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?

> the resulting theory would be able to predict these hadrons from first principles?

Not sure how bringing GR into the fray would help solve what essentially seems to be a computational complexity problem. Might actually make things worse.

It's not a computational complexity problem, it's an undefinedness problem. Proving that the lattice simulations converge has been estimated as well beyond this century's mathematics by the pair of people (Glimm and Jaffe) that have done the most to study it. In any case it is beyond today's.

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.

Give LQCD practitioners resources on the scale of the experiment, the computations will get faster!

I'm not sure what they mean by "Predictions rely on approximate analytical methods such as effective field theories." The predictions of LQCD are ab initio. Sometimes we fit EFTs to LQCD results, that's true. But EFTs are under control and have quantifiable uncertainties, they're not just willy-nilly approximations.

May be referring not to LQCD relying on approximate analytical methods but some of the other non-perturbative methods? Example would be trying to apply homotopy analysis method (HAM) or a related transform to whatever field equations to make some semi-analytical predictions.

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.

AdS/CFT is already an example of an approach to gravity yielding an approach to strongly coupled field theories.

It's an approach to a hypothetical other type of universe's gravity..