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\begin{document} \title{
Small $x$ Physics   and Diffraction } 
\author{L. Frankfurt$^1$
H. Jung$^2$}
\institute{$^1$Tel Aviv University,\\
$^2$  Deutsches Elektronen Synchrotron, Hamburg and Physics Department, 
University Antwerp\\
}
\maketitle


Measurements of structure functions and parton densities at HERA and the Tevatron have provided much insights into the high energy behavior of cross sections.  The structure functions and parton densities increase rapidly with increasing energies,  consistent with pQCD calculations. However, this increase with energy is much 
more rapid 
than for the  total cross sections of $\gamma p$ and $pp$
collisions.  Vector meson and diffractive dijet production in $ep$ provide an effective method to measure the energy dependence of the  generalized  gluon distribution of the proton as well as the 
impact parameter dependence  of the gluon distribution. 
 
At sufficiently small $x$  achievable at LHC new QCD regimes are
expected. In particular within the double logarithmic approximation the transverse momenta of  radiated partons in the current fragmentation region begin to increase with increasing energy.
Besides this,  the interpretation of parton distributions as probability distribution becomes in conflict with the probability  conservation
at the kinematics to be achieved at LHC.
Therefore, the challenging question is to quantify the boundaries of this kinematical regime and elucidate properties of the new QCD regime of strong interaction with small coupling constant.

At the high energies of the LHC multjet cross sections will become more and more important. For the detailed calculation of multi-jet cross sections of moderate transverse momentum, integrated 
single  parton density functions are no longer sufficient. 
Multi-parton densities in impact parameter space are needed.


Whereas in principle the relation between diffraction and multi-parton interaction is given by the AGK rules, the details in terms of QCD  are not yet fully understood. The topic of creation of rapidity gaps (diffractive processes) and the influence of absorptive effects, 
which can destroy the rapidity gap, is currently under detailed investigations, both theoretically and experimentally. These effects are directly related to multi-parton interaction in non-diffractive processes. 

The separation of soft and hard processes in impact parameter space  will tell whether multi-parton interactions  are dominated by the soft - strong coupling regime, or whether significant contributions come also from the weak coupling - perturbative region. Indications, that hard perturbative processes  are in the regime of strong interaction with weak 
running coupling constant 
 come from the diffractive jet  (vector meson)  production but also from investigations of multiparton interactions with Monte Carlo event generators.  To avoid too large particles multiplicities in $pp$ collisions at LHC energies the standard approaches are applicable to the regions of $p_t^2\gap  6 GeV^2$.   Below this value multi-parton interactions 
probably cannot be considered as independent.
The issue of separating soft from hard processes can be also investigated by the transverse momentum distribution of jets close to the rapidity gap and by the standard forward and Mueller-Navelet jets. At LHC energies it becomes practical to separate experimentally peripheral and central collisions. Small $x$ physics of hard processes, new heavy particle production are concentrated at central $pp$ collisions, soft QCD is mostly peripheral.  
Hard (soft) diffraction are dominated by central(peripheral) collisions


The topics of the session {\it small $x$ and diffraction} were grouped around these major areas. Much progress has been achieved in the last years, both experimentally and theoretically, which is reflected in the presentations in this session. However, a full understanding of   {\it small $x$ and diffractive} processes is still far ahead. We mention a few of the major open issues:
\begin{itemize}
\item how well do we understand PDFs at small x ?
\item  how well do we understand the properties of new regime of high density QCD in the weak coupling constant limit ?
\item what is the relation between diffraction and multiparton interaction  in the region of  high gluon density in small $x$ QCD where coupling constant is small but the interaction is strong ?
\item what is the interplay between soft and hard processes ?
\item how can diffraction and saturation be consistently implemented in Monte Carlo event generators ?
\item what are the impact parameter distributions of partons and the correlations between  partons within
 the wave functions of the colliding hadron in case of multiparton interactions ?
\end{itemize}


\end{document}
