# How can quarks exist if they are confined?

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## Main Question or Discussion Point

If you look at the history of our natural-science knowledge about matter, in physics there are two ways of investigations about the world. The one is to figure out the tinier and tinier building blocks of matter, starting from condensed matter, extracting molecules, atoms, stripping of the electrons, finding the nucleus, splitting it into protons and neutrons and finally finding out that these themselves consist of quarks or quarks and gluons, which according to todays knowledge seem to be the fundamental building blocks of all matter (together with the electrons forming the neutral atoms, molecules and matter around us).
According to nonperturbative QCD, quarks and gluons don't exist and in nonperturbative QED with two spinors (e.g. proton and electron) hydrogen isn't composed of a proton and an electron.

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A. Neumaier
According to nonperturbative QCD, quarks and gluons don't exist and in nonperturbative QED with two spinors (e.g. proton and electron) hydrogen isn't composed of a proton and an electron.
But in some approximate sense, quarks and gluons do exist in QCD, and hydrogen is composed of a proton and an electron even in full QED with protons.

If you exclude approximations, much of physics makes no sense anymore. For example, in nonrelativistic quantum mechanics of atoms, valence electrons don't exist rigorously, but nevertheless they are a very useful approximate concept and hence exist in this approximate sense.

Gold Member
But in some approximate sense, quarks and gluons do exist in QCD
In what sense? In terms of being an approximate decomposition of high energy scattering states?

If you exclude approximations, much of physics makes no sense anymore. For example, in nonrelativistic quantum mechanics of atoms, valence electrons don't exist rigorously, but nevertheless they are a very useful approximate concept and hence exist in this approximate sense.
No disagreement. I just think it should be kept in mind. Also some approximations have more validity than others. Hydrogen not being made of a proton and electron is a technical detail especially at low energies. However a proton not really being made of quarks isn't I don't think. The vast majority of the time it can't be thought of in that way.

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vanhees71
Gold Member
According to nonperturbative QCD, quarks and gluons don't exist and in nonperturbative QED with two spinors (e.g. proton and electron) hydrogen isn't composed of a proton and an electron.
How do you come to this conclusion? Only because of confinement you cannot conclude that quarks and gluons don't exist. And of course, a hydrogen atom is composed of a proton and an electron. Of course these particles are entangled in a quite complicated way within the bound state (already in non-relativistic QM), but that doesn't mean that they are not constituents of the hydrogen atom.

A. Neumaier
of course, a hydrogen atom is composed of a proton and an electron.
Not exactly, since there are contributions from soft photons and electron-positron pairs, and to a smaller extent also of proton-antiproton pairs (if the proton is taken as elementary)
But in some approximate sense, quarks and gluons do exist in QCD
In what sense?
I don't know the precise sense in mathematical terms, since QCD is not yet defined as a mathematical object. The point is that a proton behaves like a multilocal object, in a final mathematical description (that does not yet exist) it must therefore be described as such.

But experimentally, a jet can be viewed as a manifestation of a single quark. While asymptotic quarks cannot exist due to confinement, quarks fare quite well in QCD descriptions of collisions at finite times between preparation and freeze-out.
The vast majority of the time it can't be thought of in that way.
It suffices that it can be viewed as such in the most interesting time interval during a collision.

Gold Member
Note, the tone below may come off as too confident, I'm not sure I'm right, only talking things out.

But experimentally, a jet can be viewed as a manifestation of a single quark.
Experimentally it is a shower of hadrons, how can it be viewed this way?

The point is that a proton behaves like a multilocal object
In general or only at high energies in scattering processes?

It suffices that it can be viewed as such in the most interesting time interval during a collision.
Suffices for what purpose? As a mental tool for thinking of asymptotic high energy proton (in general hadron) states I agree, but if an proton just sitting there in an everyday object admits no real description in terms of being composed of quarks is it really sufficient in general? Again I get that it is a useful conceptual tool for high energy experiments, but I don't think this is sufficient to allow you to say a proton is truly "made of" quarks.

How do you come to this conclusion?
Quarks and gluons don't exist in the physical Hilbert space.

A. Neumaier
In general or only at high energies in scattering processes?
A proton behaves like a multilocal object in high energy scattering processes (i.e., processes that can probe the structure of matter at small distances).
Suffices for what purpose?
For the purpose of calling it real in an approximate sense.
I don't think this is sufficient to allow you to say a proton is truly "made of" quarks.
There are quantitatively successful ''quark models'' - effective models of mesons and baryons made of constituent quarks (rather than QCD quarks). They predict correctly most of the spectrum of known hadrons - it is the way resonances are assigned to particular quark compositions. The experimental situation is well described in summaries by the Particle Data Group updated every two years. For mesons and baryons see in particular the paper Quark Model. Section 5.5. discusses effective quark models. For a recent paper with references, see, e.g., LHCb pentaquarks in constituent quark models by Ortega et al. (2016, published 2017) .

Thus although the precise relationship between constituent quarks and QCD quarks is unknown, the statement that a proton is truly made of quarks is amply experimentally verified. What is not understood is the precise sense in which this is to be interpreted.

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A. Neumaier
Experimentally it is a shower of hadrons, how can it be viewed this way?
From https://en.wikipedia.org/wiki/Jet_(particle_physics):
wikipedia said:
A jet is a narrow cone of hadrons and other particles produced by the hadronization of a quark or gluon in a particle physics or heavy ion experiment. Particles carrying a color charge, such as quarks, cannot exist in free form because of QCD confinement which only allows for colorless states. When an object containing color charge fragments, each fragment carries away some of the color charge. In order to obey confinement, these fragments create other colored objects around them to form colorless objects. The ensemble of these objects is called a jet, since the fragments all tend to travel in the same direction, forming a narrow "jet" of particles. Jets are measured in particle detectors and studied in order to determine the properties of the original quarks.

Gold Member
Yes, but since there are no quark states in the Hilbert space there is no "hadronization" as a physical process. It's not as if we have an evolution like:
$$|hadron\rangle \rightarrow |quark\rangle \rightarrow |multi-hadron\rangle$$
as there are no quark states.

Gold Member
There are quantitatively successful ''quark models'' - effective models of mesons and baryons made of constituent quarks (rather than QCD quarks). They predict correctly most of the spectrum of known hadrons...
Thus although the precise relationship between constituent quarks and QCD quarks is unknown, the statement that a proton is truly made of quarks is amply experimentally verified. What is not understood is the precise sense in which this is to be interpreted.
I agree with you about these models and if they were the correct theory, then definitely "the proton is made of quarks", but I'm genuinely uncertain as to how to interpret them in light of the fact that no quark states exist in the QCD Hilbert space. Without quark states existing in what sense can anything be made of them.

I'd understand if there were quark states, because then it would just be the usual subtleties of composite/bound states in QFT and it would be pedantic to argue, but that's not the case here.

kith
If what @DarMM writes in #9 is true, quarks seem to be more similar to virtual particles than to real particles. Both occur as internal lines in Feynman diagrams and both don't have state vectors in the physical Hilbert space associated with them (quarks also occur as external lines but this may be a simplification to avoid the complicated jets which are actually measured).

So what's the usual justification for considering quarks to be "more real" than virtual particles?

bhobba
Mentor
So what's the usual justification for considering quarks to be "more real" than virtual particles?
Its the same reason most reject the Aether in favor of SR. Nobody can prove LET is wrong, its just SR, to most people is more elegant. The same with Quarks - it is the most elegant answer we have consistent with experience. For example I seem to recall there were these experiments when probing I think protons where what was probing it would on occasion deflect - like Rutherford when probing atoms. That suggests particles. As far as virtual particles go, they exist almost to a certainty - they are the pictorial representation of a Dyson series. They just do not exist in the sense of an actual particle - like for example deflecting something - at least how just about anybody would think was an actual particle.

A lot of this really is part of philosophy of science, most physicists just use a bit of common sense.

Thanks
Bill

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Gold Member
the same reason most reject the Aether in favor of SR
As far as virtual particles go, they exist almost to a certainty - they are the pictorial representation of a Dyson series. They just do not exist in the sense of an actual particle - like for example deflecting something - at least how just about anybody would think was an actual particle.
Perhaps I'm missing something, but I don't think this (or virtual particles) are the same as Aether theory.

Aether theory is an alternate ontology that can be made to produce similar/identical predictions to Special Relativity, so one could say distinguishing between them is philosophy. Same with the interpretations of QM that replicate its predictions via fine-tuning.

However in the case of quarks and virtual particles the theory itself does not have them as states in any sense. Virtual particles only "exist" in the sense of a way of thinking about Feynman integrals, do something like a lattice calculation with a continuum limit and they'd never even be mentioned. They exist in the same way a perturbation series of a Newtonian orbit can slowly add up to the correct path:
$$\overrightarrow{x}(t) = \overrightarrow{x}_{0}(t) + \overrightarrow{x}_{1}(t) + \cdots$$
Nobody would say $\overrightarrow{x}_{1}(t)$ is a physical prediction of the theory and exists, it's an artefact of a calculational method.

The same with quarks, only if you want to work with local charge carrying fields and then due to the noninvertability of the kinetic operator you have to enlarge to a Hilbert-Krein space, even though this introduces unphysical states.

So this isn't some indistinguishable alternate ontology for the same set of predictions, it's a statement about the predictions themselves. QCD doesn't have any quark states and no state in its Hilbert Space can be thought of as a quark combination in any sense, unless one enlarges to a much bigger space of unphysical states in order to do the decomposition. However then directly one can see the decomposition is unphysical.

Coming back to virtual particles in QCD, one can expand the action not just about the classical vacuum, but about any instanton solution regardless of Chern class. In this case the quadratic parts of the action are slightly different, as are the couplings. Thus the virtual particles have different propagators depending on which instanton solution one basis the perturbative path integral about. Hence their behavior is dependent on how one approximates/truncates the theory.

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Gold Member
If you exclude approximations, much of physics makes no sense anymore. For example, in nonrelativistic quantum mechanics of atoms, valence electrons don't exist rigorously, but nevertheless they are a very useful approximate concept and hence exist in this approximate sense.
Coming back to this, my problem is I don't think quarks are an approximation or exist in an approximate sense, rather they are like virtual particles, only showing up as a way to think about one calculational approach.

I agree with you on valence electrons and hydrogen in QED, but quarks are very different.

For instance in QED, there are proton and electron states and hydrogen does result from proton, electron scattering processes. Hence the fact that hydrogen also is a "sea" of states of other particle numbers, doesn't change the fact that at low energy the dominate contribution is an electron-proton product state and hence approximately it is the correct picture.

However in QCD there are no quark states and the proton, when using physical states predicted by the theory to exist, has no such decomposition.

Sounds like you guys are simply having somewhat different definitions of concepts like "X is made of Y" and "X exists".

Maybe the first order of business here should be to arrive to a common definition (or choose to use different words, less ambiguous ones), and then argue whether quarks "exist"?

Gold Member
I guess I mean they are real the same way virtual particles are, useful for calculating a QFT's predictions, but they're not actual physical states in the Hilbert space.

Or for a General Relativistic anology they're as real as Christoffel fields.

I won't get hung up on "real" if people think of it differently. However there is some difference to me between things like the metric and things like Christoffel fields and it's a distinction in the theory not just philosophical.

bhobba
Mentor
I guess I mean they are real the same way virtual particles are, useful for calculating a QFT's predictions, but they're not actual physical states in the Hilbert space.
True - but in the case of quarks how do you explain the deep inelastic scattering experiments?
https://en.wikipedia.org/wiki/Deep_inelastic_scattering

Like Rutherford that they are actual particles is the most reasonable explanation.

Thanks
Bill

Gold Member
True - but in the case of quarks how do you explain the deep inelastic scattering experiments?
https://en.wikipedia.org/wiki/Deep_inelastic_scattering

Like Rutherford that they are actual particles is the most reasonable explanation.

Thanks
Bill
Is it though? Quarks have color, but no physical state has color, in fact colored operators aren't even defined on the physical Hilbert space. This means no matter how deep you probe inside the proton you never unearth the one quantity that's distinctive to them and gluons.

If the theory doesn't have quark states, the charge they carry isn't present at any scale, why wouldn't you just conclude the proton deflects in a complex way?

Really I'm just not sure here. There is something true about the quark picture, but I don't think it's just as simple as quarks themselves are real even approximately. Their state vectors have negative norm and they carry an unphysical charge.

Gold Member
I should say I think the answer lies in finite density QCD where quarks and gluons are physical states, but I'm not sure of the details yet.

bob012345
Gold Member
Quarks and gluons don't exist in the physical Hilbert space.
What exactly is a physical Hilbert space? Isn't a Hilbert space a mathematical construct?

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Gold Member
What exactly is a physical Hilbert space? Isn't it a mathematical construct?
The space of states of the theory, i.e all physically realisable quantum states of the matter dealt with by the theory. Standard QM right?

It's also a term used in canonical quantization of gauge theories to distinguish it from the larger Hilbert-Krein space one gets from naive quantization.

bob012345
Gold Member
The space of states of the theory, i.e all physically realisable quantum states of the matter dealt with by the theory. Standard QM right?

It's also a term used in canonical quantization of gauge theories to distinguish it from the larger Hilbert-Krein space one gets from naive quantization.
Thanks. I've never seen it used as a physical quantity. I've always thought if it as an abstract concept describing quantum states which themselves are just abstract mathematical models of reality. I guess people use it as a physical term now.

vanhees71
Gold Member
Indeed! In our perception of physical reality there are neither Hilbert and Fock spaces, Lie and other groups in QT, nor configuration and phase spaces, no fiberbundles, Minkowksi and pseudo-Riemannian manifolds in classical physics. These are all description of our perceptions of Nature. It is an astonishing empirical fact that we can order our perceptions (at least the "objective" ones) using these mathematical entities.

Gold Member
Thanks. I've never seen it used as a physical quantity. I've always thought if it as an abstract concept describing quantum states which themselves are just abstract mathematical models of reality. I guess people use it as a physical term now.
I'm not sure what you mean. It's just the space of states admissable by the theory, or in the quantum picture it defines all the observables and their possible statistics.

It's not really being used as a physical term (although perhaps I misunderstand what you mean), it's a technical term in the quantization of gauge theories so as to distinguish the space of states that actually occur from the larger space of unphysical states one gets when you naively quantize the theory.

Gold Member
Indeed! In our perception of physical reality there are neither Hilbert and Fock spaces
Yes, but clearly naive quantization of gauge theories produces states that can't conceivably describe reality (negative-norm or zero-norm) from which one must select out the states that can via some BRST like condition. That's all that is meant here by "physical Hilbert" space, the subset of the states from naive quantization that actually do have sensible properties and are selected out by BRST conditions.

It's not "physical" in some grander or philosophical sense.