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Within Baryons is the force holding them together purely gluons or are pions involved? Between protons and neutrons in a nuclei is it purely the exchange of pions between baryons which hold the baryons together? Is the force between gluons the strong force? and the force between baryons the residual nuclear force? I feel sources online talk about each of these questions without being concise and clear about the overall strong force

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    $\begingroup$ The picture of forces being mediated by the exchange of particles is a description of computational method, not a description of the underlying principles (physics.stackexchange.com/a/339841). The gluon field is responsible for forces both within and between baryons, in the sense that deleting the gluon field would eliminate both of them (neither baryons nor pions would exist); but understanding how either of those forces comes from QCD (intuitively, not just numerically) is a hard problem that is still being studied. QCD is clear and concise, but deriving these predictions is hard. $\endgroup$ – Chiral Anomaly Apr 7 at 13:11
  • $\begingroup$ Related: physics.stackexchange.com/questions/288357/… $\endgroup$ – Lewis Miller Apr 8 at 1:59
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It is the strong nuclear force that binds quarks together into protons and neutrons, it is stronger then any other of the known fundamental forces at 10^-15m distances.

The strong force is observable at two distances mediated by two force carriers.

  1. On the larger scale, 1 to 3 fm it is mediated by mesons and the force that binds protons and neutrons. it is called the residual strong force or nuclear force

  2. on the shorter range, 0.8 fm, it is the force that is mediated by gluons that binds quarks together to form protons and neutrons and other hadrons too. It is mediated by gluons, betweeen quarks, antiquarks and other gluons.

Now, the residual strong force (between neutrons and protons), has a really interesting characteristic when it is about distance.

  1. It is very strong at about 1 fm, but it decreases very fast until it is not significant anymore at 2.5 fm.

  2. At distances less then 0.7 fm, it becomes repulsive. It is why nuclei have their physical size, because neutrons and protons cannot come any closer then this distance.

This is very interestinf because the strong force (color force) itself (between quarks and gluons) is attractive only.

This is why we call the nuclear force a residual effect of the fundamental strong force or color force.

Similarly, even though nucleons are made of quarks in combinations which cancel most gluon forces (they are "color neutral"), some combinations of quarks and gluons nevertheless leak away from nucleons, in the form of short-range nuclear force fields that extend from one nucleon to another nearby nucleon. These nuclear forces are very weak compared to direct gluon forces ("color forces" or strong forces) inside nucleons, and the nuclear forces extend only over a few nuclear diameters, falling exponentially with distance. Nevertheless, they are strong enough to bind neutrons and protons over short distances, and overcome the electrical repulsion between protons in the nucleus.

Now, you are asking about the mediators.

  1. inside the neutron and proton, the color force (strong interaction) is mediated by gluons between quarks, antiquarks, and other gluons

  2. the nuclear force (residual strong force) between neutrons and protons is mediated by virtual light mesons, pions, rho and omega. The difference between them is that the rho and omega are responsible for the spin dependence of the nuclear force. Let me explain that a little but more. You asked if the nuclear force is mediated by pions. Yes it is. But not only. Neutrons and protons were thought to be identical other than the EM charge. This is not completely true, neutrons are heavier because of one of their characteristics, that we call isospin.

Now let's clear the mediator a little bit. You would think that these interactions are mediated by real actual particles that we call pion and rho and omega. Unfortunetaly, it is a little bit more complicated. The reasidual strong force is mediated by virtual mesons. What this means is that these are just a mathematical artifact, a mathematical description of the interaction, and not actual real particles. We do not actually know physically how these interactions are mediated, so we do not know whether real actual pions would be flying between the neutron and the proton. This is not the reality. We do not know what is actually flying between them or if anything is really. What we do, is that we use virtual particles to describe the interaction between them, and fit them to the experimental data. Since the data match our theories of these virtual particles, we take them as being an accurate description of the force.

Analogically to the EM force, where we say that virtual photons are mediating the EM force, these virtual photons are not real actual particles, but a mathematical description of the EM interaction.

This is the same inside the neutron and proton. The color force is mediated by virtual gluons between real quarks, antiquarks, and real gluons. Virtual gluons are a mathematical description of the color force interactions.

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