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

Abstract

The Burkhardt-Cottingham (BC) sum rule connects the twist-3 light-cone parton distribution function (PDF) $g_T(x)$ to the twist-2 helicity PDF $g_1(x)$. The chiral-odd counterpart of the BC sum rule relates the twist-3 light-cone PDF $h_L(x)$ to the twist-2 transversity PDF $h_1(x)$. 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 ultra-violet (UV) divergent terms. We employ dimensional regularization (DR) and cut-off schemes to regulate UV divergences, and show that the BC-type sum rules hold for DR, while they are generally violated when using a cut-off. 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.

arXiv commentVersion accepted for PRD: Minor additions to text; 38 pages, 2 figures

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