Kln theorem and initial-state singularities

[eoghan]

Hi!
If I have a pair q\bar q g in a final state, I know that the gluon has a IR singularity. But KLN theorem rescues me: if I sum over all degenerate states the IR singularity cancels away.
Otherwise, if the emission of the soft gluon is in an initial state, then the IR divergence cannot be canceled. Why KLN doesn't work for initial-state singularities?
I'm thinking of the hard scattering of a parton from an hadron with a target. If the parton radiates a gluon before it hits the target, then I can't cancel the IR singularity, unless I "renormalize" the parton distribution function. Why can't I sum over all initial degenerate states to cancel the singularity?

 

[CAF123]

This is a post from 2012 but I was wondering the same question ^^ - the remnant IR divergences coming from collinear/soft gluons in the initial state are 'put under the rug' into the PDF associated with the mother hadron from which the parton came from. This is the treatment I have seen everywhere but if I did an inclusive summation over all initial degenerate states would I get no IR divergences as the KLN theorem perhaps tells me and, if so, what would such initial states look like?