Twist-2 relations for the twist-3 tensor-polarized distribution function $f_{LT}$ of a spin-1 hadron by the operator-product-expansion method

Abstract

In a spin-1 hadron, tensor-polarized parton distribution functions (PDFs) exist. The twist-2 function is $f_{1LL}$ and a twist-3 one is $f_{LT}$. Because an experiment is under preparation at the Thomas Jefferson National Accelerator Facility (JLab) to measure the cross section of electron-deuteron deep inelastic scattering with the tensor-polarized deuteron target, these PDFs need to be understood theoretically. Especially, measurements will be done in a relatively low-$Q^2$ region at JLab, so that twist-3 contributions could become sizable in the cross section. In a previous work, a twist-2 relation was derived for $f_{LT}$ in terms of $f_{1LL}$ by using a nonlocal operator, and it corresponds to the Wandzura-Wilczek (WW) relation between $g_1$ and $g_2$. In addition, another relation similar to the Burkhardt-Cottingham (BC) sum rule was obtained. It is known that a formal way to derive the WW relation and the BC sum rule is to use the operator product expansion (OPE) with local operators. In this work, the WW-like relation and the BC-like sum rule for $f_{LT}$ are derived by using the local OPE method as a reliable independent way to establish these relations.