In this Feynman diagram for the nuclear force, it labels this exchange as a pion. However, I was under the impression that this force was mediated by gluons. In the caption for this picture, it says the circles are gluons. Could someone elaborate on why there is this pion label here and what is going on with the gluons in this depiction?
The standard model of particle physics is a fundamental theory that exist at high energy or short distance scales. When we look at lower energies or larger distance scales, we don't see this fundamental theory anymore. We see effective theories that come about due to changes that occur at certain energy/distance scales. In the case of quantum chromodynamics (QCD), there is a QCD scale where the force becomes so strong that the constituents (quarks) become confined. Above the QCD scale (or at distances smaller than the QCD scale), we can still see quarks and gluons, but below it we only see the composite particles. These composite particles include the proton and neutron and all the pions. While the gluons are the exchange particles that mediate the strong force above the QCD scale, the pions are the exchange particles that mediate the strong force below the QCD scale. It is called Yukawa theory.
The diagram probably tries to represent one particular representation of the colors of quarks and the gluons that bind them together inside the composite particles. However, it is not clear what the representation should mean. Neither is this a complete picture, because it should also exist in superposition with all other possible assignments of the colors.
Quantum field theory is a mathematical tool with which to model quantum mechanical interactions, this means at the level of measurement accuracies where h, the Planck constant can no longer be considered as zero. Where classical mechanics and electrodynamics modeling fails.
Gluons are part of the quantum field theory of elementary particle interactions, and the standard model is very good in modeling the scattering and decay experimental data. This is the underlying level for all models. But for complex systems a number of quantum field theories have developed that model successfully experimental measurements. These theories use the Feynman diagram method to calculate and show how they are used, one of them is shown in the diagram of your question.
Back in 1961 I was taught this field theory in a nuclear physics course, and it has survived because of its successes in predicting the behavior of nuclear interactions, complex in elementary particle exchange.
Could someone elaborate on why there is this pion label here and what is going on with the gluons in this depiction?
At the elementary particle level the pion is a bound state of a quark and antiquark, it just happens that at certain kinematic regions, the large number of strong interaction gluon and other particle exchanges give high probability for the exchange fitting a virtual pion in a QFT model.
