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We study the $Q^2$ dependence of the chiral-odd twist-3 distribution$e(x,Q^2)$.The anomalous dimension matrix for the corresponding twist-3operators is calculated in the one-loop level. This study completes thecalculation of the anomalous dimension matrices for all the twist-3distributions together with the known results for the other twist-3distributions $g_2(x,Q^2)$ and $h_L(x,Q^2)$. We also have confirmed that in thelarge $N_c$ limit the $Q^2$-evolution of $e(x,Q^2)$ is wholely governed by thelowest eigenvalue of the anomalous dimension matrix which takes a very simpleanalytic form as in the case of $g_2$ and $h_L$.Comment: 16 pages LaTeX, 4 postscript figure

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>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>evolution of chiral-odd twist-3 distribution<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:…

Q2evolution of chiral-odd twist-3 distributione(x,Q2