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\begin{document} \title{Diffraction at LHC } 
\author{L. Frankfurt$^1$}
%\protect\footnote{\ \ speaker}}
%,Name2$^2$, Name3$^3$}
\institute{$^1$ Tel Aviv University,Israel}
%,\\ 
%$^2$Institute Name2,\\ 
%$^3$Institute Name3 }
\maketitle% {DIFFRACTION AT  LHC}
\begin{abstract}


Rapid increase with energy of cross sections of QCD processes
leads to the change of QCD environment for new particles production 
at LHC, to the new QCD phenomena. It follows from $k_t$ factorization
theorems that transverse momenta of partons are increasing within the fragmentation region, that regime of 100\% absorption dominates in the 
scattering at zero impact parameters. Biconcave form of rapid hadron and 
two phase structure of hadronic final states are explained.  
We outline here impact of understood QCD phenomena on the probability
of processes with large rapidity gaps.
\end{abstract}

\section{Introduction}

The main challenge of LHC physics is to discover new particles (Higgs boson, supersymmetric particles...)  and novel QCD phenomena.  One of barriers
for  a such study is the necessity to model QCD environment.
Usually this is made within Monte Carlo approaches which accounts for the
understood  properties of QCD (see also \cite{Sostrand, Jung} at this conference). 
The main origin of complications is evident:  cross sections of QCD  processes are rapidly increasing with energy.   Really data on the cross sections of soft QCD processes can be described as  $\sigma\propto (s/s_o)^{2\alpha_P(t=0)-2}$ i.e. as due to the exchange by Pomeron with the intercept  $\alpha_P(t=0)=1+\delta$  where $\delta=0.08-.01$. Similarily cross sections of DIS processes with the virtuality $Q^2$ observed at FNAL and at HERA can be  fitted as the exchange by hard "Pomeron" with the intercept  $\alpha_P(t=0)=1+\delta_{hard}$ where 
$\delta_{hard} (Q^2\approx 10 GeV^2) \approx 0.2$ and increasing with increase of $Q^2$. pQCD  formulae are more complicated but in the important kinematical domain can be fitted  in this form also. Different energy dependence of soft and hard QCD processes leads to change of proportions between soft and hard QCD 
contributions, to the energy dependence of QCD environment.

Rapid increase with collision energy of the radius of soft QCD interaction $b^2=B_o+ 2\alpha'_P \ln(s/s_o)$  allows experimental separation of peripheral and central collisions ($b^2\approx B_o$   at LHC, see review 
\cite{FSW}\footnote{Here B is the slope of t dependence measured in the  elastic pp collisions}.  Feasibility of the separation of pp collision into peripheral and central impact parameters collisions using different triggers (two, 4 jet production at central rapidities)  is practically important. Really collision at central impact  parameters is dominated by the novel QCD regime (QCD environment for new particles production)  which  is characterized by unbroken chiral symmetry and  certain  remnants of  conformal symmetry. This is in contrast with the peripheral pp collisions  where hadronic states are in the  phase of spontaneously broken chiral  symmetry and  no conformal symmetry.


In spite of the fact that at energies of LHC  the total contribution of hard processes into $\sigma_{tot}(pp)$ is not large but  both hard processes as well as heavy particle production are concentrated at central impact parameters. So QCD environment  for new particles production strongly depends on collision energy making difficult the separation of hadronic products of 
new particles decays  from the background from hadronic processes.  This problem is especially important  for  establishing  quantum numbers of new particles. 

Another important  feature of QCD physics which  makes  modeling of QCD processes at LHC difficult is  that  observed increase  cross sections with 
collision energy comes to conflict with probability conservation at given impact
parameter: $\sigma_{el}(s,b)\propto (s/s_o)^{2\delta} \le \sigma_{tot}(s,b)\propto (s/s_o)^{\delta}$. This restriction has simple interpretation: absorption of rapid particle can not exceed $100\%$, cf. discussion in the text. This condition restricts region of applicability  of pQCD approximations which were successful 
at lesser energies.


In the new regime of strong interaction with small coupling constant pQCD is inapplicable. However regime of  complete absorption where  partial waves achieve maximum allowed by probability conservation  some important 
properties of hard processes like total cross section, disappearance of leading hadrons, jets at zero impact parameters, cross sections of diffractive processes   can be evaluated legitimately.  In the new QCD regime multiparton interactions are not suppressed by powers of virtuality and  observation of them will be most effective method of probing novel QCD regime. Measurement of diffractive 
electroproduction of vector mesons at HERA helped to establish gluon GPD, i.e. gluon distribution in impact parameter space \cite{gluonformfactor} which is important for the analysis of new particles production. 

In the second section  we will discuss nontrivial features of impact parameter distribution. In the third section we formulate restrictions which follow from probability conservation and found two phase regime.
In the section 4 we discuss dependence on energy of QCD environment.
In section 5 we consider impact of discussed above phenomena on the gap survival probability.

\section{Impact parameter distribution for soft and hard interactions}

To formulate probability conservation it is convenient to use 
impact parameter representation for the scattering amplitude:
\begin{equation}
T(s,t)=(is/4\pi) \int exp(iq_t b)\Gamma(s,b) d^2b
\end{equation}
\label{impact}
One may easily reconstruct $\Gamma$ for the soft QCD interactions using parametrizations for elastic pp collisions. 
\begin{equation}
\Gamma_{soft}(s,b^2)=(\sigma_{tot}(pp)/\pi)exp(-b^2/2B)
\end{equation}
\label{impactsoft}
Here $B$ is the slope of t dependence of elastic cross section.

The impact parameter distribution of gluons can be reconstructed from 
gluon GPD measured in the hard exclusive processes like diffractive electroproduction of vector mesons $\gamma^{*}+p\to V+p$. It is
important that according to QCD factorization theorem of \cite{CFS}  
such processes are calculable in terms of generalized parton distributions(GPD). Thus impact parameter dependence of gluon
distribution can be reconstructed using two gluon form factor of a nucleon 
see review and references in \cite{FSW} and new calculation in \cite{BFS09}:

\begin{equation}
\Gamma_{gluon}(x, b)=(x_o/x)^{\lambda} (\mu b)K_1(\mu b)
\end{equation}
\label{impacthard}
Here K is function of Hankel of imaginary argument. Experimentally $\lambda\approx 0.2$  and increasing with virtuality, $\mu \approx 1 GeV$ and slowly decreasing with energy.
 
Comparison between Eq.\ref{impactsoft} and Eq.\ref{impacthard} allows
to establish important properties of QCD environment:

\begin{itemize}

\item  Knowledge of the slope $B$ for the soft QCD interactions and $\mu$ for hard interactions allows to derive novel and important property: impact parameter distribution characteristic for soft processes is significantly wider than for hard processes and its radius is increasing with energy. 

\item According to QCD factorization theorem hard  processes and new particles production are dominated by convolution of gluon distributions. So they have close impact parameter distributions.

\item  Amplitudes of hard processes are significantly smaller than that for soft ones (Bjorken scaling)  but  more rapidly increasing with energy.

\item Existence of correlations between partons suggest that
multiparton interactions may be characterized by more narrow distribution in impact parameter space.\cite{Sostrand}

 \end{itemize}
 
\section{Conservation of probability and two phase picture}
\label{xxx}

In a quantum theory cross sections of hadron collisions can be calculated in terms of profile function $\Gamma(s, b)$  as

\begin{equation}
\sigma_{el}=\int d^2 b \Gamma(s,b)|^2
\end{equation}
\label{elastic}
\begin{equation}
\sigma_{inel} =\int d^2 b [1-|1-\Gamma(s,b)|^2]
\end{equation}
\label{inelastic}
\begin{equation}
\sigma_{tot}=\int d^2 b~ 2 Re\Gamma(s,b)
\end{equation} 
\label{total}

Above equations are applicable also  for the scattering of spatially small dipole of a hadron target if to neglect by the increase of the number of constituents within this dipole with the increase of virtuality. Evaluation of  radiative corrections to the impact factors in \cite{Fadin} indicates that these corrections seems to be small.

It follows from these equations that : 

\begin{itemize}
\item  $\Gamma(s, b)$ is restricted from above 
by the condition: $\Gamma(s, b)\le 1$  . Upper boundary - 
\begin{equation}
\Gamma(s, b)=1 
\end{equation}
is equivalent to the requirement that absorption can not exceed 100\%. Since 
amplitudes of soft and hard interactions are increasing with energy 
see Eq.\ref{impactsoft} and Eq.\ref{impacthard}
each projectile will be absorbed with 100\% probability. Thus
at given impact parameter $\Gamma=1$ at sufficiently large energies.
This condition does not includes any dependence on virtuality. 

\item Thus Bjorken scaling completely disappears at large energies,
 in the limit of fixed $Q^2$ but $x\to 0$ .   Numerical evaluations show 
 that onset of this this novel QCD regime at 
$b=0$ requires $x\le 10^{-3}-10^{-4}$. See review \cite{FSW}.

\item Another important novel effect to reveal itself at LHC : amplitudes of hard processes should exceed amplitudes of soft QCD processes for the scattering at zero impact parameter since amplitudes of hard interactions are increasing with energy more rapidly than soft one. Moreover at given impact parameter  soft interactions disappear with increase of energy for the the review and references \cite{FSW }.

\item Two phases QCD picture emerges for high energy collisions. In the scattering at large impact parameters -peripheral collisions- nonperturbative QCD interactions would dominate. Here interaction chooses familiar phase
of spontaneously broken chiral symmetry and conformal symmetry is broken.
On the contrary -for the scattering at central impact parameters
hard interactions with unbroken chiral symmetry would dominate.
\end{itemize}


\section{Change of hadron environment}
\label{sec.xxx}

To visualize dependence of hadron environment on energy we begin from the consideration of scattering of small dipole off a hadron target.
The characteristic feature of hard processes
is the approximate Bjorken  scaling for the
structure functions of DIS, i.e. the two dimensional conformal
invariance for the moments of the structure functions. In this
approximation as well as within the leading $\log(x_0/x)$
approximation, the transverse momenta of quarks within the
dipole  produced by the local  electroweak current are restricted
by the virtuality of the external field:
\begin{equation}
\Lambda^2 \le p_t^2 \le Q^2/4.
\end{equation}
Here $\Lambda\equiv \Lambda_{QCD}=300 $ Mev is a QCD scale. However 
it follows from the QCD factorization theorem proved in Refs. \cite{FMS} that within this kinematical range the smaller transverse size $d$ of the configuration
(the transverse distance between the constituents of the dipole) corresponds 
 to a more rapid increase of its interaction with the collision energy:
\begin{equation}
\sigma= \alpha_s(c/d^2)F^2\frac{\pi^2}{4} d^2
xG_{T}(x,c/d^2),\label{1.3}
\end{equation}
here $F^2=4/3$ or $9/4$ depends whether the dipole consists of
color triplet or color octet constituents,  $G_T$ is an integrated
gluon distribution function and $c$ is a parameter $c=4\div 9$. It
is well known in the DGLAP approximation that the structure
function $G_T(x,Q^2)$ increases more rapidly with $1/x$ at larger
$Q^2$. This property agrees well with the recent HERA data.
 We shall demonstrate  using $k_t$ factorization that
the transverse  momenta of the (anti)quark of the   $q\bar q$ pair
produced by a local current  increase  with the energy and become
larger than $Q^2/4$ at sufficiently large energies. In other words
the characteristic transverse momenta in the fragmentation region
increase with the energy. Technically this effect follows from the
more rapid increase with the energy of the pQCD interaction
 for smaller dipole and the $k_t$ factorization theorem.
 \par
It is worth  noting  that this  kinematics  is very different from the central rapidity kinematics where the increase of  $p_t^2$  was  found in the leading 
$\alpha_s\log(x_0/x)$ BFKL approximation: $\log^2(p_{t}^2/p_{t 0}^2)
\propto \log(s/s_0)$. Indeed, the latter rapid increase  is the property of
the ladder: the further we go along the ladder, the larger are
characteristic transverse momenta, i.e. we have a diffusion in the
space of transverse momenta . On the other hand the
property we are dealing here with is the property of a
characteristic transverse momenta in the wave function of the
projectile.
\par
The dipole  approximation provides the target rest frame description which is   equivalent to the Infinite  Momentum Frame (IMF) description of DIS in LO DGLAP and BFKL  approximations. To achieve equivalence with the
IMF description in the NLO  approximation it
 is necessary to calculate radiative corrections to cross section in the fragmentation  region,
  i.e. to take into account the increase of the number of constituents  and related  renormalization
  of the dipole wave function.  Recent calculations \cite{Fadin} suggest that these corrections
   are small. Consequently we will neglect  these corrections.

\par
Our main result  \cite{BFS09} is that the median transverse momenta $k^2_t$ of the leading $q\bar q$ pair in the  fragmentation region grows as
\begin{eqnarray}
k^2_t&\sim& a(Q^2)/(x/x_0)^{\lambda (Q^2)}
\label{main}
\end{eqnarray}
 (The median  means that  the configurations
with the momentum/masses less than the median one contribute half
of the total crosssection). The exponential factors
 $\lambda$ and $\lambda_{\rm M}$ are both  approximately
 $\sim 0.1$.  These  factors are
  weakly dependent on the external virtuality $Q^2$. The
exact values  also depend on the details of the process, i.e.
whether we consider the DIS process
 with longitudinal or
transverse photons, as well as on the model and approximation
used. The exact form of $\lambda (Q^2)$, and $\lambda_{\rm M}
(Q^2)$ are given below.

The rapid increase of the characteristic transverse scales in the
fragmentation region has been found first in Refs.
\cite{FGMS,FSW,Rogers1,Rogers2},
 but within the black disk   regime (BDR). Our
new result is the prediction of the increase with energy of the
jet transverse momenta in the fragmentation region/the rise of the
transverse momenta in the impact factor with the energy, in
 the kinematical domain where methods  of pQCD are still applicable. This effect could be considered as
  a precursor of the black disk regime indicating the possibility of the smooth matching between two regimes.
\par
Our results can be applied to a number of  processes. First we
consider the deeply
 virtual Compton scattering (DVCS)
process, i.e. $\gamma +p\to \gamma^*+p$.
 \par We also find that
 at sufficiently large energies
\begin{equation}
\sigma_L(x,Q^2)/\sigma_T(x,Q^2)\propto (Q^2/4p_t^2)\propto
(1/x)^{\lambda}.
\end{equation}
Hence the $\sigma_L/\sigma_T$ ratio should decrease as the  power
of energy instead of being $O(\alpha_s)$.
\par Our results have an implication for the space structure of the
wave packet describing a rapid hadron. In the classical
multiperipheral picture of Gribov a hadron has a shape of a
pancake of the longitudinal size $1/\mu$ (where $\mu $ is the
scale of soft QCD) which does
 not depend on the incident energy \cite{Gribovspace-time}. On the contrary,  
 QCD predicts \cite{BFS09} the biconcave shape for the rapid hadron in pQCD with the minimal longitudinal length (that corresponds to small impact
 parameter $b$) decreasing with increase of energy and being smaller for nuclei than for the nucleons.

\section{Gap survival probability}

Evaluation of a number of a number processes with large rapidity gap
like $p+p\to p+H+p, p+p\to p+2jet +p$  etc requires evaluation of survival factor
$S^2$.   It has been shown in \cite{FHSW} that screening effects related to nonperturbative QCD can be evaluated relyably on the basis of new QCD factorization theorem.
\begin{equation}
S^2=\int d^2bP_{hard}|1-\Gamma(b)|^2
\end{equation}
Here $P_{hard}$ is impact parameter distribution of hard processes
calculable in terms of two gluon form factor of a nucleon. 
There is no need to model multi Pomeron exchanges by applying eikonal approximation which has in QCD problems with account of energy-momentum conservation.  

More tricky is evaluation of screening factor because of small x hard QCD phenomena -this job is in progress.



I am indebted to my coathors M.Strikman and B.Blok for the illuminating 
discussions of  the phenomena considered in the paper.

%\subsection{xxx}
%\label{sec:xxx}

\begin{footnotesize}
\bibliographystyle{mpi08}
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\bibitem{Sostrand} B.Sostrand. Talk at this conference
\bibitem{Jung} H.Yung Talk at this conference
\bibitem{FSW} L.~ Frankfurt, M. ~Strikman and C.~ Weiss,
Ann.Rev.Nucl.Part.Sci.55 (2005) 403-465,
     Phys.\ Rev.\  D {\bf 69}, (2004) 114010
\bibitem{CFS} J.C. Collins,  L. Frankfurt and M. Strikman, Phys. Rev. D56 (1997) 2982. L. Frankfurt, A. Freund, V. Guzey and M. Strikman,
Phys. Lett., B418 (1998) 345; Erratum-ibid, B429  (1998) 414
%\bibitem{twogluonformfactor} L.Frankfurt and M.Strikman
\bibitem{BFS09} On the shape of a rapid hadron in QCD
B. Blok , L. Frankfurt , M. Strikman . Nov 2008. 14pp.
e-Print: arXiv:0811.3737 [hep-ph]
\bibitem{Fadin} V.S. Fadin, hep-ph/9807528. F. Carporale, A. Papa, A. Sabio Vera, E. J. of Physics,C53 (2008) 525
  \bibitem{FMS}  L. Frankfurt, G.A. Miller, M. Strikman Phys.Lett.B304:1-7,1993.
B. Blaettel, G. Baym, L. Frankfurt and M. Strikman, Phys. Rev. Lett., 70 (1993) 896.  L. Frankfurt, G.A. Miller, M. Strikman, Ann. Rev.
Nucl. Part. Sci., 44 (1994) 501
\bibitem{FGMS}  V. Guzey, L. Frankfurt, M. Strikman, M.McDermott, Eur.J. of Physics, C16 (2000) 641
\bibitem{Rogers1}
T.~C.~Rogers, A.~M.~Stasto and M.~I.~Strikman, Unitarity
Constraints on Semi-hard Jet Production in Impact Parameter
Space,''arXiv:0801.0303 [hep-ph]
\bibitem{Rogers2}
  T.~C.~Rogers and M.~I.~Strikman,
  Hadronic interactions of ultra-high energy photons with protons and  light  nuclei in the dipole picture,''
  J.\ Phys.\ G {\bf 32}, (2006) 2041
\bibitem{Gribovspace-time} V. N. Gribov, Space-time description of hadron interactions at high-energies.
 In *Moscow 1 ITEP school, v.1 'Elementary particles'*,
65,1973. e-Print: hep-ph/0006158
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