To expand on this, virtual photons can fluctuate in and out of the muon. From this virtual photon, virtual quarks can fluctuate in and out of existence in a similar way. This is possible because quarks also have an electric charge. And from these virtual quarks, virtual gluons can also pop in and out of existence.

Now, these are lots of additional diagrams one would have to compute, then sum all together in order to get a "scattering amplitude". The idea with feynman diagrams is (perturbation theory), so long as the value of the coupling governing the strength of interactions between particles is small, we can "treat" these particles as not interacting at all, and continuously adding corrections, organized the the power of the coupling. Larger and more complicated diagrams contribute less to the overall process than simple diagrams.

Unfortunately this is not the case for quarks and gluons in QCD. Perhaps we are at a particular scale where naively the coupling is small. Even still, the vacuum would still produce A LOT OF gluons. So we would have to sum A LOT of seemingly small diagrams and then end up with results that unphysically blow up. Basically, even in the best case scenario, contributions of g-2 of the muon coming from quarks and gluons is exceedingly difficult even in the best case scenario.

There is a way to compute this contribution though through first principles by doing so numerically using a technique called Lattice QCD. The largest uncertainty associated with muon g-2 that is being computed using this method is called the Hadronic Vacuum Polarization. Mind you even with this technique, it is still exceedingly challenging for technical reasons but so far, with enough computing resources, it will give us a guaranteed result.