# Structure of the atom - strong interaction and colour charge.

• ajassat
In summary: But it is clear that confinement is very important in order to have hadrons at all. So it's not a minor detail. In summary, the Clay Mathematics Institute is offering a one million dollar prize for an understanding of colour charge in 4 dimensions that breaks the symmetry of the system.
ajassat
I am having some difficulty understanding the concept of colour charge.
I realize that protons and neutrons are made up of a different number of quarks, and this is how they have the charges +1 and zero.

I then realized that different quarks have color charge and that in a hadron (protons and neutrons included), the total colour charge would be zero. I have read that gluons also have some sort of colour charge and mediate a strong force, which keeps the quarks together.

Quite simple I am confused about the following:

• Why in hadrons the total colour charge is zero?
• The colour charges of the different quarks present in the proton?
• The colour charges of the different quarks present in the neutron?
• How gluons affect the colour charge?

...and finally how all of this affects the residual strong force (keeping the protons and neutrons together)??

well why they (hadrons) must have total color charge is not understood yet on theoretical level as far as I know it..
The math society Clay Mathematics Institute has a 1 milion dollar reward for an exact solution to colour con nement in 4 dimensions (3 space, 1time); http://www.claymath.org/millennium/Yang-Mills Theory/yangmills.pdf

The color charges of the quarks are constantly changing due the glouns, the gluons take away a colour of a quark and gives it new one. i.e a blue quark interact with a red-antiblue gluon -> the quark turns to red.

How one builds up the strong force between hadrons from QCD, there are many approaches. Lattice QCD and Chiral Perturbation Theory (ChPT) are the most common ones I think. In Lattice QCD one discretize the space-time and in ChPT one uses the symmetries of the QCD lagrangian to construct an effective quantum field theory where the lighest mesons (meson octuplet) and baryons are massless Nambu-Goldstone bososn. But then one has spontaneous symmetry breaking since meson octuplet only exists for pesudoscalars. Finally one has explicit symmetry breaking due to non-zero (quark and) meson masses.

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ajassat said:
I realize that protons and neutrons are made up of a different number of quarks, and this is how they have the charges +1 and zero.
They are made up of different quarks, different flavors, but to a rather very good accuracy, their structures in terms of quarks and gluons is the same provided you interchange up and down.

malawi_glenn said:
The math society Clay Mathematics Institute has a 1 milion dollar reward for an exact solution to colour connement in 4 dimensions
If I understand the Clay mathematical institute prize description, the problem is about mass-gap, not confinement. Although it's true they are probably related, in Gribov's theory of quark confinement glueballs would not exist at all, so the mass-gap problem would be ill-posed if Gribov's vision is correct (for instance).

ajassat said:
...

• Why in hadrons the total colour charge is zero?
• The colour charges of the different quarks present in the proton?
• The colour charges of the different quarks present in the neutron?
• How gluons affect the colour charge?

...

The simplest way to describe it is in terms of symmetry. The color symmetry SU(3) is exact, which means that there must be no way of telling if and when the three colors are all changed ("transformed") in a consistent way. This answers your first question -- if hadrons had an observable color, it would change during such a transformation, "breaking" the exact symmetry.

So not only are the colors of the quarks in a proton or neutron constantly changing, as malawi_glenn correctly notes, they can't individually be well defined in the first place. Whatever you chose to call the color of a particular quark in a nucleon, you could immediately transform it to a different color with no observable effects.

humanino said:
...

If I understand the Clay mathematical institute prize description, the problem is about mass-gap, not confinement. Although it's true they are probably related, in Gribov's theory of quark confinement glueballs would not exist at all, so the mass-gap problem would be ill-posed if Gribov's vision is correct (for instance).

I got distracted by the Clay Institute's http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf while writing the above, which let me see that on page three they include three parts to the problem, namely the mass gap, confinement, and chiral symmetry breaking.

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daschaich said:
I got distracted by the Clay Institute's http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf while writing the above, which let me see that on page three they include three parts to the problem, namely the mass gap, confinement, and chiral symmetry breaking.
Page 3 describes properties for QCD to be a valid description of hadrons. It is not a description of the problem. The problem is stated page 6.

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humanino said:
Page 3 describes properties for QCD to be a valid description of hadrons. It is not a description of the problem. The problem is stated page 6.

Ah, I see. Should have kept reading. They demote confinement to just one of "many natural extensions of the Millenium problem".

I should have better memory, I should have read the yang mills millenium problem again before i posted :-)

Great humanino! The true master of QCD of this forum I would say!

This has really helped me in understanding. Can someone now explain to me how the residual strong force works with quarks in the hadrons to prevent protons from repelling each other?

Some maths is ok...but don't overwhelm me (I'm just 15)

ps - this stuff is truly amazing!

That question is on nobel prize physics level...

One could try discussing it in terms of pion exchange, that could be about the right level, though I'm not volunteering.

The good ol pion-, rho- and omega exchange potentials right, which provides a quantitive feeling of the general feuatures of the nucleon-nucleon force. But what is nices is the Chiral Perturbation Theory, since it uses the symmetries of QCD and is in that way an effective QCD theory.

you first need to know lagrangians, chiral symmetry etc, graduate physics this is..

Oh...I wish I could do this right now. High school physics isn't this interesting.
Are there any alternatives?
The meson transfer theory?

yeah, one needs to know pretty much quantum field theory etc to do modern subatomic physics, one must starts from the basics hehe.

Well the pion exchange stuff was done in the 60's and is not as advanced as ChPT but still, gradudate level physics.

I see.
I am in the process of learning all the basics while still interested in the higher level physics.

At the moment I am learning calculus - something vital for the study of classical mechanics which in turn is needed for the study of quantum mechanics.

ajassat said:
I see.
I am in the process of learning all the basics while still interested in the higher level physics.

At the moment I am learning calculus - something vital for the study of classical mechanics which in turn is needed for the study of quantum mechanics.

Yes, we must all learn how to crawl before we can walk, and walk before we can run.

Calculus is important, but never underestimate algebra - linear algebra and abstract algebra. Differential geometry and complex analysis are also important in modern physics. Other physics courses which one must master (besides quantum mechanics) is electromagnetism, analytical mechanics and special relativity.

Learn slow, and make sure you learn the basics very well, it will pay off in the long run.

Something in me feels like if I can't explain something to someone intelligent but not versed in the jargon of the trade, then I haven't really understood it. So a challenge for all: explain hadron interaction, as detailed as possible, but without mentioning anything that a high school student doesn't know.

Doesn't actually need to include that much: some plausible reason for confinement (Wilson's area law, gauge theory <-> string <-> rubber bands), enough about colour to explain why mesons and hadrons are the low energy spectra, and enough of interactions to relate the mass of pions to the range of hadron interactions. Extra bonus: pion mass generation (though my instinct is that it would take too long, though not necessarily impossible).

I could probably do the first couple...but I'm afraid i wouldn't be as specific as you like, not very gud at explaining this stuff

However if you really want to nail the basics and get some good stuff as well I would check out these lectures, he really explains the basics well as well and talks about some more advanced stuff.

They're pretty long though (but interesting enough to keep you hooked!) Also if you like these ones i'd seriously recommend his one on nukes (the best one imo)

genneth said:
Something in me feels like if I can't explain something to someone intelligent but not versed in the jargon of the trade, then I haven't really understood it. So a challenge for all: explain hadron interaction, as detailed as possible, but without mentioning anything that a high school student doesn't know.

Doesn't actually need to include that much: some plausible reason for confinement (Wilson's area law, gauge theory <-> string <-> rubber bands), enough about colour to explain why mesons and hadrons are the low energy spectra, and enough of interactions to relate the mass of pions to the range of hadron interactions. Extra bonus: pion mass generation (though my instinct is that it would take too long, though not necessarily impossible).

Spot on :)
That is exactly what I want. I'm really interested in physics and want the basics, since I'm still learning all the math I need. Dreaming of the day when I can start using complex equations, and use numbers to explain concepts.

:P

ajassat said:
Spot on :)
That is exactly what I want. I'm really interested in physics and want the basics, since I'm still learning all the math I need. Dreaming of the day when I can start using complex equations, and use numbers to explain concepts.

:P

But you also, on your part, have to be reasonable and accept the fact that you do not have the full faculty to be able to understand any of these. That's why we have schools, to prepare you with the necessary tools to do these things!

I disagree with genneth's assessment. I host the general public and high school students regularly at the facility that I work with, so I am highly familiar with trying to convey science, and physics in particular, to those who are not familiar with the jargon and the physics. Just because one THINKS that one is able to explain something to the general public does NOT mean that the message being conveyed is exactly what was understood. This is an often-overlooked FACT. Try it if you don't believe me. Explain some complicated aspect of physics to someone who isn't a physicist, and then ask him/her to tell you, in her own words, what he/she had just learned. You will find that, more often than not, what you get back can be severely different than what you described, and that 10 different people hearing the same thing will understand it in 10 different ways!

So let's not pat ourselves too hard on the back here just because we think we can explain something complex to someone else. All you can do is explain this very superficially, and that in itself will inevitably cause the listener to interpret the message based on his/her background knowledge, which can very wildly from person to person.

Zz.

ZapperZ said:
But you also, on your part, have to be reasonable and accept the fact that you do not have the full faculty to be able to understand any of these. That's why we have schools, to prepare you with the necessary tools to do these things!

I disagree with genneth's assessment. I host the general public and high school students regularly at the facility that I work with, so I am highly familiar with trying to convey science, and physics in particular, to those who are not familiar with the jargon and the physics. Just because one THINKS that one is able to explain something to the general public does NOT mean that the message being conveyed is exactly what was understood. This is an often-overlooked FACT. Try it if you don't believe me. Explain some complicated aspect of physics to someone who isn't a physicist, and then ask him/her to tell you, in her own words, what he/she had just learned. You will find that, more often than not, what you get back can be severely different than what you described, and that 10 different people hearing the same thing will understand it in 10 different ways!

So let's not pat ourselves too hard on the back here just because we think we can explain something complex to someone else. All you can do is explain this very superficially, and that in itself will inevitably cause the listener to interpret the message based on his/her background knowledge, which can very wildly from person to person.

Zz.

Let us try. You explain to me and see if I can re-tell correctly.
Ok?

ajassat said:
Let us try. You explain to me and see if I can re-tell correctly.
Ok?

Not from me. You need to find someone who claims that this can be done. I'm not one of them.

Zz.

Fair enough. Genneth will have to try.

genneth said:
explain hadron interaction, as detailed as possible, but without mentioning anything that a high school student doesn't know.
On top of what has been said, there is another reason why this proposal is ridiculous : explaining hadron interaction is still an active field of research ! If you take time to read serious books about confinement, they will clearly tell you that we don't know the reason for confinement in Nature. The formation of string-like flux tubes is neither proven to occur, nor necessary for confinement.

Always when I try to explain physics in "layman"-terms, I feel that I am lying, I just tell them a stroy which they can understand - i.e they don't understand the physics, they understand the tale which I tell them, nothing more nothing less.

## 1. What is the strong interaction?

The strong interaction is one of the four fundamental forces of nature, along with gravity, electromagnetism, and the weak interaction. It is responsible for binding quarks together to form protons and neutrons, and also holds the nucleus of an atom together.

## 2. How does the strong interaction relate to the structure of the atom?

The strong interaction is responsible for holding the nucleus of an atom together by binding quarks together to form protons and neutrons. Without the strong interaction, the nucleus would not be stable and the atom would fall apart.

## 3. What is colour charge?

Colour charge is a property of quarks that determines how they interact with the strong force. It is similar to electric charge in electromagnetism, but instead of positive and negative charges, there are three types of colour charges: red, green, and blue. Quarks can also have an anti-colour charge, which is the opposite of their colour charge.

## 4. Can colour charge be observed?

No, colour charge cannot be observed directly. Quarks and gluons, the particles that carry the strong force, are always confined within particles such as protons and neutrons, making it impossible to isolate individual quarks and observe their colour charge.

## 5. How does the strong interaction affect nuclear reactions?

The strong interaction plays a crucial role in nuclear reactions by determining which particles can interact with each other and how they can combine. For example, the strong interaction allows protons and neutrons to fuse together in the process of nuclear fusion, which powers the sun and other stars.

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