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\begin{document}
\Title{Overview of soft QCD and diffractive physics at LHC}
\bigskip\bigskip
%+\addtocontents{toc}{{\it D. Reggiano}}
%+\label{ReggianoStart}
\begin{raggedright}  
{\it Eugenio Scapparone\index{Scapparone, E.}\\
INFN - Bologna\\
Via Irnerio 46\\
I-40126 Bologna, ITALY}
\bigskip\bigskip
\end{raggedright}
\section{Introduction}
The soft QCD processes dominate the  
hadronic cross section at the LHC energy. The study of the particle production at low $p_{T}$ is one of the basic measurements 
at any hadron collider, providing a wide set of observables useful to model the event generators. 
Unidentified hadron multiplicity is sensitive to multi parton interactions while identified hadrons allow to test 
the modeling of strange and heavier quarks production in the event generators. A significant fraction of the inelastic cross section comes from diffractive processes, whose
prediction is affected by large uncertainties.  
The study of the single, double and central diffraction provide a constrain to the Monte Carlo simulations and is therefore a mandatory step to understand the charged particle production at LHC.
\section{Inclusive measurements}
The study of the inclusive charged particle production was the first physics result obtained at LHC.
The 
proton-proton interactions at $\sqrt{s}$=900 GeV, detected by ALICE during the early phase of the accelerator commissioning,
showed results consistent with earlier measurements obtained in proton-antiproton interactions
at the same energy\cite{ALICE1}. 
%The outstanding performance of LHC allowed to collect in a short time a large data set,
%whose energy spanned from $\sqrt{s}$=900 GeV to $\sqrt{s}$=8 TeV. 
The charged pseudorapidity density, the multiplicity and the $p_{T}$ distributions, and the
dependence of the $<$$p_{T}$$>$  from the charged multiplicity were investigated in detail at LHC. 
From an experimental 
point of view the nice agreement in these measurements obtained by ALICE\cite{ALICE2},ATLAS\cite{ATLASsoft} and CMS\cite{CMS1} demonstrated  
the excellent detector performance and showed the experiments capability to control the systematics. 
The event generators aiming to simulate these data(PHOJET\cite{PHOJET},PYTHIA 6\cite{PYTHIA6} and PYTHIA 8\cite{PYTHIA8}) can reproduce the measured
distributions only qualitatively. 
ALICE\cite{ALICE2} studied the charged particle pseudorapidity density for inelastic collisions having at least one charged particle at
$|\eta|<$~1. 
The  charged particle pseudorapidity density, compared to the one measured at $\sqrt{s}$=900 GeV, increases by
$(23.3\pm 0.4(sta)^{+1.1}_{-0.7}(sys))$ at $\sqrt{s}$=2.36 TeV and by $(57.6\pm 0.4(sta)^{+3.6}_{-1.8}(sys))\%$ at $\sqrt{s}$=7 TeV, while the Monte Carlo with the highest values (PYTHIA tune 
ATLAS-CSC)
provides 17.6$\%$ and 47.6$\%$ respectively\cite{ALICE2}. 
%%Moreover the shape of the multiplicity distribution at $\sqrt{s}$=7 TeV is not reproduced by any of the event generators.
The multiplicity distribution
measured by ALICE at $\sqrt{s}$=7 TeV is not reproduced by PHOJET and by several PYTHIA6 tunes: ATLAS-CSC is the closest but this tune 
underestimates the average $p_{T}$ as a function of the event charged multiplicity ($n_{ch}$) at $\sqrt{s}$=900 GeV\cite{ALICE2}.
CMS found similar results at $|\eta|<$ 2.4\cite{CMS1}: PHYTIA 8 reproduces the multiplicity distribution at $\sqrt{s}$=7 TeV but overestimates 
the same distribution at $\sqrt{s}$=900 GeV. Moreover 
the agreement with PYTHIA 8 does not hold if a cut $p_{T}>$500 MeV/c is applied, showing the softer part of the hadronic 
production is the most difficult to be reproduced.
PHOJET shows an opposite trend: it reproduces the multiplicity distribution measured by ALICE\cite{ALICE2} and CMS at $\sqrt{s}$=900 GeV\cite{CMS1}, 
but underestimates the same distribution at $\sqrt{s}$=7 TeV. 
CMS showed that the average $p_{T}$ is reproduced at $\sqrt{s}$=900 GeV and $\sqrt{s}$=2.36 TeV by PHTYIA 8, but this model overestimates it at $\sqrt{s}$=7 TeV.
ATLAS\cite{ATLASsoft} measured the charged particle multiplicity distribution at $|\eta|<$ 2.5, requiring $p_{T}>$100 MeV and $n_{ch}\geq$2: 
by applying these cuts PYTHIA 8 underestimates the data
both at $\sqrt{s}$=900 GeV and $\sqrt{s}$=7 TeV by 10-15$\%$. It is worth noting, changing the above cuts to $p_{T}>$500 MeV and $n_{ch}\geq$6,
PYTHIA tune ATLAS AMBT1 reproduce nicely the data both at $\sqrt{s}$=900 GeV and $\sqrt{s}$=7 TeV.
Recently the charged multiplicity ($n_{ch}>$1) was measured by LHCb in the $\eta$ interval 2$<\eta<$4.5
%using the silicon VeLo detector
\cite{LHCb} and by TOTEM at 5.3$<\eta<$6.5\cite{TOTEMsoft}. In these $\eta$ regions the event generators (default or tuned) underestimate the charged particle multiplicity too.
%The ALICE and the CMS collaboration studied the event shape in minimum bias event. 
%CMS measured the hadronic event shape studying two event shape variable, the central transverse thrust and the
%The first one is a measurement of the radiation along the transverse thrust axias while the second one 
%is a measure of the radiation out of the plane defined by the beam axis and the axis $n_t$ which maximize the 
%sum $\Sigma_{i}{$$|p_{T,i}\cdot n_{t}|$/$\Sigma_{i}$$|p_{T,i}|$.
%Two jet events that are well balancved have low valuee of these two variables, while isotropic multijet events have high values.
%As a results the code PYTHIA 6, PHYTHIA 8 and HHERWIG++ show satisfacatory agreement with the data for a leading jet $p_{t}$ larger than 20 GeV/c.
%According to ALICE
%the event in the real data look more spherical than expected by the Monte Carlo generator, most of the
%discrepancy coming from hard events, $p_{T}>$2 GeV/c.
%An important effect is stressed by CMS, the dependence of the rapidity-density and the average transverse momentum
%indicates that particle production at LHC energies is strongly correlated with event multiplicity
%rather than with the center-of-mass energy of the collision. This is a manifestation of the 
%so called "leading effect": the characteristics of particle production in hadronic collisions
%are constrained by the amount of initial parton energy that is available in any given collision.
As a conclusion of this first part we note 
%the event generator can reproduce qualitatively the data: 
each model/tuning can reproduce a limited number of observables at few center of mass energies.
%; setting  
%a general tune describing properly all the inclusive observables from  $\sqrt{s}$=900 GeV to $\sqrt{s}$=7 TeV 
%requires further efforts.
\section{Exclusive measurements}
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CMS measured the spectra and the $p_{T}$ of identified charged particle at 
$\sqrt{s}$=900 GeV, 2.36 TeV and 7 TeV\cite{CMSident}. The experimental results obtained at
midrapidity ($|y|<1$) have been compared with the expectation provided by several event generator.
The average $p_{T}$ as a function of the track multiplicity is properly reproduced by PYTHIA~8 tune 4C and  
PYTHIA 6 tune Z2 for pion and kaons at any center of mass energy, but
none of the above models/tunes provides an acceptable
description of the protons.
%%The average $p_{T}$ as a function of $\sqrt{s}$ is almost reproduced by PHTHIA~6 tunes and by PYTHIA~8 tune 4C 
%%for charged pions and charged kaons, while the protons are missed by all tunes, PYTHIA6 tune D6T 
%%being the closest.
%%
ALICE shows\cite{ALICEstrange} the ratio $\pi$/K as a function of the $p_{T}$ is missed by PHOJET, PYTHIA tunes Perugia 0 and
D6T at $\sqrt{s}$=900 GeV for $p_{T}>$ 1.2 GeV/c. The CMS measurement shows PYTHIA 8 tune 4C is inadequate to reproduce
this ratio as a function of the track multiplicity at any center of mass energy.
The same event generator underestimate the $K^{0}$ and the $\Lambda$ production in CMS at $\sqrt{s}$=900 GeV and
$\sqrt{s}$=7 TeV: the discrepancy increases with the particle mass\cite{CMSident}.
Things get worse when focusing on multi-strange hadrons. 
The ALICE collaboration measured the production of mesons and baryons containing two or three strange quarks in 
proton-proton collisions at the LHC at $\sqrt{s}$=7 TeV.
\begin{figure}[t]
\begin{center}
\epsfig{file=Csi.eps,height=2.5in}
\caption{$($a$)$ $\Omega$ and $\Xi$ spectra measured by ALICE, shown with Tsallis fits. $($b$)$ ALICE data to Monte Carlo (PYTHIA Perugia 2011) comparison. The errors are added in quadrature.}
\label{fig:magnet}
\end{center}
\end{figure}
The ratio $N_{\Phi}$/($N_{\rho}+N_{\omega}$) measured by ALICE in the forward region (2.5$<y<$4) in the muon channel agrees nicely with 
the LHCb measurement(2.44$<y<$4.06) obtained in the $K^{+}K^{-}$ channel. The predictions underestimate
this ratio up to a factor 2\cite{ALICEstrange}, with the exception of the ATLAS CSC tune (PHOJET) giving a reasonable estimate for $p_{T}>$ 1.5 GeV/$c$(3 GeV/$c$). 
The study of the $\Xi$ and of the $\Omega$ provides an useful tool to check the strangeness 
production in proton-proton collisions, since these two baryons differ only by a valence quark, with the u-quark replaced 
by a s-quark in the $\Omega$.
ALICE showed\cite{ALICEstrange} PYTHIA~6 tunes Z1, Z2 and Perugia 0 are up to an order of magnitude
below the $\Omega$ measured spectra and yield and the ratio $\Omega$/$\Xi$ is also underestimated by a factor up to $\simeq$4\cite{ALICEstrange}.
The Perugia 2011 gives better results, but underestimates by a factor 4(2) the $\Omega$($\Xi$) yield(Fig. 1). 
Simulating the strange hadrons is a difficult task:
%% the discrepancy is larger
%%at low $p_{T}$ and for hadrons containing two or three s-quarks.
in PYTHIA
the strangeness production is controlled by several parameters, as the suppression of the s quark pair production in the field compared with the $u$-pair or $d$-pair production, the extra suppression of strange diquark
production compared with the normal suppression of strange quarks, etc.
It is worth noting the Perugia 2011 tune makes use of the CTEQ5L parton distribution function, and has
a significant 
increase in multi-strange baryon yields with respect to other tunings/models. Nevertheless
the production of strangeness in ALICE is not adequately described by this tune too.
An effort to increase the strangeness production has been attempted by the Z1C tuning, increasing the above parameters: as a result
the $\Lambda$/K ratio increases but the K/$\pi$ ratio has to be improved
at $p_{T}>$ 1GeV/c, where the ratio is still underestimated. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%   use this format to include a LaTeX table  into your paper
%%
%\begin{table}[b]
%\begin{center}
%\begin{tabular}{l|ccc}  
%Patient &  Initial level($\mu$g/cc) &  w. Magnet &  
%w. Magnet and Sound \\ \hline
% Guglielmo B.  &   0.12     &     0.10      &     0.001  \\
% Ferrando di N. &  0.15     &     0.11      &  $< 0.0005$ \\ \hline
%\end{tabular}
%\caption{Blood cyanide levels for the two patients.}
%\label{tab:blood}
%\end{center}
%\end{table}
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\section{Inelastic cross section}
%The inelastic cross section was measured at LHC by 
%ALICE\cite{ALICEcross}, ATLAS\cite{ATLAScross} and CMS\cite{CMScross} measured the inelastic cross section relying
%They relied 
%mostly on forward region counters: ALICE used
%the V0 detector ( 2.8$<|\eta|<$5.1 and 3.7$<|\eta|<$1.7), ATLAS the Minimum Bias Trigger Scintillator(MBTS) at 
%2.1$<|\eta|<$3.8 and CMS the Hadronic Forward Calorimeter(HF) at 2.9$<|\eta|<$5.2.
The inelastic cross-section is the sum of several contributions: the single diffractive(SD),
the double diffractive(DD), the central diffractive(CD) and the non diffractive (ND) cross section. 
Diffraction study is challenging: most of the proton excitation remains into the beam pipe and low pile-up runs are required.
In addition the transition from ND to DD events is smooth; experimental observables requires Monte Carlo corrections to be linked with physics quantities. 
ATLAS relied on the calorimeters to study the distribution of the forward gap $\Delta \eta^{F}$\cite{ATLASgap}, defined as 
the larger of the $\eta$ regions extending to the limits of the ATLAS sensitivity ($\eta=\pm 4.9$), in which no final state particles are produced
above a given $p_{T}$ threshold. ND events correspond to $\Delta\eta^{F}\simeq$0, while SD events have large $\Delta \eta^{F}$.
PYTHIA 8 reproduces the $\Delta\eta^{F}$ distribution at low and high $\Delta\eta^{F}$, while the central region (3~$\leq\Delta\eta^{F}\leq$~6)
is overestimated. On the contrary this region is nicely reproduced by PHOJET, missing the low and the high $\Delta\eta^{F}$ region.
%%This may come from global $\sigma$
None of the models can reproduce the raise 
at $\Delta\eta^{F}>$6. This region can be matched by decreasing the pomeron intercept  
from $\alpha\simeq$~1.085 to $\simeq$~1.058, but the price to be paid is an
underestimate of the central region (3~$\leq\Delta\eta^{F}\leq$~6).
The fraction of diffractive events in the Monte Carlo has to be constrained from the data: ATLAS used the fraction
of events ($R_{ss}$) giving a signal only in one of the two Minimum Bias Trigger Scintillator detector (single-sided events)\cite{ATLAScross}. 
The MC generators predict that less than 1$\%$ of the ND process pass the single-sided event selection, 
whereas 27$-$41$\%$ of the SD and DD processes pass the single-sided selection. 
$R_{ss}$ was computed for different 
Monte Carlo codes by varying the fraction of the diffractive cross section with respect to 
the total inelastic cross section($f_{D}$). The experimental value $R_{ss}$=$(10.02\pm 0.03(stat)^{+0.1}_{-0.4}(sys))$
is reproduced assuming a diffractive fraction $f_{D}$=$(26.9^{+2.5}_{-0.1}$)$\%$. The model closest to the central value is PYTHIA 8 with the 
Donnachie-Landshof(DL) model with $\epsilon$=0.085 and $d$=0.25 $GeV^{-2}$, where $\epsilon +1$ is the 
intercept of the pomeron trajectory and $d$ is the pomeron trajectory slope. 
This code was selected by ATLAS as reference model.
The cross section for values of the fractional momentum loss of the scattered
proton 
$\xi=M_{x}^{2}/s>$5$\cdot 10^{-6}$ is $\sigma_{inel}$($\xi>$5$\cdot 10^{-6}$)=$(60.3\pm 0.05(stat)\pm 0.5(sys)\pm 2.1(lumi))$ mb.
To extrapolate the above cross section to the full cross section ($\xi>m_{p}^{2}/s$),  
the fractional contribution to the inelastic cross-section of events passing the cut  $\xi>$5$\cdot 10^{-6}$ 
is determined from the models.
The reference model, PYTHIA 8~+~DL, gives 87.3$\%$, while other models considered give fractions ranging from 96$\%$ 
(PHOJET) to 86$\%$ (DL with $\epsilon$=0.10). The inelastic cross section at $\sqrt{s}$ = 7 TeV for $\xi >m_{p}^{2}/s$ 
measured by ATLAS is
$\sigma_{inel}$=$(69.1\pm 2.4(exp.)\pm 6.9(model))$ mb,
where the experimental error includes both the statistical and the systematic error.
Similar procedures were used by ALICE and CMS, finding respectively 
$\sigma_{inel}$=$(73.2^{+2.0}_{-4.6}(model) \pm 2.6 (lumi))$mb\cite{CMScross} and
$\sigma_{inel}$=$(64.5\pm 1.1(exp.)\pm 1.5(model)\pm 2.6(lumi))$mb\cite{ALICEcross}.
ALICE used the distribution of the largest pseudorapidity gap in the event and the ratio of events with a single arm to those
with two arms to constrain the fraction of the SD and the DD cross section\cite{ALICEcross}.
The result obtained was $\sigma_{SD}$/$\sigma_{inel}$=$(0.21^{+0.04}_{-0.07})$ and $\sigma_{DD}$/$\sigma_{inel}$=$(0.12^{+0.05}_{-0.04})$.
The cross sections measured by ALICE, ATLAS and CMS agree within the quoted uncertainties, the first one
being slighty larger.
%It is worth noting that ALICE uses a different Monte Carlo code for the extrapolation to $\xi>m_{p}^{2}/s$\cite{ALICEcross}, predicting a dN/d$\xi$ with a steeper slope and therefore gets a larger contribution in the extrapolation to lower $\xi$. 
%A different strategy to measure to cross section is used by
TOTEM\cite{TOTEMcross} used the elastic cross section and the optical theorem. The result is  
%%The extrapolation of the cross section to t=0 was obtained
%%by fitting the data taken at 0.02 $<|$t$|<$0.33 $GeV^{-2}$, and is therefore model independent. 
%%The final inelastic cross
%%section is 
$\sigma_{inel}$=$(73.4\pm 0.1(stat)\pm 1.9(sys)\pm2.9(lumi)$)$mb$, in good agreement with the measurements quoted above, specially the ALICE one.
\section{Hard diffraction dijet production}
Diffractive dijet production is characterised by the presence of a high-momentum proton which escapes undetected,
and by a system X, which contains high-$p_{T}$ jets and is separated from the proton by a large rapidity gap(LRG). 
One proton emits a pomeron with fractional
momentum $\xi$ and then the pomeron interacts with the other proton.
This process
has been studied at Fermilab and at HERA. 
%One proton emits a Pomeron with fractional
%%momentum $\xi$ and then the Pomeron interacts with the other proton.
Hard-diffractive processes can be described by the convolution of diffractive parton distribution functions (dPDFs) and hard scattering
cross sections, which are calculable in pQCD. 
\begin{figure}[h]
\begin{center}
\epsfig{file=Figure10.eps,height=2.5in}
\caption{The CMS differential cross section for dijet production as a function of $\tilde{\xi}$.} 
%The points are plotted at the centre
%of the bins. The predictions of non-diffractive (PYTHIA6 Z2
%and PYTHIA8 tune 1) and diffractive (POMPYT SD, POMWIG SD and PYTHIA8 SD+DD) MC
%generators are also shown, along with that of the NLO calculation based on POWHEG (first
%bin only).}
\label{fig:magnet2}
\end{center}
\end{figure}
While in e-p scattering the cross section can be succesfully factorized, in hadron-hadron collider the factorisation
is broken because of soft rescattering between the spectator partons. The related cross section reduction factor is usually 
referred in terms of Rapidity Gap Survival (RGS) probability. 
Dijets events were selected by CMS at $\sqrt{s}$=7 TeV\cite{CMSdijet} requiring transverse
momentum $p_{T}>$20 GeV for both jets, jet axis pseudorapidity in the range -4.4$<\eta<$4.4 and $\eta_{max}<$3($\eta_{min}>$-3).  
The dijet cross section was studied as a function 
of $\tilde{\xi}$$^{\pm}$=
C$\Sigma(E^{i}\pm p^{i}_{z})/\sqrt{s}$, a variable that
approximates the fractional momentum of the pomeron, where $E^{i}$ and $p_{z}^{i}$ are the energy and the longitudinal momentum of the 
$i^{th}$ particle-flow object and C is a correction factor for detector effects.
The data were compared with several Monte Carlo models: as a first step 
non diffractive (ND) events were generated by PYTHIA 6 and by PYTHIA 8.
These Monte Carlo, as expected, cannot reproduce the data at low $\tilde{\xi}$. Then
diffractive events were generated by PYTHIA8(SD+DD),   
POMWIG (based on HERWIG) and by POMPYT(based on the PYTHIA framework), all of them 
using a diffractive parton distributions based on H1 experiment data fit.
%%In the three above models the diffractive 
The main difference between POMWIG or POMPYT with respect to PYTHIA 8, is a different pomeron flux parametrization. 
POMWIG and POMPYT overestimate the event yield at low  $\xi$, while PYTHIA 8(SD+DD) has to be scaled 
by a factor $\simeq$2 to match the data.
Considering both POMWIG and POMPYT do not include the RGS, and that in the data 
a fraction of the scattered proton excites
into a low-mass state which escapes undetected in the forward region, the discrepancy between 
their expectation and the data, (0.21$\pm$0.07) can be considered as a RGS upper limit.
After a correction for the proton dissociation, an estimate of the RGS probability can be extracted,
giving (0.12$\pm$0.05).
\section{Conclusions}
The data collected from $\sqrt{s}$ = 0.9 to 7 TeV offered the possibility
to study many aspects of the soft QCD at LHC. 
The results from different experiments are in excellent agreement but 
the event generators still need further improvements to give appropriate predictions: 
as an example the strangeness production is not properly reproduced yet.
%%noone can simulate correctly all the observables.
The study of the minimum bias event topology allowed a reasonable tuning of the single and double diffraction in the event generators, 
leading to a succesfull measurement of the total inelastic cross section.
The ATLAS and CMS calorimeters succesfully studied the rapidity gap, the dijet and the W production in
diffractive events,
providing informations on the pomeron flux and on the diffractive structure functions.
In the next years 
%the higher energy available at 
LHC will unveil the evolution of the hadronic
system beyond 10 TeV and the study of other soft processes, as the central diffraction,
will give a more detailed picture of the low $p_{T}$ event production at high energy.
\begin{thebibliography}{99}
%%
%%  bibliographic items can be constructed using the LaTeX format in SPIRES:
%%    see    http://www.slac.stanford.edu/spires/hep/latex.html
%%  SPIRES will also supply the CITATION line information; please include it.
%%
\bibitem{ALICE1}
The ALICE collaboration, 
Eur. Phys. J. C65 (2010) 111.
\bibitem{ALICE2}
The ALICE collaboration, 
Eur. Phys. J. C68 (2010) 89; Eur. Phys. J. C68 (2010) 345.
\bibitem{ATLASsoft}
The ATLAS collaboration, New J. Phys. 13 (2011) 053033.
\bibitem{CMS1}
The CMS collaboration, JHEP 01 (2011) 079.
\bibitem{PHOJET}
R. Engel, Z. Phys. C66 (1995) 203. 
%%CITATION = PWASA,13,1564;%%
\bibitem{PYTHIA6}
T. Sjostrand et al. JHEP 05(2006) 026.
\bibitem{PYTHIA8} 
T. Sjostrand et al., Comput. Phys. Comm. 178 (2008) 852. 
\bibitem{LHCb}
The LHCb collaboration, Eur. Phys. J. C72 (2012) 1947.
\bibitem{TOTEMsoft}
The TOTEM collaboration, Eur. Lett. 98(2012) 31002.
\bibitem{CMSident}
The CMS collaboration, CMS PAS FSQ-12-014, CMS PAS QCS-10-007.
\bibitem{ALICEstrange}
The ALICE collaboration, Eur. Phys. J. C71 (2011) 1594;
Eur. Phys. J. C71 (2011) 1655; Phys. Rev, B710 (2010) 557;
Phys. Rev. Lett. B712 (2012) 309.
%\bibitewm{ATLASstrange}
%The ATLAS COllaboration, Phys. Rev. D 85 (2012) 012001.
\bibitem{ATLASgap}
The ATLAS collaboration, Eur. Phys. Jour. C72(2012) 1926.
\bibitem{ATLAScross}
The ATLAS collaboration, Nature Comm.2 (2011) 463.
\bibitem{ALICEcross}
The ALICE collaboration, arxiv.org/1208.4968v1.
\bibitem{CMScross}
The CMS collaboration, CMS PAS QCD-11-002.
\bibitem{TOTEMcross}
The TOTEM collaboration, CERN-PH-EP-2012-239;
see also the talk by F. Ferro at this conference.
\bibitem{CMSdijet}
The CMS collaboration, CMS PAS FWD-10-004.
\end{thebibliography}
\def\Discussion{
\setlength{\parskip}{0.3cm}\setlength{\parindent}{0.0cm}
     \bigskip\bigskip      {\Large {\bf Discussion}} \bigskip}
\def\speaker#1{{\bf #1:}\ }
\def\endDiscussion{}
\end{document}
%% ~~
