Burkhardt-Cottingham-type sum rules for light-cone and quasi-PDFs

The Burkhardt-Cottingham (BC) sum rule connects the twist-3 light-cone parton distribution function (PDF) gT(x) to the twist-2 helicity PDF g1(x). The chiral-odd counterpart of the BC sum rule relates the twist-3 light-cone PDF hL(x) to the twist-2 transversity PDF h1(x). These BC-type sum rules can also be derived for the corresponding quasi-PDFs. We perform a perturbative check of the BC-type sum rules in the quark target model and the Yukawa model, by going beyond the ultraviolet (UV) divergent terms. We employ dimensional regularization (DR) and cutoff schemes to regulate UV divergences, and show that the BC-type sum rules hold for DR, while they are generally violated when using a cutoff. This violation can be traced back to the breaking of rotational invariance. We find corresponding results for the sum rule relating the mass of the target to the twist-3 PDF e(x). Moreover, we supplement our analytical results with numerical calculations.

Automated summary

In this study, we perform a perturbative check of the BC-type sum rules in the quark target model and the Yukawa model, and find that the BC-type sum rules hold for dimensional regularization (DR) but are generally violated when using a cutoff.