# Cusp anomalous dimension in QCD

What is the "cusp anomalous dimension", starting from the basics? I came across this term while reading some QCD papers.

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Better to ask what it is than to ask where to read about it. People will provide references if they need to. I'm editing accordingly. – David Z Dec 2 '11 at 9:40
@David: I looked up the reference, as the original question asked. I hope this is still useful. – Ron Maimon Dec 2 '11 at 11:38
Yeah, of course. If you don't know what something is but you can find a reference for it, that's generally a fine answer to a question asking what it is. – David Z Dec 2 '11 at 15:16
I think it's best as a comment, since it no longer answers the question. It is described here: arxiv.org/abs/hep-ph/9210281 . This is referenced by: arxiv.org/abs/hep-th/0204051 , which describes the string theory point of view about this. – Ron Maimon Dec 2 '11 at 18:25

So basically you start with some current in SCET. You do the matching on the full QCD and you observe that not all of the divergences cancel. As usual you have to introduce a counter-term in your effective theory. What is special in SCET is that at the one loop level your bare Willson coefficient will have terms of the order of $\frac{1}{\epsilon^2}$ and $\frac{1}{\epsilon}\ln\frac{Q^2}{\mu^2}$. So when you introduce a counter-term your renormalized coefficient will have double logs $\ln^2\frac{Q^2}{\mu^2}$. These are the so-called Sudakov double logarithms. As usual, you can calculate the anomalous dimension and after differentiating the double logarithmic term you will have following equation $$\frac{d}{d\ln\mu} C(Q^2,\mu) =\left[ \gamma_{cusp}\ln\frac{Q^2}{\mu^2}+\gamma_C\right] C(Q^2,\mu).$$ Because you had a double pole in $\epsilon$ your anomalous dimension has got a logarithmic term in it (in a typical field theory you would expect only $\gamma_C$ term to appear). And this term is called the cusp anomalous dimension. It allows to re-sum the Sudakov double logs.