Tensor-polarized twist-3 distribution function $f_{LT}$ of spin-1 deuteron

Abstract

We investigate the twist-2 and twist-3 tensor-polarized partonic structures of the spin-1 deuteron. Using the operator product expansion with local operators, we derive a Wandzura-Wilczek (WW)-like twist-2 relation between the tensor-polarized twist-2 quark distribution $f_{1LL}$ and the twist-3 distribution $f_{LT}$, together with a Burkhardt-Cottingham (BC)-like sum rule. The local-operator formalism makes the Lorentz structure and rotational invariance manifest and provides useful constraints on the twist-3 sector. We then use a phenomenological parametrization of the twist-2 distribution $f_{1LL}(x)$, constrained by HERMES data on the deuteron structure function $b_1$ at $Q^2=2.5~\text{GeV}^2$, to quantitatively estimate the twist-3 distribution $f_{LT}(x)$ within the WW approximation. The resulting $f_{LT}(x)$ has a shape and magnitude comparable to those of $f_{1LL}(x)$, indicating that subleading-twist effects may be relevant for future experiments at relatively low $Q^2$. In this contribution, we summarize the theoretical derivation of the WW-like relation and BC-like sum rule and present a phenomenological estimate of the tensor-polarized twist-3 quark distribution $f_{LT}$ in the deuteron.