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We investigate the $Q^{2}$-evolution of the chiral-odd spin-dependent partondistribution $h_{L}(x, Q^{2})$ relevant for the polarized Drell-Yan processes.The results are obtained in the leading logarithmic order in the framework ofthe renormalization group and the standard QCD perturbation theory. Wecalculate the anomalous dimension matrix for the twist-3 operators for $h_{L}$in the one-loop order. The operator mixing among the relevant twist-3 operatorsincluding the operators proportional to the QCD equations of motion is treatedproperly in a consistent scheme. Implications for future experiments are alsodiscussed.Comment: HUPD-9419, Latex file, 21 pages, 7 figures available on reques

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>evolution of the nucleon’s chiral-odd twist-three structure function:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">h</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">L</mml:mi…

Q2evolution of the nucleon’s chiral-odd twist-three structure function:hL