NLO $Q^2$-evolution of the nucleon's transversity distribution $h_1(x, Q^2)$

Hayashigaki, A.; Kanazawa, Y.; Koike, Yuji

NLO $Q^2$-evolution of the nucleon's transversity distribution $h_1(x, Q^2)$

Authors

Hayashigaki, A.

Kanazawa, Y.

Koike, Yuji

Description

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. 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 $h_1$), $γ^{h(1)}_n$ is significantly larger than $γ^{f,g(1)}_n$ (the anomalous dimension for the nonsinglet $f_1$ and $g_1$), but approaches $γ^{f,g(1)}_n$ 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 $f_1$ $(g_1)$ and $h_1$. We also show that this difference in the anomalous dimension between $h_1$ and $g_1$ leads to a drastic difference in the $Q^2$-evolution of those distributions in the small $x$ region.
10 pages, latex. Proceedings of the DESY workshop, "Deep inelastic scattering off polarized targets: Theory meets experiment" held at DESY-Zeuthen, Sep. 1-5, 1997. Published in the proceedings, DESY 97-200, pages 157-166. Proper macros for the eps files are appended