I How Many Different Quarks Are There in Each Generation?

[friend]

Quarks carry one of three possible color charges. (Antiquarks carry them with opposite sign, usually called "antigreen" etc).

Gluons, roughly speaking, carry a pair of color charges, one positive and one negative: for example, "green+antired".

A "green" quark can emit any "green+anti<COLOR>" gluon, changing its color charge from "green" to "<COLOR>".
A "green" quark can absorb any "<COLOR>+antigreen" gluon, changing its color charge from "green" to "<COLOR>".
In both cases, balance of charges is conserved.

https://en.wikipedia.org/wiki/Gluon#Eight_gluon_colors

Your post indicates that gluons carry two colors (e.g. You wrote, "green+anti<COLOR>" gluon, changing its color charge from "green" to "<COLOR>"). But the link to the gluon table shows that each gluon is a superposition of multiple color states (e.g.

). So I'm wondering how these combination color states change the color charge of a quark. Perhaps you were oversimplifying. Thanks again.

 

[Orodruin]

What you have given here is a possible linearly independent basis for the gluon colour states. That does not mean gluons can only exist in those states - as little as giving the possible spin states of a spin 1/2 fermion as $|+\rangle$ and $|-\rangle$ in the $S_z$ basis means that these are the only possible spin states.

 

[nikkkom]

https://en.wikipedia.org/wiki/Gluon#Eight_gluon_colors

Your post indicates that gluons carry two colors (e.g. You wrote, "green+anti<COLOR>" gluon, changing its color charge from "green" to "<COLOR>"). But the link to the gluon table shows that each gluon is a superposition of multiple color states (e.g.

). So I'm wondering how these combination color states change the color charge of a quark. Perhaps you were oversimplifying. Thanks again.

You can change the basis so that one of "new" gluons is (

+ i *

) / sqrt(2), and thus simply "red+antiblue".

But there is simply no basis where *all* eight gluons have a simple, "color+anticolor" form.

 

[friend]

So I'm getting the impression that at the QCD level, everything is described as a superposition of possibilities because nothing is directly measurable at that scale. Is this right?

 

[nikkkom]

All quantum field theories are like that.

 

[friend]

All quantum field theories are like that.

Do you mean as opposed to quantum mechanics where particles have wave functions and observables?

 

[nikkkom]

Quantum mechanics is a simpler theory. For example, it does not deal with creation/annihilation of particles.

 

[friend]

But there is simply no basis where *all* eight gluons have a simple, "color+anticolor" form.

But does each gluon convert the color of one quark? Or if a gluon is a superposition like,

, does it convert a quark that is also in a superposition of states. Then what is that superposition of quark states? Thanks.

 

[nikkkom]

But does each gluon convert the color of one quark?

That's a simplification, suitable when you are explaining QCD to a layman.

To get quantitatively precise results, you need to consider _all_ possible gluon emissions, with all permitted colors. And then take a weighted sum (integrate) over all these possibilities.

When you go that deep, you no longer need to have a simple intuitive picture, with "color-anticolor" gluons - they don't make your life any easier.

 

[friend]

That's a simplification, suitable when you are explaining QCD to a layman.

To get quantitatively precise results, you need to consider _all_ possible gluon emissions, with all permitted colors. And then take a weighted sum (integrate) over all these possibilities.

Yes, you seem to be arguing for a superposition of possible states in order to calculate numbers. But at the heart of each member of the superposition isn't there something that we can describe that is in superposition with other events we can describe? Isn't that what is meant be each interaction in the path integral. Electrons and positrons interact with photons is the basic interaction of the how these propagate. And then we add in other more complicated iterations of this. Likewise, in QCD isn't it the quarks interacting with gluons that we take as the basic interaction before considering superpositions? If so, then isn't there a list of which gluons interact with which quarks without complicating the question with superpositions (that would come after we define the basic interactions, right)?

 

[Orodruin]

Of course there is, but talking about them as rgb makes no real sense apart for the purposes of a popular discussion. Physicists do not go around talking about red, green and blue quarks. We use the appropriate mathematical framework to compute cross sections and decay rates.

 

[friend]

Of course there is, but talking about them as rgb makes no real sense apart for the purposes of a popular discussion. Physicists do not go around talking about red, green and blue quarks. We use the appropriate mathematical framework to compute cross sections and decay rates.

It seems to me that if you go around talking about electrons, positrons, and photons, before talking about propagation in the EM field, then for the same reason you should be just as able to talk about quarks and gluons. Are electrons and positron just for popular discussion?

 

[Orodruin]

It seems to me that if you go around talking about electrons, positrons, and photons, before talking about propagation in the EM field, then for the same reason you should be just as able to talk about quarks and gluons. Are electrons and positron just for popular discussion?

How did you get that from what I said?

 

[friend]

How did you get that from what I said?

It sounds like we are avoiding talking about the ontology of unobservables, again, because quarks and gluons are not directly observable, though electrons and positrons are observable. Tell me, do we have just as much trouble talking about the properties of W^-, W⁺, and Z⁰ boson? For those aren't directly observable either as I recall, since their half-life is 3*10^-25s.

 

[Orodruin]

If you read what I said instead of what you wanted to read I think you would learn more. You have not addressed what I asked you in the slightest. I am done with this thread.

 

[friend]

I'm sorry, but it's frustrating to hear that quarks have certain properties on the one hand, and then hear that they don't on the other.

 

[nikkkom]

SU(3) gauge symmetry of quarks says that you can look at them as having r,g,b charges; _and also_, you can look at them as having charges in any other valid basis of "color space".

Same goes for gluons.

For quarks, "r,g,b basis" looks easy and natural.

Gluons don't have a "nice looking" basis. Sorry. Complain to the gods of group theory.

 

[friend]

SU(3) gauge symmetry of quarks says that you can look at them as having r,g,b charges; _and also_, you can look at them as having charges in any other valid basis of "color space".

Same goes for gluons.

For quarks, "r,g,b basis" looks easy and natural.

Gluons don't have a "nice looking" basis. Sorry. Complain to the gods of group theory.

I appreciate your efforts. So I'm looking for how gluons interact with quarks. I've seen a basis showing a combination of color and anticolor for each gluon. And I'm trying to visualize which gluons interact with which quarks. I've been told that a quark of a particular color can change that color by emitting a gluon. And likewise they can change their color by absorbing a gluon. But the labels I've seen so far on the gluons suggest that they interact with quarks of a certain color. So instead of every gluon interacting with every quark, the labeling suggest that there are restrictions on the kinds of interaction. Is there a simple list or table stating, for example, that this gluon interacts with these quarks an no others, etc? Thanks.

 

[nikkkom]

I appreciate your efforts. So I'm looking for how gluons interact with quarks. I've seen a basis showing a combination of color and anticolor for each gluon. And I'm trying to visualize which gluons interact with which quarks. I've been told that a quark of a particular color can change that color by emitting a gluon.

This is a _layman_ description. Because layman wouldn't understand gauge invariance.

Technically speaking, there are no "quarks with a particular color". Color's value is not a gauge-invariant concept: gauge invariance, by definition, is the freedom to arbitrarily change quark and gluon field values (by multiplying them by suitable 3x3 complex matrix), this can be done _locally_ (the matrix can vary from point to point!), and this change will not be physically observable.

IOW: you can repaint any quark however you want, including any complex superposition of colors (as long as they add up to 1).

Since there are no "quarks with a particular color", you don't have to limit yourself to imagining only quarks with a particular color, and to gluons with only a pair of color-anticolor. Color superpositions are _fine too_.

 

[friend]

IOW: you can repaint any quark however you want, including any complex superposition of colors (as long as they add up to 1).

OK I can accept that. It's like expressing a wave function in various basis but the operator math is still the same.

But still, somewhere in the math they came up with a specific number of quarks and a specific number of gluons that transcends color labels. Does this math also specify the number of ways these gluons interact with these quarks? Does every gluon interact with every quark? Or, perhaps, does each gluon only interact with two quarks?

 

[friend]

Does every gluon interact with every quark?

I think not. (That was probably a stupid question.) For if that were the case, then it would be impossible to enumerate various kinds of gluons. They would be indistinguishable. In fact, aren't the gluons specifically distinguished from each other by the fact that they interact with quarks differently?