# Is even the perturbative expansion of the QCD beta function expected to be divergent?

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The usual QCD folklore tells us that perturbative expansions are (at best) asymptotic. Recently a colleague of mine told me that the expansion of the beta function is thought to be convergent because , and I quote, "it only sees the UV".

This would-be argument does not convince me at all but I wonder if he really is full of shit or for some reasons that I don't yet comprehend he is right. So, is he right? and if so, why?

asked Apr 17, 2016
retagged Apr 18, 2016

I don't know if your college supplemented it with other arguments, but just "it only sees the UV" looks completely nonsensical.

In the absence of theory, guesses about convergence are sujective plausibility reasoning. I think you should ask your collegue about what precisely he meant with his cryptic remark, and then expand here on your question. There may be something less trivial behind it.

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