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Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with a coupling constant given via the beta function?

Qmechanic
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dan-ros
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  • Related: http://physics.stackexchange.com/q/118825/2451 and links therein. – Qmechanic Jun 11 '15 at 16:50
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    Because we only know how to calculate $\beta$ function through perturbative expansion (i.e. Feynman diagrams), no matter how many loops you go to. And the real puzzle is about the dynamics at IR, which is almost for sure controlled by non-perturbative expansion at strong coupling. – Meng Cheng Jun 11 '15 at 17:19
  • @Meng that's basically a short answer, or the beginning of an answer – innisfree Jun 11 '15 at 17:39

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