Determine whether the evanescent-operator prescription extends consistently beyond one loop

Determine whether the finite-renormalization prescription associated with retaining the evanescent operator generated by the loop-contracted transverse index can be organized consistently beyond one loop for unpolarized gluon pseudo-distribution matching.

Background

The paper finds that a published gluon matching kernel omits an evanescent operator because a loop-generated Lorentz index is summed over two transverse directions instead of d-2. Since the omitted operator multiplies a collinear pole, its omission generates a finite polynomial difference in the one-loop kernel.

The authors express the published prescription as matching to a finitely renormalized gluon distribution, denoted f_4, and explicitly leave unresolved whether this prescription can be extended consistently beyond one loop.

References

Whether this prescription can be organized consistently beyond one loop we do not address.

— Unpolarized quasi- and pseudo-distributions at one loop: gluon correlator decomposition, matching, and the region $|x|>1$  (2609.40205 - Monahan et al., 30 Sep 2026) in Section 6, subsection “Gluon in gluon,” paragraph beginning “Comparison with refs.”