Small-x behaviour of the polarized structure function $F_3^{\gamma }(x,Q^2)$

Abstract

We study the small-$x$ behaviour of the polarized photon structure function $F_3^{\text{ga}}$, measuring the gluon transversity distribution, in the leading logarithmic approximation of perturbative QCD. There are two contributions, both arising from two-gluon exchange. The leading contribution to small-$x$ is related to the BFKL pomeron and behaves like $x^{-1-{\text{om}}_2}$, ${\text{om}}_2=\mathcal{O}({\text{al}}_S)$. The other contribution includes in particular the ones summed by the DGLAP equation and behaves like $x^{1-{\text{om}}_0^{(+)}}$, ${\text{om}}_0^{(+)}=\mathcal{O}(\sqrt{{\text{al}}_S})$.

Comments: 19 pages LATEX, 7 EPS figures included, minor corrections