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Could color "charge" be an indication of quark compositeness.

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I have been bothered for some time that the word "charge" is used in the color quantum numbers. Electromagnetic charge is an indestructible element of elementary particles, it cannot be exchanged, in the sense that an electron has always charge -1, and an up quark charge 2/3.  This recent question in physics.SE  clarified it for me, in the answer by Jeb who  wants to illustrate how color works with quarks and gluons

"As an analogy, consider the deuteron. It's S-state (symmetric) and spin-1 (symmetric), so to be overall antisymmetric, the isospin state is singlet: 12√(nppn). What that means is that there is not "a proton" and "a neutron" inside, rather, the nucleons are mixed, and if you address one of them, it's both proton and neutron--as a superposition."

The deuteron  is a composite particle  . This is not true about quarks and color. Quarks are considered elementary, non-composite particles in the standard model.

Is there any compositeness model that takes this into account? As an experimentalist I would consider the very existence of the mobility of color identification of quarks as a datum supporting compositeness, in analogy with the deuteron example above.

asked Aug 15 in Theoretical Physics by anna v (1,735 points) [ revision history ]
edited Aug 15 by anna v

3 Answers

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I am not sure if it directly addresses the question but I would like to recall that for a gauge theory of gauge group G, the intrinsic notion of "charge" of a particle is an irreducible representation of G. This charge is intrinsic to a given particle, as the usual electric charge. For G=U(1), as in electromagnetism, all irreducible representations are one dimensional and can be indexed by a number which is the usual electric charge. The red/blue/green for quarks refer to a choice of basis of the charge representation (the fundamental representation of the gauge group SU(3)) but there is no intrinsic meaning in such a choice (one way to say it is that it is not gauge invariant).

answered Aug 16 by 40227 (4,660 points) [ no revision ]

You are stating the consistency of the SU(3)xSU(2)xU(1) model with the data up to now, and I can accept this.  I am trying to see if there are models with composite quarks which will simulate the effect, similar to  the compositeness of the deuteron, so that color does not come from intrinsic SU(3) but from underlying compositeness. .

Maybe this phrase will help: Originally in QM we quantized (and classified) bound states.

@vladimir  and I am asking about bound states that may make up quarks.

Dear Anna, I did not miss your question. I do not know what makes up quarks, I just point out that it is well possible to consider them as a composite states. Take, for example, a complex system of many bound point particles. On one hand, we call them elementary; on the other hand they are strongly interacting and bound together. If we perturb this system, it starts moving as a whole and the "internal" (relative) degrees of freedom get excited. What we normally observe is normal (collective) modes of motion of this system (proper frequencies, for example). These collective (normal) modes may be nearly independent (if the excitation energy is not too huge). Those modes are quasi-particles with certain quantum numbers, and they are nearly "free". They have the corresponding "coordinates" and can be equally considered as fundamental constituents of the system.

In my answer, I interpreted "charge" as characteristic of a coupling with a gauge field, because it is the only way that makes sense for color. Another meaning for "charge" could be conserved charge for a global symmetry. In electromagnetism, the electric charge can be seen that way, in particular, there is a conserved current. But it is not the case in a non-abelian gauge theory: the analogue current is not conserved because gluons have color too (it is analogue to what happens in general relativity: there is no conserved energy-momentum tensor because the gravitational field has some energy-momentum). Concretely, you can measure an electric chage by measuring the flux of electric field through a sphere surrounding the system but if you do the same thing for color, it is not clear what is the contribution of the system we want to study and what is the contribution of gluons.

I am not sure if it makes sense to ask if quarks and gluons are elementary because they are not (even in an approximated sense) asymptotic state of some scattering experiments. It would make more sense if quarks and gluons were not confined (even if for strongly coupled relativistic quantum system, there is no absolute notion of elementary versus composite). But in such case, the fact that the color current is not conserved is not an indication of compositeness, in the contrary: it implies that gluons cannot be bound states in some underlying quantum field theory ("Weinberg-Witten theorem", similar argument with the energy-momentum tensor implies that the graviton cannot be  a bound state in some underlying quantum field theory).

@40227: I do not think that "asymptotic states" are impossible for quarks and gluons (partons, by R. Feynman). High-energy QCD is asymptotically free. Even in Classical Mechanics we can consider one body $m_1$, connected to another body $m_2$ with a spring, as a free mass $m_1$ if we scatter a third body $m_3$ from it very rapidly and look solely at the final state of $m_3$. Then the presence of the spring cannot be noticed due to too short displacement of $m_1$ during impact and we look solely at $m_3$ in the final state (the coupled system gets "excited", but we do not look at the target state, i.e., we measure an inclusive cross section). On the other hand, if the scattering process is "slow enough", the spring couples $m_1$ and $m_2$ too strongly and the system is effectively looks like a solid one with $M=(m_1+m_2)$ in a low-energy scattering process.

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Models in which quarks are composite are called preon models. 

http://cds.cern.ch/record/133861/files/198008108.pdf

There is a book about them: 

D'Souza and  Kalman., Preons: Models of Leptons, Quarks and Gauge Bosons as Composite Objects, 1992.

Quite a number of them seem to be consistent with the experimental record, but apparently nothing forces preons to exist. For a recent search, see:

Resonance search for new physics in the photon+jet final state at 13 TeV, https://pos.sissa.it/282/

answered Sep 11 by Arnold Neumaier (12,160 points) [ no revision ]

Thanks, yes there are these models.

I am just asking whether the different behavior of colored charge than em charge with respect to particle characterization can be used as an argument for a composite structure. Analogy: charge distributions argue for composite atomic structures.

@annav: Maybe as hints for a composite structure, but not more than that. It is like the hints for unification. 

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Electromagnetic charge is an indestructible element of elementary particles, it cannot be exchanged.

Yes, it can be exchanged. Charged bodies exchange with charges ;-)

More seriously, it is all context-dependent. For example, take a Hydrogen atom and scatter a charged particle from it. If the projectile velocity is relatively small ($v\ll v_0$), then an adiabatic approximation (Born-Oppenheimer) is good to study the target. But if $v\gg v_0$, then the first Born approximation works fine and you can, in principle, see $|\psi_{nlm}({\bf{r}})|^2$. For $n\ge 2$, there are "free charged sub-clouds" hanging in space with the charges less than unity, like this, for example:

                           

The elastic cross section is expressed via those clouds: the scattering amplitude is a sum over each sub-cloud. (The scattering is elastic with respect to atomic transitions $|n,l,m\rangle$, but it is in fact deep-inelastic and inclusive with respect to soft photon emission during scattering.)

If you take a free electron at rest and transfer some momentum ${\bf{q}}$ to it, it not only starts moving, but also emits some soft electromagnetic waves, which can be received far away. In other words, a charge as an interaction property of the electron, can be felt far away, so the notion of charge is not limited to Faraday's law of electrolysis (conservation of charge). Similarly for quarks. It is context dependent and resembles the atomic picture.

answered Aug 15 by Vladimir Kalitvianski (12 points) [ revision history ]

Well, I am talking on whether the electron is called an electron if it has lost its charge (which experimentally it does not no matter what the mathematical model) . So the model you are describing is again like the deuteron example a composite model. Not tlaking about  interaction properties, but identification in the table of elementary particles. Color is a transferable property between the elementary quarks, charge is not so, even for quarks. There really is no red up quark in that table, it can be red green or blue, but a given quark does not retain the color as an identity in the table. I have clarified what I mean by "exchanged"

Seeing different regimes of interactions of "elementary" particles, I would say that those properties that are used for classifications are nothing but resulting properties of interactions and represent more quasi-particles or composite particles or normal modes in complex systems. Because again, one thing is to place something into a table, and another thing is to express observable cross sections via quarks, gluons, etc.

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