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\begin{document} \title{Monte Carlo generators \\ for the LHC } 
\author{Roberto Chierici}
\institute{ Institut de Physique Nucleaire de Lyon, IN2P3-CNRS, Universit\'e Claude Bernard Lyon 1, Villeurbanne, France }
\maketitle
\begin{abstract}
This contribution briefly reviews the Monte Carlo choices in CMS and ATLAS for the generation
of signals and background for Standard Model physics. Emphasis will be given to the generator 
validation and the Monte Carlo set-up for interpreting the first LHC data.
\end{abstract}

\section{Introduction and desiderata}

The year 2009 is crucial for the Monte Carlo (MC) production at the LHC experiments, that 
will allow interpreting the first data. The experiments are preparing their event generation 
strategies and are producing large-scale samples of events
for training tools and analyses. \\
In a modern generation setup for physics at the LHC there are certain requirements that
need to be fulfilled. They can be summarised as follows:
\begin{itemize}
\item {an event generator with a description of the hard scattering process with a matrix element 
(ME) calculation at the highest possible QCD order} 
\item {the possibility of interfacing, directly or via intermediate parton level files, 
to generic tools used for the parton showering (PS) and for parton hadronisation. 
The most known, and largely used, 
are PYTHIA~\cite{pythia} and HERWIG~\cite{herwig}}
\item {the presence of models for the description of the underlying event (UE), representing 
all what is in the event except the primary interaction. PYTHIA and HERWIG already present
models for this task}
\item {a coverage, as large as possible, of Standard Model (SM) and Beyond the Standard Model (BSM)
processes, with a good flexibility for implementing new physics models in the event generation}
\item {standard output formatting of parton level files, in particular the possibility
of outputting events in the Les Houches format~\cite{leshouches}}
\end{itemize}

The current article should not be intended as a review of generators, but rather a picture of 
the current MC set-up chosen by ATLAS and CMS, and of the current 
validation activities on this subject.
I will focus in what follows on generic SM and BSM physics from pp collisions, without 
discussing generators for heavy ions studies, or dedicated tools for new physics signatures 
(like black holes generators) or dedicated detector studies (like generator of cosmics, beam 
halo or beam-gas intercations). These generators remain however essential for the physics
programme of ATLAS and CMS.

\section{Generators for LHC physics}

\subsection{Event generators}

Both the ATLAS and CMS Collaborations try to use as many event generators as reasonable.
The reference generic purpose event generators for SM and BSM physics and beyond are 
PYTHIA, HERWIG and SHERPA. 
The first two, whose original version is written in FORTRAN, are now also used in their
C++ versions (PYTHIA8, HERWIG++), that will be the only ones maintained in the long term.
The main common feature of all generic purpose generators is that they provide a fully hadronised
event to be passed directly to the detector simulation. All of them implement models for 
the description of the radiation, fragmentation and the underlying event.
The models in PYTHIA and HERWIG have been extensively tuned to LEP, SLD and Tevatron data
for what concerns PS-fragmentation~\cite{tunes} and UE~\cite{UEtunes}. 
If PYTHIA and HERWIG include LO descriptions of very many SM and BSM processes, in some 
cases with the additional corrections to PS for a description of the first QCD emission 
at NLO, SHERPA also include the possibility of matching PS with ME at higher leading 
order, for both SM and BSM processes.     
General interest decay/correction tools, interfacable to all kind of general purpose event 
generators, are typically used in both Collaborations. Most noticable ones are TAUOLA,
for $\tau$ decays~\cite{tauolaphotos}, EvtGen, for hadron decays~\cite{evtgen}, extensively tuned
at the Tevatron and at B-factories, and PHOTOS, for including real QED corrections~\cite{tauolaphotos}.

If generic purpose event generators represent the 'work-horses' for the MC productions
at the LHC, there has been an enormous progress in the last years on implementing
ME descriptions of beyond-leading order QCD processes in event generators. 
This allows to improve the predicitons for observables sensitive 
to hard QCD emission (multi jet final states, typically).
This has been achieved either with techniques matching higher leading order (HLO) ME with PS
(examples are given by ALPGEN~\cite{alpgen}, MadGraph~\cite{madgraph}, 
SHERPA~\cite{sherpa}, HELAC~\cite{helac}), and by next-to-leading order (NLO) generators 
(like MC@NLO~\cite{mcatnlo} and POWHEG~\cite{powheg}).
The fundamental difference between the two categories of calculations is that the HLO maintains
a precision that is typically LO, but more correctly predicts shapes of differential 
distributions sensitive to real QCD emission, even at several orders beyond the leading,
whereas NLO calculations are correct in shape and normalisation at NLO for inclusive variables, 
but they count on PS for all extra emission beyond the first. \\   
Both CMS and ATLAS have interest in all those generators, and there is already an extensive
experience in their use in the collaborations. MadGraph, ALPGEN and MC@NLO are indeed references
in the current Monte Carlo productions for physics.
The event generators in the HLO and NLO categories remain parton level event generators, and
need therefore to be interfaced to PS and hadronisation for use in the experiments. Most of 
them provide direct interfaces to PYTHIA, or parton level output in the standard Les Houches
Accord format~\cite{leshouches}, that can be input to any hadroniser. Noticeable exception is 
MC@NLO, directly built on top of HERWIG.

The present list of generators does not exhaust what experiments have used and are using
for physics results. Some of them represent useful crosschecks, like AcerMC~\cite{acermc}
or TopRex~\cite{toprex} for top physics, or are in place for the description of particular
processes, like SingleTop~\cite{singletop} for single top physics or Phantom~\cite{phantom}
for the description of full six fermion processes at LO.  

\subsection{Generators tuning and set-up}

A full event generation often implies approximations by use of models, whose parameters 
need typically to be tuned to data. 
Examples are the parton showering, fragmentation, the description of 
the proton PDFs, the modelisation of the underlying event. Without entering a detailed 
explanation of each topic, I will briefly review the current settings chosen by ATLAS and
CMS. \\
The first essential ingredient, since protons are composite objects, is to describe the 
probability of the initial state at the hard process scale $Q^2$ with a certain fraction 
$x$ of the total proton momentum. Since the $Q^2$ evolution can be calculated perturbatively 
in the framework of QCD, PDFs are fitted to a set of heterogeneous data from DIS, Drell-Yan 
and jet data. Both Collaborations are currently using the LO CTEQ6L1 fit~\cite{cteq} with 
NLO PDF used only for NLO ME calculations. Errors from the fits, currently only available for
NLO fits, are then propagated to the final observables.
The scheme adopted at present is likely to change since no one of the generator used is purely
LO. There is more and more consensus, in the theory community, for using modified leading order
PDFs~\cite{modifiedpdf} for all LO calculations, or calculations including LO ME corrections. 
Modified PDFs are, essentially, LO PDF that relax the partonic momentum sum rule to get predictions 
artificially closer to NLO.

From parton level four-momenta configurations, initial and final state QCD and QED radiation are produced, 
via parton showering algorithms down to a certain energy scale: from that scale on 
fragmentation transforms coloured partons to colourless hadrons according to specific
models. Radiation parameters are typically fitted together with the fragmentation parameters,
and for the moment both ATLAS and CMS make use of fits from LEP/SLD~\cite{tunes,mynote}, 
assuming jet universality. The fragmentation functions chosen for heavy quark fragmentation
are the ones better describing LEP/SLD data, namely Bowler~\cite{bowler} and 
Peterson~\cite{peterson}.
With data available, those fits will have to be re-made at the LHC, taking care of the 
additional complication that initial state radiation at hadron machines contributes to the
description of the underlying event as well, so it will be essential to disentangle the 
two. Moreover, with the use of modern ME-PS matching, tunings of the PS part will 
have a new meaning with respect to previous tunings.

\begin{figure}
\includegraphics[width=\textwidth]{UE.eps}
\caption{Average number of charged tracks (left) and average track p$_{\mathrm{T}}$ sum in 
the transverse region (right) as a function of the transverse momentum of the leading jet 
in the event. The extrapolated predictions at the LHC are compared to CDF data.}
\label{ue}
\end{figure}
The underlying event corresponds to what else is present in an event, except the 
hardest interaction. Multiple parton interaction models turn out to be particularly adequate 
to describe this kind of physics. 
Examples of these models are implemented in the general purpose simulation programs 
PYTHIA, HERWIG/JIMMY~\cite{jimmy}, and SHERPA. 
Huge progress in the phenomenological study of the underlying event in jet events have been achieved 
by CDF~\cite{UEtunes} using, for the tuning of the models, the multiplicity and transverse momentum 
spectra of charged tracks in different regions in the azimuth-pseudorapidity space, defined with 
respect to the direction of the leading jet. 
The main problem of extrapolating the predictions of the multiple interactions models to the LHC
is that some of the parameters are explicitly energy dependent. Some of the tunes, used by 
ATLAS and CMS~\cite{atlas_tuning,lhc_workshop}, have put enphasis in the energy extrapolation
by also fitting lower energy data. 
The results are shown in figure~\ref{ue}, where the predictions of JIMMY and PYTHIA are extrapolated 
to the LHC energy for the average number of charged tracks and the average p$_{\mathrm{T}}$ sum of tracks in 
the transverse region (with respect to the leading jet in the event) as a function of the 
transverse momentum of the leading jet in the event.
The curves are compared to CDF data, and it is clear that the extrapolation to CMS energies
implies very different shapes compared to Tevatron. Moreover, the extrapolated predictions can 
differ widely according to the model used, therefore it will be mandatory to use LHC data 
themselves to validate them.

\section{Generator validation}

The validation of generators prediction in an experimental framework is an invaluable exercise
to gain confidence in the tools being used and to learn about the difference in the physics
contents between generators. A few important examples are presented in this section.

\subsection{Multiple parton interactions}

The presence of multiple parton interactions, i.e. the possibility of having multiple parton-parton
interactions overlapping in the same event, has been established already at the Tevatron, as illustrated
in figure~\ref{mpi}.
\begin{figure}
\begin{tabular}{cc}
\includegraphics[width=0.51\textwidth]{MPI1.eps}
\includegraphics[width=0.48\textwidth]{MPI2.eps} \\
\end{tabular}
\caption{Azimuthal distance between $\gamma$+j and j+j systems in $\gamma$+jets events at CDF, 
comparing data with MC, with or without MPI component (left).Validation of PYTHIA8 with MPI in 
CMS (right).}
\label{mpi}
\end{figure}
The left part of the figure shows, for $\gamma$+3jets events, the azimuthal distance between the 
transverse momentum vectors formed by the photon and the most back-to-back jet, and by the other
two jets. The MPI component is expected to have a flat
behaviour in this variable, and the figure clearly shows that the CDF data can not be described
without accounting for it.
The most recent PYTHIA version includes MPI interleaved to PS, and it is essential to validate this
tool in the experimental framework. \\
The right-hand part of figure~\ref{mpi} shows a preliminary study
by CMS where the prediction of PYTHIA8 with MPI for the same azimuthal variable are compared with 
PYTHIA6 and HERWIG with the most uptodate UE tune~\cite{dwt, s0}, and the 
same generators without the inclusion of MPI. The plot shows that the newest version of PYTHIA 
agrees with the default tuned one, and that there are important discrepancies between HERWIG (+JIMMY)
and PYTHIA. One more time it is shown that MPI effects are non negligible and should be accounted
for.

\subsection{Hard QCD emission in boson production}

Recent developments in ME generators allow to describe QCD radiation much more accurately. 
It is instructive to compare, for high p$_{\mathrm{T}}$ physics, the prediction of those calculations 
with respect to LO ones for observables that are sensitive to (gluon) radiation.
\begin{figure}[ht]
\includegraphics[width=\textwidth]{WjetsATLAS2.eps}
\caption{Transverse momentum of the first four highest p$_{\mathrm{T}}$ jets in W+jets events.}
\label{wjetsatlas}
\end{figure}
One of such comparison comes from W+jets production. The ATLAS Collaboration compared the
transverse momentum of the first four highest p$_{\mathrm{T}}$ jets in the event for ALPGEN and PYTHIA.
The results are shown in figure~\ref{wjetsatlas}, and large difference are observed in the high
momentum tails, as expected by a more accurate ME description. Also, the total number of high p$_{\mathrm{T}}$
jets increases very significantly going from a pure LO description to a higher order one
with matching to PS.

One important question for the analyses is about the residual uncertainty on total and differential 
cross-sections when going to high jet multiplicity in the final state. This question addresses
the problem of quantifying the confidence on the description of W boson production as background
to more complex process like top-pair production, where an associated many-jets production is 
necessary. To assess this, ATLAS have calculated the predicted cross-sections for all
jet multiplicities in W+jets with ALPGEN by varying both the matching scale (from 10 to 40 GeV)
and the minimum $\Delta$R ($\sqrt{\Delta\eta^2+\Delta\phi^2}$) that defines a parton (from 0.3 
to 0.7). The result, confirming that
the relative importance of the cross-sections at a fixed parton multiplicity varies according to 
the choice, shows that also the total cross-section, i.e. the sum of all fixed multiplicities
contributions, varies quite significantly in the different scenarios, up to around a factor 50\%.
This is shown in fig.~\ref{wjets}, left, where the reconstructed top mass for candidate 
semileptonic events in signal and W+jets background samples is shown for two choices of the matching 
scale, 20 and 40~GeV, respectively, at the same parton separation definition of $\Delta$R~=~0.7. 
The event selection is kept very simple with one reconstructed charged electron or muon 
with p$_{\mathrm{T}}>$~20~GeV
and $|\eta|<$~2.5, missing transverse energy greater than 20~GeV, and at least four
reconstructed jets, each with transverse energy of at least 20~GeV and for three of them 
larger than 40~GeV.  
\begin{figure}
\begin{tabular}{cc}
\includegraphics[width=0.57\textwidth]{Wjets.eps}
\includegraphics[width=0.43\textwidth]{WjetsTevatron.eps} \\
\end{tabular}
\caption{Reconstructed top mass in ATLAS for \tt signal and W+jets background (left) and 
ratio between data and different theory predictions for the inclusive jet multiplicity in
W events at the Tevatron (right).}
\label{wjets}
\end{figure}
Though the shape of the signal is unchanged, the W+jets background scales by a factor 1.5.
This reflects an uncertainty of the matching procedure itself that grows as the final 
parton multiplicity gets higher. Though the matching itself can be 
constrained using data at the LHC, present comparisons data-MC 
made at the Tevatron still show an insufficient statistics to constrain such predictions
at the LHC. This is shown in fig.~\ref{wjets}, right, where the CDF collaboration shows
the ratio between data and theory for the inclusive jet multiplicity in W events~\cite{cdf}.
As can be seen, the error bands of the matching codes get bigger at high multiplicity and 
current data is not enough to constrain them significantly.

\subsection{Hard QCD emission in top production}

A thourough test of the different description of QCD was also made by the CMS Collaboration
in the case of top-pair production: differences may manifest themselves in distortions of the 
top quark angular distributions and transverse variables. \\
The most spectacular effect is in the transverse momentum of the 
radiation itself, which equals the transverse momentum of the \tt system recoiling against it:
this is what is shown in fig.~\ref{pttt1}, left, for two leading order generations 
by MadGraph and TopRex (with PS) in comparison to the ME-PS matching scheme in
MadGraph. The contributions to a fixed ME order, ie tt+0jets, 
tt+1jets, tt+2jets and tt+3jets, are explictly indicated. 
On the right hand side of the same figure the corresponding distribution of 
the azimuthal difference between the two tops is also shown. The centre of mass
energy is 14 TeV, and it is important to notice that the input parameters settings (cuts, 
scales, PDFs) of the various generators shown in the figure are kept 
as uniform as possible to avoid any possible bias in the comparison. 
From the picture it is evident that gluon production via ME predicts
a much harder transverse spectrum. The difference in shape reaches orders of magnitude in 
the ratio at very high values of p$_{\mathrm{T}}$.
The increased activity in hard gluon emission for the ME-PS matched case also
explains a generally decreased azimuthal distance between the two top
quarks, which tend to be closer to each other. 
The distributions confirm the fact that having more ME radiation tends to 
increase the event transverse activity. 
The predicted average p$_{\mathrm{T}}$ of the radiation by MadGraph is 62~GeV/c
(72~GeV/c with ALPGEN), with a 40\% probability of having 
more than 50~GeV/c as gluon p$_{\mathrm{T}}$ in \tt events. This large 
gluon activity will certainly have an impact in the capability of 
correctly reconstructing top quark events at the LHC, and correctly 
interpreting radiation as a background for new physics searches.   
\begin{figure}
\begin{tabular}{cc}
\includegraphics[width=0.5\textwidth]{Pttt.eps}
\includegraphics[width=0.5\textwidth]{DPhitt.eps} \\
\end{tabular}
\caption{Transverse momentum of the \tt system (left), azimuthal angle between the two 
tops (right). All distributions are normalised to unity.}
\label{pttt1}
\end{figure}

An important validation step comes from the comparison of the predictions from different 
ME-PS matched codes.
Fig.~\ref{ptttmatched} shows the same distributions of fig.~\ref{pttt1}, but for
ALPGEN and MadGraph with ME-PS matching, respectively. 
For the p$_{\mathrm{T}}$ of the \tt system the individual parton multiplicity 
components are also shown. The agreement is more than acceptable, and remarkable 
for the azimuthal difference between the top quarks. Especially in the tails of the 
distributions, corresponding to high radiation conditions, the disagreement goes from
orders of magnitude of fig.~\ref{pttt1}, to a maximum discrepancy of 50\%. 
To properly appreciate the difference between the two predictions one should,
however, account for the theory errors on them. Scale and PDF dependencies, PS
tuning uncertainties could very well account for any residual difference in the tails.
\begin{figure}
\begin{tabular}{cc}
\includegraphics[width=0.52\textwidth]{Pttt2.eps}
\includegraphics[width=0.49\textwidth]{DPhitt2.eps} \\
\end{tabular}
\caption{Transverse momentum of the \tt system (left), azimuthal angle between the two 
tops (right). All distributions are normalised to unity.}
\label{ptttmatched}
\end{figure}

Another important test for the description of radiation in the top-pair production comes
from the comparison of matched ME-PS calculations to NLO predictions. This study was 
made by comparing the previous predictions to MC@NLO. A general very good agreement 
was found in all distributions, including the transverse ones. In fig.~\ref{mcnlo} 
the p$_{\mathrm{T}}$ of the \tt system and the p$_{\mathrm{T}}$ of the top are shown
for ALPGEN, MadGraph and MC@NLO.
As can be appreciated from the figure, it is particularly relevant the fact that the tails 
of the radiation are very well reproduced. The discrepancy in the very soft region is mostly due 
to the different showering, since MC@NLO is only interfaced to HERWIG whereas the other
predictions use PYTHIA as tool for PS and fragmentation. 
\begin{figure}
\begin{tabular}{cc}
\includegraphics[width=0.5\textwidth]{Pttt3.eps}
\includegraphics[width=0.5\textwidth]{Pttop.eps} \\
\end{tabular}
\caption{Transverse momentum of the \tt system (left), transverse momentum of the top
quark (right). All distributions are normalised to unity.}
\label{mcnlo}
\end{figure}


\section{Summary and outlook: towards data}

The LHC experiments are preparing their MC production to be ready for the interpretation of
the imminent data. There are a few important lessons that have been learned from previous
experiments and via the generator validation efforts in ATLAS and CMS, that help planning
a winning generation strategy:
\begin{itemize}
\item {make sure to use the best available tools for the description of the signal and the main 
backgrounds. For high jet multiplicity signals it is of utmost importance to include higher QCD 
corrections with now available ME generators.}  
\item {plan a very accurate MC tuning by using LHC data. All event generators use models 
for PS, fragmentation and UE/MPI, that need to be tuned. Moreover, interfacing external NLO or HLO 
generators to more standard 
PS tools opens new scenarios for the MC tunings. The PDF fits will also be enriched by the use of 
LHC data at higher value of Q$^{2}$}
\item {diversify the event generation and make it redundant, in such a way to compare different 
tools in the interesting regions of the phase space, or put in place parameter scans to understand 
possible systematic effects due to theory. Particular attention has to be put to the dependency
of the analyses to chosen scales, PDFs and ME-PS matching schemes.}
\item {make the reference SM and BSM generation as much as possible coherent (same input settings and cuts)
and consistent (full coverage of phase space). This will help correctly interpreting
analyses' results and in shortening the time for any discovery claim}
\end{itemize}  

ATLAS and CMS are preparing at their best the start-up of the LHC for what concerns 
the Monte Carlo set-up and productions. New C++ event generators, as well as more complex
HLO/NLO ME tools are used extensively in the analyses, and the level of communication with the 
theory communities, often a key to success in data interpretation, is constantly increasing. 
The choices made now will certainly shape the way the collaborations will be doing physics 
at the start-up, and not only.    

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\end{document}
