A bestiary of exotic hadrons

>The dynamics of quarks and gluons can be described perturbatively in hard processes thanks to the smallness of the strong coupling constant at short distances, but the spectrum of stable hadrons is affected by non-perturbative effects and cannot be computed from the fundamental theory. Though lattice QCD attempts this by discretising space–time in a cubic lattice, the results are time consuming and limited in precision by computational power. Predictions rely on approximate analytical methods such as effective field theories.

I'm glad this was mentioned, non-perturbative effects are not well understood and this is a big part of why it's worthwhile to study bound states of the strong force.

I assume that if we ever unify QCD with General Relativity, the resulting theory would be able to predict these hadrons from first principles?

No. The reason perturbation theory doesn’t work as well for QCD as it does for QED is because of two reasons:

1. The coupling constant of QCD is much higher than QED so contributions to the overall result from Feynman diagrams that have more vertices (the multiplicative factor of each element in the sum is proportional to the power of the number of vertices) don’t vanish as quickly as they do for QED

2. The gauge bosons in QCD (i.e. gluons) themselves have colour charge whereas those in QED (i.e. photons) do not have electrical charge.

You can't give a definite no to that because, since gravitons have stress-energy and are non-perturbative, a field theory advance that worked for them could also help with the strong force.

I mean sure, since we don't know what GR + QFT could look like, the result could be just about anything and somehow give us nice closed solutions to QCD problems. But I don't feel like that line of reasoning is particularly useful.