Next-to-leading order Q^2-evolution of the transversity distribution h_1(x, Q^2)

Abstract

We present a calculation of the two-loop anomalous dimension for the transversity distribution h_1(x,Q^2), $γ^{h(1)}_n$, in the MS scheme of the dimensional regularization. Due to 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), $γ^{h(1)}_n$ is significantly larger than $γ^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $γ^{f(1)}_n$ very quickly at large n, keeping the relation $γ^{h(1)}_n > γ^{f(1)}_n$. This feature is in parallel to the relation between the one-loop anomalous dimension for f_1 and h_1.