Higher-twist hadronic tensor in deep inelastic scattering with massive quarks

Abstract

In this paper, we calculate the inclusive deep inelastic scattering (DIS) with finite quark masses up to twist-4 accuracy based on collinear expansion method. The collinear expansion method not only naturally leads to gauge-invariant correlation functions and parton distribution functions, but also yields a remarkably compact expression for the hadronic tensor. The resulting hadronic tensor can be organized according to the corresponding power behavior in $1/Q$. In particular, the explicit quark-mass dependence gives rise to additional power-suppressed contributions and the ratio $m/Q$ can be counted as a twist-3 contribution in the power expansion. As an application, we further investigate the role of transversity in inclusive DIS with a transversely polarized target. We find that the transversity distribution appears explicitly in the quark-quark correlation function and gives rise to a contribution proportional to $m~h_{1T}/Q$. However, this contribution is exactly cancelled in the hadronic tensor by the one arising from the corresponding quark-gluon-quark correlation function. This cancellation shows that, within the one-photon-exchange approximation, the mass-induced transversity term cancels in the complete twist-3 hadronic tensor, and no net transversity contribution remains at twist-3 accuracy in inclusive DIS. We complement this analytical study with numerical estimates of the $g_T$-related twist-3 asymmetry, comparing predictions with and without the mass-dependent $x\rightarrowχ$ rescaling at the same measured $x$. The results show that these kinematic mass effects become more important at lower $Q^2$ and larger $x$.