Tensor-polarized twist-3 parton distribution functions $f_{LT}(x)$ for the spin-1 deuteron by using twist-2 relations

Abstract

Tensor-polarized twist-3 parton distribution functions (PDFs) $f_{LT}(x)$ are calculated for the spin-1 deuteron by using twist-2 relations, which are similar to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule in the spin-1/2 nucleon, together with tensor-polarized twist-2 PDFs $f_{1LL}(x)$. The PDFs are shown for $f_{LT}(x)$ at $Q^2 =2.5$ GeV$^2$, where the tensor-polarized PDFs $f_{1LL}(x)$ are provided. The $x$-dependence of $f_{LT}(x)$ is similar to $f_{1LL}(x)$, and the magnitude of $f_{LT}(x)$ is roughly of the order of $f_{1LL}(x)$. In experiments at the Thomas Jefferson National Accelerator Facility (JLab), higher-twist effects could be sizable because $Q^2$ values are not very large in comparison with the hadronic scale of 1 GeV$^2$. Therefore, the JLab experiments could provide a good opportunity to investigate the twist-3 distributions $f_{LT}(x)$ in addition to the twist-2 ones $f_{1LL}(x)$. Furthermore, these tensor-polarized PDFs could be investigated at future Electron-Ion Colliders (EICs) and hadron accelerator facilities such as the Fermi National Accelerator Laboratory (Fermilab), the Nuclotron-based Ion Collider fAcility (NICA), and the Large Hadron Collider (LHC).

Figures (4)

• Figure 1: Tensor polarized PDFs $\delta_T f$ for the deuteron at $Q^2=2.5$ GeV$^2$ for explaining the HERMES data. The PDFs are shown by the ones per nucleon.
• Figure 2: Tensor-polarized twist-2 distribution functions $xf_{1LL}^{\, q/D +} = x f_{1LL}^{\, q/D} + x f_{1LL}^{\, \bar{q}/D}$ are shown for the deuteron at $Q^2=2.5$ GeV$^2$. The solid curve indicates the distribution for $q=u$ or $d$, and the dashed curve is the distribution for $q=s$. The PDFs are shown by the ones per nucleon.
• Figure 3: Tensor-polarized twist-3 distribution functions $xf_{LT}^{\, q/D +} = x f_{LT}^{\, q/D} + x f_{LT}^{\, \bar{q}/D}$ are shown for the deuteron at $Q^2=2.5$ GeV$^2$. The solid curve indicates the distribution for $q=u$ or $d$, and the dashed curve is the distribution for $q=s$. The PDFs are shown by the ones per nucleon.
• Figure 4: Tensor-polarized twist-3 distribution functions $xf_{2LT}^{\, q/D +} = x f_{2LT}^{\, q/D} + x f_{2LT}^{\, \bar{q}/D}$ are shown for the deuteron at $Q^2=2.5$ GeV$^2$. The solid curve indicates the distribution for $q=u$ or $d$, and the dashed curve is the distribution for $q=s$. The PDFs are shown by the ones per nucleon.