I How Many Different Quarks Are There in Each Generation?

[friend]

I understand there are three generations of quarks, which have the same charge but different mass. My question is, in a single generation how many different kinds of quarks are there. For example, in the first generation there are the up quark and down quark, each of which has an antiquark. So far, this is four different quarks in the first generation. Are there other properties in the first generation of quarks that would account for more first generation quarks? Thanks.

 

[dukwon]

Sure, you could also count the 3 different values of colour charge.

 

[friend]

Sure, you could also count the 3 different values of colour charge.

So how many different first generation quarks does that give us?

As I understand it, quarks interact with the electromagnetic force and with the Weak nuclear force. Does that mean each quark has an electromagnetic charge and Weak nuclear charge numbers?

 

[mfb]

So how many different first generation quarks does that give us?

It depends on how you want to count them. 2, 4, 6 and 12 are all somewhat justifiable answers.

As I understand it, quarks interact with the electromagnetic force and with the Weak nuclear force. Does that mean each quark has an electromagnetic charge and Weak nuclear charge numbers?

Yes, and you can look them up.

 

[friend]

Yes, and you can look them up.

I've tried to look it up, but those articles don't distinguish very well the case of a single generation.

 

[friend]

I find on Wikipedia,

The black dots seem to be for gluons. The colored triagles seem to be for quarks. Is this just for a single generation of quarks?

The diagram seems to indicate that the upsidedown triangles represent the anticolor charge of the rightsideup charge. Is this correct? If so, does the diagram indicate that whenever the color charge is reversed there is also a reversal of electric charge? Thanks.

 

[mathman]

There are six basic different quarks: down, up, strange, charm, bottom, and top. Each has an antiquark. Also each comes in three colors (red, green, blue - labels which have nothing to do with color as such). You can count them anyway you want.

Color charge and actual charge are not connected. up, charm, and top have charge +2/3, down, strange, and bottom have charge -1/3. All quarks may come in any color.

 

[friend]

Each has an antiquark. Also each comes in three colors (red, green, blue ).

OK Thanks. So I take it that the diagram in my previous post was for one particular quark, say the up quark, for example. So if I'm understanding you correctly, this means there are six possible ways to assign electric charge and color charge to the up quark. (+, - electric charge times red, green, blue, color charge). Is there an anti color charge? The wikipedia site I link to says there is an anti-red, anti-green, and anti-blue color charge as well. Is this right? Or is anti-red just the red charge with the opposite electric charge? I'm still a little confused.

Reading the linked article, I read, "Antiquarks have the opposite charge to their corresponding quarks; up-type antiquarks have charges of − 2⁄3 e and down-type antiquarks have charges of + 1⁄3 e". This tells me that antiquarks differ from quarks by electric charge, e. I also read, "Every quark carries a color, while every antiquark carries an anticolor." which tells me that there is such a thing as anticolor, but that property changes with electric charge so that there are still only six possible ways to assign electric and color charge to, say, an up quark. Could someone please confirm this?

Here's a question that may answer: do mesons have electrical charge. For mesons have a quark and antiquark. If this involve anticolor but not anti-electric charge, then perhaps that answers my question.

Thanks.

 

[jtbell]

do mesons have electrical charge. For mesons have a quark and antiquark.

Some do: $\pi^+ = u \bar d$. Some don't: $J/\Psi = c \bar c$.

 

[friend]

Some do: $\pi^+ = u \bar d$. Some don't: $J/\Psi = c \bar c$.

If there were no mesons with electrical charge, then I'd say that anticolor is the electrical negation of the color charge. But if there are mesons with electrical charge, I don't know that if I can say that an anticolor is the electrical negation of a color charge. Any help out there?

 

[friend]

So I think there is a correction for first generation quarks. They have either up or down flavor, +2/3e or -1/3e, and red, green, or blue color charge. So that means there are 2X2X3=12 different first generation quarks, right?

 

[Orodruin]

up or down flavor, +2/3e or -1/3e

These are equivalent based on the Gell-Mann-Nishijima formula $Q = Y/2 + T_3$. There is no up quark with charge -1/3.

If you want to count degrees of freedom (and the argument can be made for this - I would therefore add 24 to the list of @mfb), then there are:

• Quark-antiquark (2)
• Spin/handedness (2)
• Colour (3)
• Up/down type (2)

which in total would make 24 per generation.

 

[friend]

So maybe we can construct a table for first generation quarks only. Now that up or down is correlated with electric charge and color charge is correlated to electric charge, how many first generation quarks are there with just these quantum numbers?

 

[mathman]

So I think there is a correction for first generation quarks. They have either up or down flavor, +2/3e or -1/3e, and red, green, or blue color charge. So that means there are 2X2X3=12 different first generation quarks, right?

No! The up quark has a +2/3 charge and the down quark has a -1/3 charge. Both come in all 3 colors, so the total is 6.. If you add in the first generation anti-quarks, then you can get 12.

 

[Orodruin]

No! The up quark has a +2/3 charge and the down quark has a -1/3 charge. Both come in all 3 colors, so the total is 6.. If you add in the first generation anti-quarks, then you can get 12.

From a theoretical point of view, I would also count left- and right-handed separately (see #12). After all, the left- and right-handed components are parts of different SU(2) representations. There are many ways to count here, but for me the more natural one is to count degrees of freedom, of which there are 24 per generation. Before electroweak symmetry breaking you have

• The SU(2) doublet and SU(3) triplet $Q_L$. (6 Weyl fermions = 12 degrees of freedom)
• The SU(2) singlet and SU(3) triplets $u_R$ and $d_R$. (6 Weyl fermions = 12 degrees of freedom)

Therefore, the total number of degrees of freedom among the quarks are 24.

 

[friend]

I understand that the quarks interact with the Weak force particles. Are all the quarks effected equally by all the Weak force particle, W⁺, W^-, and Z⁰? Or does each Weak force particle interact differently with each quark? Thanks again for your help.

 

[Orodruin]

No. The weak force treats left- and right-handed particles differently. The couplings to the Z also depend on the charge of the particle and whether it is up or down type. The Ws couple (left-handed) up and down type quarks with a strength proportional to the elements of the CKM matrix.

 

[friend]

Do quarks rotate into each other like neutrinos?

Do quarks decay into only Weak particles, say, a W^- and Z⁰?

 

[Orodruin]

Are you referring to neutrino oscillations or neutrino mixing? They are related but different things. Neutrino mixing (or more accurately, lepton mixing) is necessary for neutrino oscillations to occur and quarks mix in much the same way. However, the big difference is that typically the neutrino mass states are quite degenerate in mass and so you will typically produce a linear combination of them that will continue to have coherence over long distances. For quarks however, the large mass differences means that the different mass states will lose coherence practically immediately, leading to no quark flavour oscillations (as you can tell which mass state has been produced by looking at the kinematics of the process).

What does happen in the baryon sector due to CKM mixing is neutral meson oscillations, for example between $K_0$ (quark content $d\bar s$) and $\bar K_0$ ($s\bar d$).

 

[friend]

For quarks however, the large mass differences means that the different mass states will lose coherence practically immediately, leading to no quark flavour oscillations (as you can tell which mass state has been produced by looking at the kinematics of the process.

OK. So I'm hearing that quarks can oscillate a little between mass generations (flavor). Do they oscillate between up and down type, or between color charge or electric charge? Thanks again.

 

[Orodruin]

OK. So I'm hearing that quarks can oscillate a little between mass generations (flavor).

I do not understand how you got that from what I said. What you have is neutral meson oscillations.

 

[friend]

I do not understand how you got that from what I said. What you have is neutral meson oscillations.

I may have misunderstood your reply. But the question still remains. Do quarks oscillate between up and down type, or between color charge or electric charge? Perhaps there are W⁺ or W^- bosons that fluctuate into existence long enough to change a quarks electric charge, for example. And perhaps there is a similar mechanism to change an up quark to a down quark or a red quark into a blue quark for a moment before it changes back.

 

[Orodruin]

Do quarks oscillate between up and down type, or between color charge or electric charge? Perhaps there are W+ or W- bosons that fluctuate into existence long enough to change a quarks electric charge, for example.

This would violate charge conservation!

a red quark into a blue quark for a moment before it changes back.

There is no way that you can call a "particular" quark that is in a bound singlet state a "red" quark.

 

[nikkkom]

OK. So I'm hearing that quarks can oscillate a little between mass generations (flavor). Do they oscillate between up and down type, or between color charge or electric charge? Thanks again.

These oscillations are interference effects when the propagating state is a mix of similar particles from different generations.

Conversion from down-particle to up-particle is not an oscillation, it's usually classified as "decay", e.g. "muon decay": muon (which is a "down-type particle") gets converted to a neutrino by emitting W-, then W- decays to electron and anti-neutrino.

 

[friend]

There is no way that you can call a "particular" quark that is in a bound singlet state a "red" quark.

As opposed to what? When can you call a quark red or green or blue? And isn't there a color charge conservation law as well? Or within a baryon or meson do the quarks there exchange color or charge? Thanks.

 

[Orodruin]

When can you call a quark red or green or blue?

Due to confinement, never. The quark states inside a meson are a linear combination of all sorts of colour combinations in such a way that a colour singlet state is formed. You should not imagine a baryon as three small balls flying around each other with every ball having a definite colour charge. A baryon is a quantum state with a number of valence quarks that form a colour singlet state. The same thing goes for mesons. The colour singlet state they form is a linear combination of $r\bar r$, $b\bar b$, and $g\bar g$.

 

[friend]

I'm trying to read that quark-gluon table, but I need to be sure of my assumptions. Does every quark exchange gluons with every other quark? Or do the eight gluons specify that each quark only exchanges gluons with just a few particular quarks? Thanks.

 

[Orodruin]

All colour charged particles exchange gluons with all other colour charged particles in the same way that all particles with electric charge exchange virtual photons. However, keep in mind that you can never say "these two quarks just exchanged a gluon" or "these two electrons just exchanged a photon". It is a quantum process and saying so would be to specify one of many paths that the system can take. Elementary particles are not small balls flying around.

 

[friend]

However, keep in mind that you can never say "these two quarks just exchanged a gluon" or "these two electrons just exchanged a photon". It is a quantum process and saying so would be to specify one of many paths that the system can take. Elementary particles are not small balls flying around.

Yes, I get it, the various alternatives are in superposition. But you have to be able to say what is in superposition. Yet take the diagram in post #6, here. We have 6 quarks and 8 gluons. But there are 14 different interactions between the 6 different quarks in diagram (14 different combinations of 2 quarks). But the gluons seem to be labeled with two indices. So the gluons seemed to be labeled to suggest they only interact with the quarks with those two labels. This would mean there are not enough types of gluons for every quark to interact with every other quark. I could use some help with this. Much appreciated. Thanks.

 

[nikkkom]

Yes, I get it, the various alternatives are in superposition. But you have to be able to say what is in superposition. Yet take the diagram in post #6, here. We have 6 quarks and 8 gluons.
...
This would mean there are not enough types of gluons for every quark to interact with every other quark. I could use some help with this. Much appreciated. Thanks.

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.

The finer point here is that gluons don't _really_ have a pair of "color-anticolor". If they'd do so, there would be nine of them. The gauge symmetry would be U(3). And this would make "red+green+blue" set of quarks emit gluons, which is not observed.

To make theory consistent with observations, gauge symmetry should be SU(3), and there should be eight gluons, with much less intuitive charges. See here:

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

 

[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?