# B Quark confinement and the Higgs mechanism

1. Feb 22, 2018

### bluecap

There is something that perflexed me. First here are the references to my questions:

http://www.latticeguy.net/mypubs/pub017.pdf

http://bose.res.in/~bossar/chandu.pdf

What I'd like to know is the following:

Without superstrings. Quark confinement and asymptotic freedom says as you pull the quarks apart.. the forces get stronger such that you need infinite energy to pull them apart. However, if quarks confinement were due to being ends of a superstring. And the temperature of the higgs field go above the critical temperature which makes the vaccum expectation value zero (or reform the symmetry), would the quarks be able to to be pulled apart because the superstrings is not longer exposed to non zero higgs field..

What is really the connection between higgs field and superstrings and quarks confinement?

To rephrase it. If the higgs field is above critical temperature or in the condense matter analogy.. in normal rather than superconducting state, would this destroy the string bonds between the quarks or destroy the confining property of the colour force which would no longer become stronger the further they are apart? Is this concept a popular one or just a one of those many Beyond Standard Model physics variants?

2. Feb 23, 2018

### mitchell porter

If we forget string theory for a moment... Within the standard model, quark confinement and Higgs spontaneous symmetry breaking are different things and set in at different temperatures.

Higgs dynamics are much more straightforward - the Higgs field has a potential energy which is minimized at a nonzero value, and it will be in that minimum unless there is a plasma hot enough that Higgs bosons are constantly being created in particle collisions. That requires a temperature far far above the quark deconfinement temperature.

The exact mechanics of quark confinement are still unknown because of strong coupling. In a quark-gluon plasma, the strong force is weak enough that you can use Feynman diagrams to describe quark and gluon interactions. As in quantum electrodynamics, the diagrams with just a few quark-gluon interactions account for most of what happens.

But below the confinement temperature, the strong force is strong and, if you think in terms of Feynman diagrams, it should be that the more interactions there are in a process, the more it should dominate events. So strings of chromodynamic flux may emerge from a sheet of quark and gluon interactions.

The ground state of the electroweak vacuum is relatively simple: a "Higgs condensate", a nonzero value of the Higgs field. But the ground state of the QCD vacuum apparently has a scalar gluon condensate, a quark-antiquark condensate called the chiral condensate, a tensor gluon condensate, higher-order quark condensates... And then moving through this background, and interacting with it, are the baryons (proton, neutron, and many other unstable multiquark particles) and the mesons (pion and other quark-antiquark particles).

If we put electroweak and QCD together in the standard model (forget gravity and any new physics for a moment), then we get a picture of the basic quantum fields according to which, at temperatures below the deconfinement temperature, you have a Higgs condensate; you have all those QCD condensates; you have those bound states of quarks interacting with each other and with the QCD condensates; and you also have fermions and W+, W-, Z particles obtaining mass from their interactions with the Higgs condensate.

However, the exact QCD vacuum has not been worked out rigorously. We have lattice QCD, which is brute-force computer calculation, and we have various approximations to QCD whose validity has not been mathematically proven. Confinement in QCD really might be due to strings of flux plus a kind of condensation that forces the charges at the end of the string together, but for now there's no proof. There's a million-dollar prize waiting for whoever proves or disproves it.

3. Feb 23, 2018

### Orodruin

Staff Emeritus
Let me just add the following:

I suggest that you do not read too much into every 40+ years old paper that you find. This paper was published in 1974 when quark confinement and asymptotic freedom was a hot topic. Coincidentally, it is the same year as Wilczek wrote his thesis including the negative sign of the beta function of QCD, thus giving an explanation for asymptotic freedom for which he won the Nobel prize.

Bottom line: Read textbooks, not papers, until you have the proper knowledge to separate what has since been verified with what has not.

4. Feb 24, 2018

### bluecap

If asymptotic freedom solved the whole QCD mystery, how come we still have the following description:

https://en.wikipedia.org/wiki/QCD_vacuum
"Unsolved problem in physics:
QCD in the non-perturbative regime: confinement. The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei and nuclear constituents?"

And there is still the string model. Btw.. I mistakenly initially thought the string in the following is about string theory (superstring theory) but realized they were actually unrelated.. lol.

"String models
String models of confinement and hadrons have a long history. They were first invented to explain certain aspects of crossing symmetry in the scattering of two mesons. They were also found to be useful in the description of certain properties of the Regge trajectory of the hadrons. These early developments took on a life of their own called the dual resonance model (later renamed string theory). However, even after the development of QCD string models continued to play a role in the physics of strong interactions. These models are called non-fundamental strings or QCD strings, since they should be derived from QCD, as they are, in certain approximations such as the strong coupling limit of lattice QCD.

The model states that the colour electric flux between a quark and an antiquark collapses into a string, rather than spreading out into a Coulomb field as the normal electric flux does. This string also obeys a different force law. It behaves as if the string had constant tension, so that separating out the ends (quarks) would give a potential energy increasing linearly with the separation. When the energy is higher than that of a meson, the string breaks and the two new ends become a quark-antiquark pair, thus describing the creation of a meson. Thus confinement is incorporated naturally into the model.

In the form of the Lund model Monte Carlo program, this picture has had remarkable success in explaining experimental data collected in electron-electron and hadron-hadron collisions."

I'm interested in models where they connect the string and higgs field... in the original peered reviewed paper I shared.. isn't it about the strong force being string-like excitations of the superconducting Higgs vacuum? Again.. even when asymptotic safety was discovered.. it didn't remove the need for understanding the qcd vacuum. Asymptotic safety seems to be related to effective theory and renormalization and perturbation and this still required to know the full theory.

My question at present is. What must be the energy of LHC or other particle accelerators so it can produce the unbroken massless electroweak bosons? If this energy is reached, does it mean the higgs field or vev becomes zero in the region of the collision? Has this been reached already? If yes, can it test whether the string being excited of the superconducting higgs vacuum can lose the confinement and produce free quarks when higgs vev is zero? If we have reached the energy required already, and we still haven't seen any free quarks.. then it means the string-higgs strong confinement model of the qcd vacuum mystery is refuted already?

Last edited: Feb 24, 2018
5. Feb 25, 2018

### bluecap

Anyway here's a related question. How large a particle accelerator before it has energy to or detection capability to even see a free quark? I read at wiki that:

"Quark–gluon plasma is a state of matter in which the elementary particles that make up the hadrons of baryonic matter are freed of their strong attraction for one another under extremely high energy densities. These particles the quarks and gluons that compose baryonic matter.[13] In normal matter quarks are confined; in the QGP quarks are deconfined. In classical QCD quarks are the fermionic components of hadrons (mesons and baryons) while the gluons are considered the bosonic components of such particles. The gluons are the force carriers, or bosons, of the QCD color force, while the quarks by themselves are their fermionic matter counterparts.

Although the experimental high temperatures and densities predicted as producing a quark–gluon plasma have been realized in the laboratory, the resulting matter does not behave as a quasi-ideal state of free quarks and gluons, but, rather, as an almost perfect dense fluid.[14] Actually, the fact that the quark–gluon plasma will not yet be "free" at temperatures realized at present accelerators was predicted in 1984 as a consequence of the remnant effects of confinement."

What would it take for it to behave as quasi-ideal state of free quarks and gluons?

How big is the biggest particular accelerator that can ever be designed on earth? What is the energy if the circumference of the accelerator is the circle of the earth where they would create a tunnel literally around the earth in the distant future.

Would this be enough to see individual quark or will we never see it because it needs solar system size particle accelerator or impractical ones?

6. Feb 25, 2018

### bluecap

Related to the above questions.. I just read this article "The Glue that Binds Us" https://www.bnl.gov/physics/NTG/linkable_files/pdf/SciAm-Glue-Final.pdf and surprised to learn there were still so much unknown about the quarks and gluons:

"Despite all this insight—and a good understanding of how individual quarks and gluons interact with one another—physicists, to our dismay, cannot fully explain how quarks and gluons generate the full range of properties and behaviors displayed by protons, neutrons and other hadrons. For example, adding up the masses of the quarks and gluons inside protons does not begin to account for the total masses of protons, raising the puzzle of where all this missing mass comes from. Further, we wonder how exactly gluons do the work of binding quarks in the first place and why this binding seems to rely on a special type of “color” charge within quarks. We also do not understand how a proton’s rotation—a measurable quantity called spin—arises from the spins of the quarks and gluons inside it: a mystery because the smaller particles’ spins do not easily add up to the whole"

Asymptotic safety concept seems to be only a small part of the solution...

"The quark antiquark fluctuation makes the interaction strength between color charges stronger, whereas the gluon-pair fluctuation makes it weaker. Because such gluon oscillations are more prevalent than the quark exchanges in QCD, they win. (Physicists David J. Gross, Frank Wilczek and H. David Politzer won the 2004 Nobel Prize in Physics for this discovery.) In the decades since the advent of QCD, experiments worldwide have confirmed the theory’s claim as one of the pillars of the Standard Model of physics. Yet many details of QCD remain elusive. Curiously, for instance, although the three quarks in a proton individually carry one of three, say, red, green and blue color charges, the proton does not have a net color charge. Likewise, the quark and the antiquark in a hadron known as a pimeson (often called pion) carry color charges, but the pion is colorless. Color neutrality of hadrons is analogous to the electrical charge neutrality of atoms. But whereas the zero net charge of atoms is a clear consequence of the canceling out of the proton’s positive charge and the electron’s negative charge, how colored quarks and colored gluons combine to make colorless hadrons is not clear in QCD."

Any updates about the solutions? What resources (articles, papers, etc.) to find at least summary of the updates since 2015? Reading each paper about QCD at Arxiv would be too time consuming.

7. Feb 26, 2018

### nikkkom

I don't understand this part. What's curious about it?
Any system of elementary particles with net color charge would be very strongly interacting with color-charged particles.
IOW: rearranging the particles into color-neutral systems results in states with much lower energy. Thus, it is in no way surprising that it happens, and we are left with color-neutral hadrons.

8. Feb 26, 2018

### nikkkom

At a closer look, this PDF poster is full of pop-sci simplifications and at places is plain wrong. "When protons are accelerated to extreme speeds, the gluons inside them multiply" - what?? This is obviously wrong.

9. Feb 26, 2018

### bluecap

It's Scientific American article written by professionals (see below) but presented in pop-sci simplications. The authors are:

"Rolf Ent has worked at the Thomas Jefferson National Accelerator Facility in Newport News, Va., since 1993. He is associate director of experimental nuclear physics there and has been a spokesperson for multiple experiments studying the quark-gluon structure of hadrons and atomic nuclei.

Thomas Ullrich joined Brookhaven National Laboratory in 2001 and also conducts research and teaches at Yale University. He has participated in several experiments, first at CERN near Geneva and later at Brookhaven, to search for and study the quark-gluon plasma. His recent efforts focus on the realization of an electron-ion collider.

Raju Venugopalan heads the Nuclear Theory Group at Brookhaven National Laboratory, where he studies the interactions of quarks and gluons at high energies"

Do you have other articles where the puzzles of confinement is presented in more correct manner?

I've been googling for an hour why the gluon-quark plasma behave like a liquid instead of gas. And there are over 250,000 hits. I can't find the answer. Do you know why it behaves like liquid?

10. Feb 26, 2018

### bluecap

what part of the sci-am article is true and not true? At least this part is true:
"And we lack a mathematical proof of how the QCD equations ensure that colored quarks and gluons are confined within colorless hadrons. Confinement is literally a $1-million problem—it is one of six outstanding puzzles identified by the Clay Mathematics Institute, whose solution will result in the award of$1 million to anyone who provides the answer."

googling this I found at physicstack answer by "levitopher"
"As a sidenote, only the strong force is asymptotically free. The E/M and weak force become stronger as the energy gets higher. In addition, it is important to realize that we cannot solve problems involving the strong force at low energies (if you could, the Clay Mathematics Institute would give you $1 million!). Once they are at high energies, the strong coupling is weak so QCD acts quite a bit like QED." and https://arxiv.org/pdf/1603.02722.pdf Confinement seems to be an empirical fact; but a mathematical proof is lacking. Partly as a consequence, the Clay Mathematics Institute oﬀered a “Millennium Problem” prize of$1-million for a proof that SUc(3) gauge theory is mathematically well-deﬁned.

Is there a possibility the strong force is not described by SU(3) gauge theory but a larger group?

and direct from the Clay Mathematics Institute itself for the \$1 million reward:

http://www.claymath.org/millennium-problems/yang–mills-and-mass-gap

11. Feb 26, 2018

### nikkkom

12. Feb 26, 2018

### bluecap

13. Feb 26, 2018

### Orodruin

Staff Emeritus
I would say it is a popularisation of the solutions to the DGLAP equations and the resulting parton distribution functions at different momentum transfer.

14. Feb 26, 2018

Staff Emeritus
Bluecap, you seem to be looking for a B-level explanation of all of QCD, without any oversimplications. I doubt such a thing exists. If it did, people would be using that instead of QCD.

15. Feb 27, 2018

### nikkkom

A blog about current state of QCD calculations in non-perturbative low-energy regime:
latticeqcd.blogspot.com

16. Feb 27, 2018

### bluecap

The best articles I found about the spin and mass problem of QCD from dozens I read are the following written by Ethal Siegel (with very good graphics and it is so optimistic).

https://www.forbes.com/sites/starts...-the-mass-of-a-proton-come-from/#51005842e1d7

Question. For Lattice QCD to work. Do you need to input a model? For example If supposed QCD ultimately had preons (or subquarks) or there was bigger symmetry than SU(3). Can Lattice QCD figure it out? Or does it depend how you input in the model.. so garbage in garbage (or diamond in diamond out) out also applies here?

17. Feb 27, 2018

### nikkkom

Of course you need to write lattice QCD code using math provided by the QCD theory, i.e. SU(3) gauge theory.

18. Feb 27, 2018

### bluecap

Thanks. Ethan was just so enthusiastic in contrast to the sci-am article.. he wrote "With 70% of the proton's spin coming from gluons and orbital interactions, and with experiments and Lattice QCD calculations improving hand-in-hand, we're finally closing in on exactly why the proton "spins" with the exact value that it has.".. this is assuming SU(3) is all there is to QCD.. but this seems unlikely.

19. Feb 27, 2018

### nikkkom

You do not understand. "SU(3) gauge theory" and QCD is the same thing.

20. Feb 27, 2018

### bluecap

Are there no QCD model that has bigger symmetry group where SU(3) color force is just a residual. Many preon (subquark) models has bigger symmetry group like SU(9). Are they not QCD too?