In higher-spin CFT, operators organize themselves into additive multi-twist. I am a bit confused as to the use of "twist-two", "leading-twist", etc. Especially when it mentioned in the context of QCD as it is used in a matter of a fact way.
Is it just the decomposition of a higher-spin operator so that it remain a primary traceless symmetric tensor operator? What I mean by that is: would a spin $J$ trace-two operator $\mathcal{O}_J$ look like $$\mathcal{O}_J = :\phi \partial_{\mu}^{J} \phi: + \partial_{\mu}(\cdots)~?$$ How do I reach this expression from the index-free notation of a higher-spin operator?
Why is twist-two the leading twist? In Lorentzian signature, why is normal ordering necessary when defining such operators?
