Comment by photochemsyn
3 years ago
As I understand it, the reason Feynman diagrams in quantum electrodynamics (where the primary entities are electrons and photons) can be used to calculate properties very accurately is that the electromagnetic coupling constant (1/137) results in the higher-order terms in a series eventually vanishing away to nothing, while with the strong force the coupling constant is >= 1, so the higher-order terms have to be included, leading to things like infinities (or at the very least, ratios of very large quantities with correspondingly large uncertainties).
The strong force is a bit confusing, as it binds boths quarks with the proton and neutron, as well as binding the neutrons and protons into atomic nuclei, over short ranges (accounting for the upper size limit / stability limit of the largest nuclei). Mesons are the force-carrying entity that bind the neutrons and protons together, but gluons are the force-carrying entity that bind the quarks together, as per this wiki article:
https://en.wikipedia.org/wiki/Strong_interaction
Is it the case that theoretical strong-force calculations have just hit a dead-end and there's no way out in sight, due to the coupling constant issue?
Actually there's a bit more to it than that. Coupling constants change as a function of their energy, they're called 'running coupling constants'. As a result of this phenomenon, there are domains where alpha_s is small and therefore a perturbative expansion of terms is possible. This happens at very high energies, so at the LHC we can happily calculate the higher order terms that you talk about and each successive term is a smaller contribution than the last.
Unfortunately, alpha_s is large at low energies, and by low I mean at the atomic and nuclear scale. There you are well and truly in the domain that perturbative QCD is impossible. The only option at that point is something called lattice QCD at the quark/gluon level.
Edit: Typo
I have idly wondered whether or not there could be a completely different approach to QCD from the usual perturbative techniques. I remember reading in one of Zee's books that back 80s he pointed out to Feynman that the path integral formalism that QFT is based on has no natural way to treat something as simple as a particle in a box. And an object like a proton seems to be more like a particle in a box than a free particle undergoing an interaction.
Yeah as someone who spent 4 years of his life calculating a second order term (Next-to-Next-to-Leading-Order), I have often wondered the same thing! In my original post I grossly simplified how challenging it is to calculate terms in perturbative QCD, even when in the perturbative regime. To name a few:-
* Two loop calculations are extremely challenging on an algebraic level
* You get low energy (called 'infrared red') infinities appearing at low energies. These need to cancel between all your contributing terms, and getting them to cancel is really really challenging.
* The numerical Monte Carlo approaches become extremely computationally intensive because of high dimensional integrals and numerical instability caused by point 2
It was not uncommon for calculations of single terms to involve multiple PhD students over a decade or more.
Throughout my PhD I certainly felt like something was fundamentally 'wrong' with the approach. Alas, I wasn't smart enough to rewrite the field with a whole new way of thinking so bailed instead.
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Lattice methods are probably the most common nonperturbative approach to QCD.
How does the strong force bind neutrons to protons? Is it connecting the quarks inside the proton with those of the neutron?
How nucleons (neutrons and protons) are bound together is similar to a molecule. If they are close enough, they can 'share' their constituent quarks. You can calculate the interaction by a feynman diagram where the two nucleons exchange one quark in each direction. This is technically the same as one nucleon sending and the other absorbing a quark-antiquark pair, which is why physicists like to say that the nucleon attraction is transmitted by mesons (quark-antiquark pairs). Of course fundamentally the strong force still facilitates the whole interaction, as it's the one preventing nucleons from just falling apart into quarks.
That's the role the meson (a quark-antiquark pair particle) carries out, but I agree it's confusing. Here's a question from physics stack exchange (without any really clear answers, other than "go look up 'residual strong force'", not very helpful) that spells it out:
> "I just read somewhere that both gluons and mesons transmit the strong force, gluons between quarks inside hadrons, but mesons between nucleons. I thought that the strong force would have one field, and one associated particle, whether inside hadrons, or between nucleons"
https://physics.stackexchange.com/questions/296457/gluons-an...
no, you're just going wrong about it; nothing Feynman was doing was new. Except for the fact he had a nice semi-directed graph to make sense of the celestial equations and the quintuple of the time; the Dirac Sea, etc