Establish a consistent beyond-one-loop prescription for the polarized gluon matching kernel

Establish whether the dimensional-regularization prescription for the Levi-Civita tensor, together with the transverse-trace prescription, can be organized consistently beyond one loop for polarized gluon matching, and determine the finite conversion required to obtain the polarized gluon distribution in the MS-bar scheme.

Background

The paper identifies two scheme choices in polarized gluon matching: the treatment of the transverse trace and the continuation of the antisymmetric tensor epsilon{mu nu rho sigma} away from four dimensions. Both choices affect operators multiplying collinear poles and therefore can produce finite scheme-dependent differences in the matching kernel.

The authors state that the relevant prescription is not specified in the cited polarized calculation and that the calculation has not been repeated, leaving both the convention and the required conversion unresolved.

References

Neither prescription is stated in ref., and we have not repeated that calculation, so the convention of the polarized kernel, and the conversion it requires to reach the polarized gluon distribution in , are left open.

— 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 7, “Conclusions and Outlook,” paragraph beginning “The form-factor decomposition separates”