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) $g_{T}(x)$ to twist-2 helicity PDF $g_{1}(x)$. chiral-odd counterpart of BC relates $h_{L}(x)$ transversity $h_{1}(x)$. These BC-type rules can also be derived for corresponding quasi-PDFs. We perform a perturbative check in quark target model and Yukawa model, by going beyond ultra-violet (UV) divergent terms. employ dimensional regularization (DR) cut-off schemes regulate UV divergences, show that hold DR, while they are generally violated when using cut-off. This violation traced back breaking rotational invariance. find results relating mass $e(x)$. Moreover, we supplement our analytical with numerical calculations.