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\begin{document}

\title{TEMPLATE FOR THE HSQCD'04 PROCEEDINGS \\
PREPARED BY LATEX
\thanks{This work is
supported by the High-Energy Physics  Foundation}}

\author{H.~S.~QCD-AUTHOR \\
St. Petersburg Nuclear Physics Institute \\
Gatchina 188300, Russia\\
E-mail: hsqcd.author@hsqcd.org }

\maketitle

\begin{abstract}
\noindent This is abstract for your HSQCD'04 contribution. It should
be a few lines briefly describing your contribution to the
Proceedings. Please, remember that deadline for your contribution is
December 25, 2004.
\end{abstract}

%\markright{}

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\markboth{\large \sl H.S. QCD-Author  \hspace*{2cm} HSQCD 2004}
{\large \sl \hspace*{1cm} TEMPLATE FOR THE HSQCD'04 PROCEEDINGS}

\section{Guidelines} Please, take from
the HSQCD web-site ({\it http://hepd.pnpi.spb.ru/hsqcd/}) a Latex
class file: $'hsqcd.cls'$ for preparation of your HSQCD'04
contribution. We recommend all HSQCD speakers also to use this
Latex-file $'hsqcd\underline{\;\;\;} temp.tex'$ with EPS-figure
$'hsqcd\underline{\;\;} temp \underline{\;\;} fig.ps'$ as a template
for their Proceedings contributions.


\section{Limits of HSQCD'04 contributions}
The limit for the size of a HSQCD'04 contribution: \\
6 pages for parallel/plenary session (15+5 minutes) talks, \\
10 pages for plenary (25+5 minutes) talks.

\section{Where to send your contribution}
Please, send your contribution by e-mail: \\
{\it hsqcd@pnpi.spb.ru} \\
with subject: speaker name

\section{Deadline for your contribution to the HSQCD'04 Proceedings}
December 25, 2004

\section{Figures} We advised to prepare your figures in
black and white. Please prepare the figures in high resolution
(300 dpi) for half-tone pictures. Half-tone pictures must be sharp
enough for reproduction, otherwise they will be rejected.

\section{Text sample}
QCD is an essential ingredient of the Standard Model, and it is
well tested in  hard processes when transferred momentum is of the
order of the total collision energy (Bjorken limit: $Q^2 \sim s
\rightarrow \infty$). The cornerstones of perturbative QCD at this
kinematic regime (QCD-improved parton model):
 the Gribov--Lipatov--Altarelli--Parisi--Dokshitzer
(GLAPD) evolution equation and factorization of inclusive hard
processes provides a basis for the successful QCD-improved parton
model. The factorization theorem for inclusive hard processes
ensures that the inclusive cross section factorizes into partonic
subprocess(es) and parton distribution function(s). The GLAPD
evolution equation governs the $\log Q^2$-dependence (at $Q^2
\rightarrow \infty$) of the parton distribution functions and the
hard subprocess cross-sections at fixed scaling variable
$x=Q^2/s$.

Another kinematic domain that is very important at high-energy is
given by the (Balitsky--Fadin--Kuraev--Lipatov) BFKL limit
\cite{FKL,BL78}, or QCD Regge limit, whereby at fixed $Q^2 \gg
\Lambda_{QCD}^2$, $s \rightarrow \infty $. In the BFKL limit, the
BFKL evolution in the leading order (LO) governs $\log(1/x)$
evolution (at $x \rightarrow 0$) of inclusive processes. Note that
the BFKL evolution in the next-to-leading order (NLO)
\cite{FL,CC98,BFKLP}, unlike the LO BFKL \cite{FKL,BL78}, partly
includes GLAPD evolution with the running coupling constant of the
LO GLAPD, $\alpha_S(Q^2) = 4 \pi / \beta_0
\log(Q^2/\Lambda_{QCD}^2) $.

Photon--photon collisions, particularly $\gamma^* \gamma^*$
processes, play a special role in QCD~\cite{Budnev75}, since their
analysis is under much better control than the calculation of
lepton--hadron and hadron--hadron processes, which require the
input of non-perturbative hadronic structure functions or wave
functions.  In addition, unitarization (screening) corrections due
to multiple Pomeron exchange should be less important for the
scattering of $\gamma^*$ of high virtuality than for hadronic
collisions.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=hsqcd_temp_fig.ps voffset=-60 vscale=40 hscale= 40
hoffset=10 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*]{ The energy dependence of the total cross section for
highly virtual photon--photon collisions predicted by the BLM
scale-fixed NLO BFKL \cite{BFKLP2} compared with recently
finalized OPAL \cite{OPAL} and L3 \cite{L3} data from LEP2 at
CERN. The (solid) dashed curves correspond to the (N)LO BFKL
predictions for two different choices of the Regge scale: $s_0=
Q^2$  for upper curves and $s_0=4 Q^2$ for lower curves}
\end{center}
\label{fig1}
\end{figure}

The high-energy asymptotic behaviour of the $\gamma \gamma$ total
cross section in QED can be calculated~\cite{GLF} by an all-orders
resummation of the leading terms:\\
$\sigma \sim \alpha^4 s^{\omega}$, $\omega = \frac{11}{32} \pi
\alpha^2 \simeq 6 \times 10^{-5}$. However, the slowly rising
asymptotic behaviour of the QED cross section is not apparent
since large contributions come from other sources, such as the cut
of the fermion-box contribution: $\sigma \sim \alpha^2 (\log s)/s$
\cite{Budnev75} (which although subleading in energy dependence,
dominates the rising contributions by powers of the QED coupling
constant) and QCD-driven processes.


The photon--photon cross sections with LO BFKL resummation was
considered in Refs.~\cite{BL78,Bartels96,Brodsky97}.

Although the complete NLO impact factor of the virtual photon is
not known yet,  one can use the LO impact factor of Refs.
\cite{GLF,Brodsky97}, assuming that the main energy-dependent NLO
corrections come from the NLO BFKL subprocess rather than from the
photon impact factors \cite{BFKLP2}.


Fig.~\ref{fig1} compares the LO and BLM scale-fixed NLO BFKL
predictions $\sigma \sim \alpha^2 \alpha_S^2
s^{\omega}$~\cite{BFKLP,BFKLP2} with recent CERN LEP2 data from OPAL
\cite{OPAL} and L3 \cite{L3}.


\section*{Acknowledgements} We thank all HSQCD'04 participants
for their contributions to the HSQCD'04 Proceedings. This work was
supported in part by the High Energy Foundation and the World
Science Agency.

\section*{Appendix}
This is place for Appendix, if any.


\begin{thebibliography}{0}

\bibitem{FKL}   V.S.~Fadin, E.A.~Kuraev, and L.N.~Lipatov,
Phys. Lett. B {\bf60}  (1975) 50; \\
E.A.~Kuraev, L.N.~Lipatov, and V.S.~Fadin, Zh. Eksp. Teor. Fiz.
{\bf 71} (1976) 840 [Sov. Phys. JETP {\bf 44} 443 (1976)]; {\it
ibid.} {\bf 72} (1977) 377 [{\bf 45} (1977) 199].

\bibitem{BL78}
I.I.~Balitsky and L.N.~Lipatov, Yad. Fiz. {\bf28} (1978) 1597
[Sov. J. Nucl. Phys. {\bf28} (1978) 822].

\bibitem{FL}
V.S.~Fadin and L.N.~Lipatov, Phys. Lett. {\bf B429} (1998) 127.

\bibitem{CC98}  G.~Camici and M.~Ciafaloni, Phys. Lett.
{\bf B430} (1998) 349.

\bibitem{BFKLP}  S.J.~Brodsky, V.S.~Fadin, V.T.~Kim,
L.N.~Lipatov, and G.B.~Pivovarov, Pis'ma ZhETF {\bf70} (1999) 161;
[JETP Lett.\ {\bf 70} (1999) 155].


\bibitem{Budnev75}
V.M.~Budnev, I.F.~Ginzburg, G.V.~Meledin, and V.G.~Serbo,
Phys.~Rep. {\bf C15} (1975) 181.

\bibitem{GLF} V.N.~Gribov, L.N.~Lipatov, and G.V.~Frolov,
Phys.~Lett. {\bf B31} (1970) 34; Yad. Fiz. {\bf12} (1970) 994
[Sov. J. Nucl. Phys. {\bf 12} (1971) 543]; \\
H. Cheng and T.T. Wu, Phys. Rev. D {\bf1} (1970) 2775.

\bibitem{Bartels96}
J.~Bartels, A.~De~Roeck, and H.~Lotter,
Phys. Lett. {\bf B389} (1996) 742;\\
M.~Boonekamp, A.~De~Roeck, C.~Royon, and S.~Wallon, Nucl. Phys.
{\bf B555} (1999) 540.

\bibitem{Brodsky97}  S.J.~Brodsky, F.~Hautmann, and D.E.~Soper,
Phys.~Rev. {\bf D56} (1997) 6957; Phys.~Rev.~Lett. {\bf78} (1997)
803; (E) {\bf79} (1997) 3544.

\bibitem{BFKLP2}
S.J.~Brodsky, V.S.~Fadin, V.T.~Kim, L.N.~Lipatov and
G.B.~Pivovarov, Pisma ZhETF  {\bf76} (2002) 306 [JETP Lett. {\bf
76} (2002) 249].

\bibitem{OPAL}
OPAL, G. Abbiendi {\it et al.},  Eur. Phys. J. {\bf C24} (2002)
17.

\bibitem{L3} L3, P.~Achard {\it et al.},
Phys. Lett. {\bf B531} (2002) 39.

\bibitem{HERA98}
ZEUS, J. Breitweg {\it et al.},
Eur. Phys. J. {\bf C6} (1999) 239; \\
H1, C. Adloff {\it et al.}, Nucl. Phys. {\bf B538} (1999) 3.

\bibitem{D099}
D$\emptyset$, B.~Abbott {\it et al.}, Phys. Rev. Lett. {\bf 84}
(2000) 5722.



\end{thebibliography}

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