Comment by morbia

3 years ago

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

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morbia

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antognini  3 years ago

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.

  • morbia  3 years ago

    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.