What keeps quarks separate (strong force pulls, but what repels to equal out)

We know that the strong force keeps quarks together, that is mediated by gluons (and their charge is called color charge). We know that the residual strong force keeps neutrons and protons together in the nucleus (called the nuclear force), and that is mediated by Pions (quark and anti-quark). We know that electric charge can repel (same charge) or pull (opposite charge). But I do not see anywhere if color charge can repel, i only see that it can pull. We know that protons and neutrons are stable together in a nucleus, because two forces equal out (nuclear force pulls and electric charge repels).

Questions:

1. Since strong force (mediated by gluons) pulls quarks together, what keeps quarks separate from each other, meaning why are quarks not coming closer together and crush into each other? I only see the strong force pulling, but what is the other force, that repels here and equals out?

2. I understand that in case of two Protons, two forces equal out, electric force repels, and nuclear force pulls. That is why two protons are stable in a nucleus and are not flying away and are not crushing into each other either. In case of a Neutron, there is no electric force to repel, but there is still nuclear force to pull, so a neutron is pulled together to another neutron or a proton, but what keeps the neutron from crushing into another neutron or proton?

Since strong force (mediated by gluons) pulls quarks together, what keeps quarks separate from each other, meaning why are quarks not coming closer together and crush into each other? I only see the strong force pulling, but what is the other force, that repels here and equals out?

To start with quarks , in contrast to protons and neutrons, are not composite, they are elementary particles in the standard model of particle physics which describes the data up to now .

Here is an illustration that describes what is happening within the composite proton: Quarks and antiquarks and gluons dance around and annihilate and pair produce in a non stop manner, so they do "overlap" in the feynman diagrams of the individual interactions, and annihilate. The three valence quarks are lost in the soup, and in any case it is a matter of conservation of quantum numbers, there should be an excess of one down and two up for the proton.

So it is not a matter of repelling, it is just that overall the quarkness up and down should add up to the valence quarks of a proton, and the same holds for the neutron two down one up excess in the soup .

I understand that in case of two Protons, two forces equal out, electric force repels, and nuclear force pulls. That is why two protons are stable in a nucleus and are not flying away and are not crushing into each other either. In case of a Neutron, there is no electric force to repel, but there is still nuclear force to pull, so a neutron is pulled together to another neutron or a proton, but what keeps the neutron from crushing into another neutron or proton?

A neutron, as well as a proton, is a bound state of QCD. As bound as a hydrogen atom. For the same reason that if you hit two hydrogen atoms on each other at low energies they remain hydrogen atoms, hitting two neutrons at low energy on each other they remain neutrons, a specific(complicated) bound state of quarks. At high energy they will create a lot of quark antiquark pairs, the same as the results seen in the LHC proton proton scatters, though baryon number conservation holds in all elementary particle interactions.

In conclusion it is not about pushing and repelling but about conserved quantum numbers and/or bound states.

In lattice QCD they assume a potential and there they can approximately solve to find masses for pions and kaons, within the limits of the model.

• There are actually two more features in the soup that might address the OP's question. First, as two quarks get far too close, asymptotic freedom makes their gluon interaction essentially insignificant -- their are freed from each other. And if they are the same kind they exclude each other by the Pauli principle; if not some type of antisymmetrization may also be provided by a generalized version of that principle. It may be his vision of "crushing" quarks that's obscure... – Cosmas Zachos Mar 27 '18 at 14:12
• Dear Anna v, thank you so much, now i understand that there is a sea of quarks and that they pop out of vacuum and annihilate all the time so there is no need for repulsion so I understand your answer for question #1. But what I do not understand is, the answer to #2. In the case of protons it is obvious, because they repel each other electomagnetically, and stick together because of the nuclear force. But in the case of neutrons, there is no electomagnetic repulsion. Just the residual force pulling them. So why are two neutrons not pulling each other too close and becoming one sea of quarks? – Árpád Szendrei Mar 27 '18 at 16:38
• So what keeps two neutrons separate? Why is the two seas of quarks not coming together into one sea? What is the separating line between two neutrons? Why is a neutron strictly a certain amount of quarks making a certain size of sea, that is confined by what? So why cannot two neutrons, become a bigger sea of quarks? There must be something separating them or something confining the separate neutrons and a strict rule that prohibits neutrons from having more then a certain number of quarks? – Árpád Szendrei Mar 27 '18 at 16:43
• I thought I explained that. Because the neutron is a bound state, and bound states need energy to free the contents (quarks) from their potential trap , and the energy within nuclei is not enough for that. – anna v Mar 27 '18 at 16:43
• Oh OK, so you are saying that this is the strict rule that I was asking about, so this bound state is what determines how many quarks can be in the neutron? I understand that the bound state traps the quarks into a neutron. Does this bound state have any explanation? Is this like a rule that says a certain amount of quarks can be together, not less and not more, and that is a neutron? Anything else is not stable? Or is this bound state explained with a boundary layer around the neutron? – Árpád Szendrei Mar 27 '18 at 16:50
1. The strong force does pull quarks together, but it also gets weaker as the quarks get closer (i.e. it acts sort of like a spring), in a phenomenon known as "asymptotic freedom." In this way, the strong force is very different than electromagnetism, where the force gets stronger if the charges are closer together. As such, there's no reason to expect that quarks which are placed close together will immediately annihilate, as there's just not a lot of force on them in the first place.

2. The force that holds nucleons together is described by the nucleon-nucleon (NN) potential, which looks like this (horizontal axis is $r$, vertical axis is $V$): The NN potential is a residual interaction resulting from very long-range reactions between quarks in adjacent nucleons. Since the reaction is long-range, color charge (and therefore gluons) cannot be exchanged. As such, the mediators for this force are color-neutral, and consist of the lighter mesons (like $\pi$, $\rho$, and $\sigma$). Because of this, the nature of this residual interaction is completely different from the quark-level strong interaction. In particular, note the strong repulsion that happens at distances less than 1 fm (i.e. the diameter of a nucleon). This repulsion, mediated by vector-meson ($\rho$) exchange, is what keeps protons and neutrons apart.

• Dear probably_someone, you are saying that the residual strong force is a repulsion? So the pion that is mediated between two neutrons is making them repulse? So then what keeps neutrons stick together? I thought it is the nuclear force (residual strong force) that keeps neutrons together? Is it then repulsive or attractive? – Árpád Szendrei Mar 27 '18 at 16:30
• No, I'm saying that the residual strong force obeys the potential I displayed. It's attractive at long distances and repulsive at short distances. – probably_someone Mar 27 '18 at 16:31
• OK so one force acts like two forces, depending on the distance? It mediates the same particles, pions, and the same pions mediate repulsion at short distances and mediate attraction at long distances, and that equals out in a middle distance? – Árpád Szendrei Mar 27 '18 at 16:53
• I'm saying that I'm not sure that you can picture individual mesons as contributing only attraction or repulsion (as opposed to some combination of both). Look at the $\sigma$-exchange region, for instance. – probably_someone Mar 27 '18 at 17:16
• I'm saying that the notion that an individual force must be either purely attractive or purely repulsive is incorrect. Even in classical mechanics, the force on a mass attached to a wall by a spring is attractive if the mass is further from the wall than the spring's equilibrium length, and is repulsive if the mass is closer to the wall than the equilibrium length. – probably_someone Mar 27 '18 at 17:21