${\mathit{Q}}^2$ evolution of the nucleon’s chiral-odd twist-three structure function: ${\mathit{h}}_{\mathit{L}}$(x,${\mathit{Q}}^2$)

We investigate the ${\mathit{Q}}^2$ evolution of the chiral-odd spin-dependent parton distribution ${\mathit{h}}_{\mathit{L}}$(x,${\mathit{Q}}^2$) relevant for the polarized Drell-Yan processes. The results are obtained in the leading logarithmic order in the framework of the renormalization group and the standard QCD perturbation theory. We calculate the anomalous dimension matrix for the twist-three operators for ${\mathit{h}}_{\mathit{L}}$ in the one-loop order. The operator mixing among the relevant twist-three operators including the operators proportional to the QCD equations of motion is treated properly in a consistent scheme. Implications for future experiments are also discussed.