%% slac-pub-7204: page file slac-pub-7204-0-0-4-4.tcx.
%% subsection 4.4 Transverse cross section [slac-pub-7204-0-0-4-4 in slac-pub-7204-0-0-4: \gamma'\sim\Lambda^2/Q^2$,
the integration leads to a $\ln Q^2/\Lambda^2$ enhancement,
which was absent in the leading order diffractive structure function given
in Sect.~\docLink{slac-pub-7204-0-0-3.tcx}[qq]{3}.
The $\beta$-spectrum is determined by the dimensionless function
\beq
g_T^{(1)}(\beta)=\int_0^\infty\frac{(1+u)u^2\,du}{16(\beta+u)^2}\int
d^2s_\perp'(s_\perp'^2)^2\int_{x_\perp}\left|\int\frac{d^2s_\perp}
{(2\pi)^2}\cdot\frac{\mbox{tr}[\tilde{W}^{\cal A}_{x_\perp}(s_\perp-s_\perp')]
\, t^{ij}_T}{s_\perp'^2(\beta+u)+s_\perp^2(1-\beta)}\right|^2\, ,\label{g1t}
\eeq
where
\beq
t_T^{ij}=\frac{1}{2}\left(\delta^{ij}+\frac{2s_\perp^is_\perp^j}{s_\perp'^2}
\cdot\frac{1-\beta}{\beta+u}\right)\sqrt{1+\left(\frac{\beta(1+u)}
{u(1-\beta)}\right)^2}.
\eeq
Contraction of the transverse tensor indices is
assumed in Eq.~(\docLink{slac-pub-7204-0-0-4.tcx}[g1t]{62}).
It can be shown, following the discussion at the end of the last subsection,
that $g_T^{(1)}(\beta)\sim 1/\beta$ at $\beta\to 0$, resulting in a constant
behaviour of the diffractive structure function in this region. The same
effect has previously been observed in \cite{20}, where the diffractive
interaction with the proton is treated by means of 2-gluon exchange.
The sum of the contributions from the region of high-$p_\perp$ quark-gluon
or antiquark-gluon jets is given by
\beq
F_T^{D,qg}=\frac{4\alpha_S}{(2\pi)^5\xi}\ \beta(1-\beta)^2\!\!\!\!
\int\limits_{\gamma_{min}}^{1-\gamma_{min}}\!\!\!\!d\gamma\left[g_T^{(2)}
(\beta)+\frac{1}{\gamma(1\!-\!\gamma)}g_T^{(3)}(\beta)+\frac{\gamma^3+(1\!-
\!\gamma)^3}{\gamma(1\!-\!\gamma)}g_T^{(4)}(\beta)\right]\, ,
\eeq
where for $m=2,3,4$ the functions $g_T^{(m)}(\beta)$ are defined by
\beq
g_T^{(m)}(\beta)=\int_0^\infty\frac{2(1+u)u\,du}{9(\beta+u)^2}\int
d^2s_\perp'(s_\perp'^2)\int_{x_\perp}\left|\int\frac{d^2s_\perp}
{(2\pi)^2}\cdot\frac{s_\perp\,\mbox{tr}[\tilde{W}_{x_\perp}(s_\perp-s_\perp')]
\, t^{(m)}}{s_\perp'^2(\beta+u)+s_\perp^2(1-\beta)}\right|^2\, ,
\eeq
\beq
t^{(2)}=1\quad,\quad t^{(3)}=-\frac{\beta+u}{u(1-\beta)}\quad,\quad
t^{(4)}=t^{(2)}+t^{(3)}\, .
\eeq
As in the longitudinal case, the contribution from the region with a
high-$p_\perp$ gluon-jet is negligible at small $\beta$.
The results of the present section are the above explicit expressions for
hard radiative corrections to the diffractive structure functions,
calculated in the semiclassical approach of \cite{8}. These radiative
corrections yield high-$p_\t$ jets, whereas the leading contribution is
kinematically dominated by the aligned-jet configuration with small
transverse momentum. This is similar to expectations based on the
QCD-improved aligned-jet model \cite{15}.
Final states with high-$p_\t$ jets in diffractive electroproduction have
recently been also considered in \cite{21,22}. The
main difference to our approach is the assumption of two-gluon exchange in
these calculations. This leads to a different $x$-dependence of the
jet cross sections.