" at page 11 of QCD Phenomenology. The section is about one page long.
I have long been fascinated by Gribov's views on physics in general, and on quark confinement in particular. It is actually in his work that I first read that the problem of confinement is with light quarks.
Gribov program of understanding confinement
QCD at large and short distances (annotated version)