-evolution of the Nucleon's Transversity Distribution H 1

We present a calculation of the two-loop anomalous dimension for the transversity distribution h1(x,Q ), γ n , in the MS scheme of the dimensional regularization. Because of the chiral-odd nature, h1 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 h1), γ h(1) n is significantly larger than γ n (the anomalous dimension for the nonsinglet f1 and g1), but approaches γ n very quickly at large n, keeping the relation γ h(1) n > γ f,g(1) n . This feature is in parallel to the relation between the one-loop anomalous dimension for f1 (g1) and h1. We also show that this difference in the anomalous dimension between h1 and g1 leads to a drastic difference in the Q-evolution of those distributions in the small x region.