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If I have a pair [itex]q\bar q g[/itex] 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?

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# Kln theorem and initial-state singularities

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