Next-to-leading orderQ2evolution of the transversity distributionh1(x,Q2)

We present a calculation of the two-loop anomalous dimension for the transversity distribution $h_1{(x,Q}^2)$, ${\gamma }_n^{h\left(1\right)\mathrm{}}$, in the MS scheme of dimensional regularization. Because of the chiral-odd nature, $h_1$ does not mix with the gluon distributions, and thus our result is the same for the flavor-singlet and -nonsinglet distributions. At small $n$ (moment of $h_1)$, ${\gamma }_n^{h\left(1\right)\mathrm{}}$ is significantly larger than ${\gamma }_n^{f\left(1\right)\mathrm{}}$ (the anomalous dimension for the nonsinglet $f_1)$, but approaches ${\gamma }_n^{f\left(1\right)\mathrm{}}$ very quickly at large $n$, keeping the relation ${\gamma }_n^{h\left(1\right)\mathrm{}}>{\gamma }_n^{f\left(1\right)\mathrm{}}$. This feature is in parallel to the relation between the one-loop anomalous dimension for $f_1$ and $h_1$.