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The operator product expansion systematically expands QFT interactions in terms of a sum of local operators.

Is the leading twist of this expansion identifiable with collinear factorisation and, if so, how is this reconciled with the fact that the input Parton densities are quantum field theoretically defined in terms of non-local operators?

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I'm not well-educated on this topic but maybe this helps you anyway:

In Weinberg's vol. 2 there is a section about deep inelastic scattering, in which it is shown that the correspondence between the local operator expectation values of the OPE and the PDF holds only for the moments (i.e. Mellin transform) of the PDF (but without using operator definitions of the PDFs). So you can not just identify the PDFs with the local operators of the OPE.

You might want to take a look at this paper which defines the operator representations of PDFs. It has a section on how to relate these to local twist-two operators. But it is also noted that the relation is approximate.

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  • $\begingroup$ Thank you for the answer and your reference! As I understand, the relation between the Mellin moments of the PDFs and the local operators of the OPE are exact but that the relation between the DIS structure function and the local operators is only approximate. The latter relation then becomes exact when one restores the Wilson coefficients as multiplicative coefficients of the local operators. $\endgroup$
    – CAF
    Commented Oct 1, 2020 at 8:00

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