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\begin{document}
\title{LHC potential: Energy and Luminosity}

\author{W. J. Murray, CERN - STFC/RAL, Harwell Science and Innovation Campus,
  Didcot, Oxon., UK\\
On behalf of ALICE, ATLAS, CMS and LHCb}

\maketitle
\begin{abstract}
   The prospects for discovery physics in 2011 at LHC are
   reviewed. With 3.5~\TeV\ per beam and 1~\ifb\ 
   per experiment the exclusion of the Standard Model Higgs boson
   by ATLAS and CMS combined is possible from 120 GeV up to over 600~\GeV.
   Raising the beam energy to 4~\TeV\ will gain  30\%
    in the      Higgs cross-section
while for many other searches the gain is even larger.


\end{abstract}

\section{The Scenarios before us}

The excellent performance of the LHC machine in its initial run
in 2010 has encouraged speculation into the energy and integrated
luminosity
which might be achieved before the long shutdown. The influence on
the physics potential 
%of the energy-frontier experiments 
of these is considered here, with the focus on ATLAS and CMS
because the  programmes of ALICE and LHCb are not as
influenced by increasing energy, and their luminosity requirements do
not press as hard upon the machine performance.
In contrast, ATLAS and CMS essentially want as much  luminosity as possible at
the highest energy which can safely be reached.

The experiments are working remarkably well. The first
50~\ipb\ delivered
has been recorded with excellent efficiency and detector performance, 
and modelling  are  better than could have been hoped for. The detectors have
reported the observation of all the fundamental SM particles 
(except the Higgs boson), usually 
with cross-sections and more measured too.

Searches for new physics have been made with sensitivity well beyond
the Tevatron in 
%excited quarks\cite{excited}, quark
%substructure\cite{qsub}, SUSY\cite{susy}, 
%W'\cite{wprime}, Z'\cite{zprime}, lepto-quarks\cite{leptoquark} and
%many other
many
 areas, which are changing and constraining our picture
of the HEP world. So far most surprises in the p-p physics have been in
details of QCD predictions, which are interesting but  not
paradigm-changing. 
The lead ion run produced good evidence that matter formed in these
collisions is denser, hotter, and larger then that at RHIC, still
having properties close to ideal liquid. 

%The Lead ion run produced good evidence that
%a quark-gluon plasma is indeed formed, and this promises well for
%future study.
 

\section{LHCb goals in 2011}

The principle requirement of LHCb is to run stably at about 2-3
10$^{32}$~cm$^{-2}$~s$^{-1}$, for as long as possible. Such a run should
produce of order 1~\ifb\ which will allow the possibility of
discoveries
in many channels. A few highlights are $B_s\rightarrow\mu\mu$, $B_s$
CP-Violation (CPV) measurements, $B_s \rightarrow K^* \mu\mu$ studies,
CPV search in 
the charm system and of course the unitary triangle angles, especially
$\gamma$. 

Each of these will have the worlds best sensitivity already with less than a
third of the data discussed, and so there are exciting prospects for
new physics. It should be noted that the beam energy plays a
relatively minor role in those searches.

\section{ALICE programme}

The instantaneous luminosity for p-p collisions in ALICE must be limited to 
10$^{30}$~cm$^{-2}$~s$^{-1}$, (or possibly a little more), and 
the
limitation of interpreting the Pb-Pb data often comes from the p-p
statistics used for comparison. Therefore ALICE is interested
in maximum stable running of p-p collisions.
In addition, in pp collisions ALICE will be studying soft processes
and charm production. 


There is the need for a special p-p run of about 50M events with the beam
energy reduced to 1.38~\TeV\ to match the Pb-Pb energy per
nucleon. This is to allow direct comparison between the two sorts of
collisions, and will take a few days. There is no need to repeat this
if the beam energy is changed to 4~\TeV.

\section{High energy frontier}

The main reason to wish to raise the beam energy is the increased
production rate of heavy objects. This fractional increase is shown in
Fig.~\ref{fig:stirling}~\cite{ref:stirling}.

% The heavier the object being discussed, the
%larger the gain from increased beam energy.

\begin{figure}[htb]
    \centering
    \includegraphics*[width=80mm]{lumi_LHC_789-1.eps}
    \caption{The effective gain in the rate of interactions 
      from raising 
      the centre-of-mass energy to 8 or 9~\TeV. 
%For  Higgs
 %     production at around 100~\GeV 30\% gain is seen, while for
  %    searches like supersymetry at around 1000~\GeV the gain is
  %    80\%. Similar but smaller
  %    gains are seen in other processes.}
}
    \label{fig:stirling}
\end{figure}

%\begin{figure*}[tb]
%    \centering
%    \includegraphics*[width=168mm]{lumi_LHC_789_v2b.eps}
%    \caption{The effective gain in the rate of gluon-fusion processes
%      from raising 
%      the centre-of-mass energy to 8 or 9~\TeV. For  Higgs
%      production at around 100~\GeV 30\% gain is seen, while for
%      searches like supersymetry at around 1000~\GeV the gain is
%      80\%. Similar but smaller
%      gains are seen in other processes.}
%    \label{fig:stirling}
%\end{figure*}

\subsection{Standard Model}

The 2011 data will be used to extend the suite of measurements,
particularly in heavy gauge bosons, W and Z, and top quark studies.
The production rate of these particles, and the quality of the
detectors, gives good prospects for precise measurements such as the
mass of the W boson, a key ingredient of the Standard Model. 
However it is top studies where the advantage of the LHC energy is
most apparent. The first measurements of the top cross-section at 
LHC have been made on the first 3~\ipb\ of data and have  errors of
order 40\%. This helps to understand the gluon distribution inside the
proton and hence better estimate  the expected Higgs
cross-section. The errors will
be reduced enormously, but the top pair 
production would gain a 40\% rate enhancement from 4~\TeV\ operation,
which would of course help greatly.

Another interesting subject in top physics is the production of single
top quarks. This is an important test of the model and detectors and was only
first reported by the Tevatron in 2009.  The expected error  in
two different production modes~\cite{ref:singletop} can be seen in
Table~\ref{ta:singletop}.
A dataset of around 5~\ifb\ will be required to make meaningful
measurements of the more difficult W plus top mode, but the signal
rates in these channels increase 20-40\% by raising the beam energy
0.5~\TeV. This will be an important test of the experiments abilities
to undertake searches for rare objects.


\begin{table}[hbt]
   \centering
   \caption{Predicted error on the single top cross-section in two
     production modes as projected by the ATLAS experiment.}
   \begin{tabular}{lcc}
       \toprule
       \textbf{Mode} & \textbf{1~\ifb} & \textbf{5~\ifb} \\ 
       \midrule
           t-channel         & 32\%    & 13\%        \\
          Wt production      & 68\%    & 32\%        \\
       \bottomrule
   \end{tabular}
   \label{ta:singletop}
\end{table}


\subsection{Exotics searches}

There is a large range of exotic models which have been
investigated with a large range of possible signatures. The
example of the sensitivity of the search for a $Z^{\prime}$~\cite{ref:zprime}  is
used here. Figure~\ref{fig:zprime} shows  the sensitivity of the
expected limits to the energy and luminosity available.

\begin{figure}[htb]
   \centering
   \includegraphics*[width=80mm]{zp_limit_emu.eps}
   \caption{The estimated mass limits on a $Z^{\prime}$ from the ATLAS
     collaboration which can be      obtained as a function 
     of centre of mass energy and integrated luminosity. }
   \label{fig:zprime}
\end{figure}

As the current data provides limits at just over 1~\TeV, raising the
$E_{\mathrm CMS}$ by 1~\TeV\ roughly halves the amount of data 
required to set a new limit. For higher mass exotic scenarios, 
such as quark substructure or black hole production, the increased
cross-section will in general give rise to a larger increase.

\subsection{SUSY Searches}

The search for supersymmetry is one of the key goals of LHC. CMS
produced the first result on the total 2010
dataset~\cite{ref:cms-susy}, which placed limits on the CMSSM model
using events with jets and missing energy. The results can be seen in
Fig.~\ref{fig:cms-susy}. These are complemented by ATLAS
results~\cite{ref:atlas-susy} 
showing that, in a very simplistic scenario where squarks and gluinos
have the same mass, that mass scale is over 0.7~\TeV.

\begin{figure*}[tb]
    \centering
    \includegraphics*[width=168mm]{cms-susy.eps}
   \caption{Limits on SUSY parameter space from the CMS experiment. The
     coloured (grey) lines show the expectations for sensitivity, calculated
     beforehand and the black is the actual limit obtained.}
   \label{fig:cms-susy}
\end{figure*}

The limits obtained with 35~\ipb\ are a significant extension of the
previous bounds. They represent a major constraint on
SUSY model building, and are one of the most important LHC results to
date. It can be seen that they approximately match the sensitivity
which was estimated for 100~\ipb~\cite{ref:cms-susy-proj};
there is a certain tendency to be
conservative in making these estimations. ATLAS has provided some sensitivity
projections showing how the discovery reach in the future evolves with
energy and luminosity which are shown in Table~\ref{ta:susyproj}. It
can be seen that there is good discovery potential passing 1~\TeV,
provided 5~\ifb\ at 7~\TeV\ or 2~\ifb\ at 8~\TeV\ is available.


\begin{table}[hbt]
   \centering
   \caption{The projected 5$\sigma$ SUSY discovery ranges in~\TeV\ by
     ATLAS for different 
     scenarios of energy and luminosity. Note that exclusion limits
     would be larger. }
   \begin{tabular}{lcccc}
       \toprule
       \textbf{E$_{\mathrm CMS}$} & \multicolumn{4}{c}{Integrated Luminosity}\\ 
                  & 1~\ifb & 2~\ifb & 5~\ifb & 10~\ifb \\
       \midrule

     7~\TeV  & 0.7 & 0.8 & 1.0 & 1.2 \\
     8~\TeV  & 0.8 & 1.0 & 1.2 & 1.4 \\
     9~\TeV  & 0.9 & 1.1 & 1.3 & 1.6 \\
       \bottomrule
   \end{tabular}
   \label{ta:susyproj}
\end{table}



\subsection{Higgs searches}

A major goal for the current run is to maximise sensitivity to the
Standard Model Higgs boson. The LEP~\cite{ref:lep} lower limit of
114.4~\GeV\ has been augmented by the Tevatron~\cite{ref:tevatron}
exclusion of the region from 158-175~\GeV. The consistency of fits to
the electroweak data~\cite{ref:ew-fit} points to an upper limit of
185~\GeV, but this limit  assumes no additions to the Standard Model.
The LHC will be sensitive to a SM-like Higgs from the LEP bound to
over 600~\GeV. 

The search strategy depends upon the Higgs boson mass and hence its
decay modes, but it depends critically on the production
cross-section. The gain in this from increasing the beam energy is
shown in Fig.~\ref{fig:higgsxs} for various production modes, of
which the gluon fusion is probably the most important. The gain can 
be seen to be 30\% for a light Higgs boson in this channel on raising
the energy to 8~\TeV.

\begin{figure}[htb]
    \centering
    \includegraphics*[width=80mm]{Higgs_XS_Ratio.eps}
    \caption{The ratio of the Higgs boson cross-section at 8 or 9~\TeV\ to
      that at 7~\TeV\ as a function of mass.
}
    \label{fig:higgsxs}
\end{figure}


The sensitivity of ATLAS and CMS has been assessed by the
collaborations~\cite{ref:cms-higgs-sensitivity},~\cite{ref:atlas-higgs-sensitivity}, and is very similar. The sensitivity
of the CMS experiment, combining several decay modes, can be seen in
Fig.~\ref{fig:cms-result}. With a baseline run of 1~\ifb\ at
7~\TeV\ the two sigma sensitivity region covers 130 to
600~\GeV. 5~\ifb\ at 8~\TeV\ allows three sigma evidence across the
entire region investigated.

\begin{figure}[htb]
    \centering
    \includegraphics*[width=80mm]{Significance_mH_100_600_LogScale.eps}
    \caption{The significance of the expected observation of the
      Standard Model  Higgs boson at 7 or 8~\TeV\ for various
      assumed luminosity scenarios.
}
    \label{fig:cms-result}
\end{figure}


The gain from higher energy can be assessed in terms of the amount
of integrated luminosity at 8 or 9~\TeV\ giving the same Higgs boson sensitivity 
as 1~\ifb\ at 7~\TeV. This is done in Fig.~\ref{fig:higgs-effect}. If
can be seen that for a low-mass Higgs, favoured by the electroweak
fits, 20\% less data is needed to have the same sensitivity at 8~\TeV.

\begin{figure}[htb]
   \centering
   \includegraphics*[width=80mm]{effectivelumi.eps}
   \caption{Effective luminosity, (see text) }
   \label{fig:higgs-effect}
\end{figure}

\begin{table}[hbt]
   \centering
   \caption{Higgs mass range coverage at 8~\TeV.}
   \begin{tabular}{lccc}
       \toprule
       \textbf{Mode} & \textbf{2~\ifb} & \textbf{5~\ifb}  & \textbf{10~\ifb} \\ 
       \midrule
           95\% C.L. & Any           & Any         & Any \\
           3$\sigma$ & 118-500+~\GeV & Any         & Any \\
           5$\sigma$ & 130-200~\GeV & 120-500~\GeV & Any \\
       \bottomrule
   \end{tabular}
   \label{ta:higgs}
\end{table}


The Tevatron will continue to run through 2011
and produce new results. In the area of Higgs searches it
will remain competitive for some while. The aim is to have
2.4~$\sigma$ sensitivity for Higgs boson masses below 185~\GeV.
This is similar to the minimum sensitivity of the combined LHC
experiments given 2.5~\ifb\ at 7~\TeV\ each, however the LHC
experiments would be more powerful everywhere other 115~\GeV.


\section{Conclusions}


The LHC physics programme has got off to an excellent start in 2010,
and we thank all the LHC team that have made it possible.
There is an extremely exciting programme awaiting the LHC in 2011, in
which we envisage two orders of magnitude more data and significant
possibilities for a breakthrough in many areas.
If the beam energy can be raised to 4~\TeV\ there are important gains
to be made. Some of these are itemised in Table~\ref{ta:gains}.

\begin{table}[hbt]
   \centering
   \caption{Gain from raising the E$_{\mathrm CMS}$  to 8~\TeV\ for
     various analyses.} 
   \begin{tabular}{lc}
       \toprule
        & \textbf{Gain} \\
       \midrule
           SUSY                      & Needs 60\% as much data \\
           W$^{\prime}$, Z$^{\prime}$  & Half the data needed \\
           Black holes  & Factor 5 increase in production \\
           top  & 40\% more top quarks \\
           Higgs & Needs 80\% as much data\\
       \bottomrule
   \end{tabular}
   \label{ta:gains}
\end{table}



It must be stressed that these projections have many
assumptions. Typically the effects of pileup have not been completely
included, which will degrade the results. However, the analyses used
are generally rather simple and robust, and it is likely that the
combined work of many highly motivated people will produced more
finally-honed results. 

Assuming 3.5~\TeV\ beam energy, with about 2.5~\ifb\ ATLAS and CMS can
each independently 
exclude at 95\% CL or more the Standard Model (SM) Higgs
with every mass. With about 6~\ifb\ ATLAS and CMS can
each independently obtain at least a 3$\sigma$ observation from the 
LEP bound at 114.4~\GeV\ to about 500 GeV.



\begin{thebibliography}{9}   % Use for  1-9  references
%\begin{thebibliography}{99} % Use for 10-99 references

\bibitem{ref:stirling}
W.J. Stirling, private communication. 
{\tt http://projects.hepforge.org/mstwpdf/}
\bibitem{ref:singletop}
ATLAS collaboration, Aad, G. et al., 
	``ATLAS top physics potential as a function of LHC integrated
luminosity'', 
ATL-PHYS-PUB-2011-004.
\bibitem{ref:zprime}
ATLAS collaboration, Aad, G. et al., 
	``Physics potential of Z' and W' searches with the ATLAS
Detector as a function of the LHC center-of-mass energy'', 
ATL-PHYS-PUB-2011-002.
\bibitem{ref:cms-susy}
CMS collaboration, Khachatryan, Vardan et al., ``Search for
Supersymmetry in pp Collisions at 7 TeV in Events with Jets and
Missing Transverse Energy'', 
     2011, arXiv:1101.1628, submitted to Phys. Lett. B.
\bibitem{ref:atlas-susy}
ATLAS collaboration, Aad, G. et al.,  ``Search for supersymmetry using final states with one lepton, jets, and missing transverse momentum with the ATLAS detector in $\sqrt{s}$ = 7 \TeV\ pp'', 
     2011, arXiv:1102.2357v2, accepted by Phys. Rev. Lett.
\bibitem{ref:cms-susy-proj}
The CMS collaboration, ``The CMS physics reach for searches at 7 TeV''
July 2010, CMS NOTE 2010/008.
\bibitem{ref:lep}
The LEP Higgs working group,  2003 Phys. Lett. B 565 61.
\bibitem{ref:tevatron}
CDF and D0 collaborations, 
``Combined CDF and D0 Upper Limits on Standard Model Higgs-Boson
Production with up to 6.7 fb$^{-1}$ of Data.'', arXiv:1007.4587v1.
\bibitem{ref:ew-fit}
The LEP Electro-weak working group, July 2010, 
http://lepewwg.web.cern.ch/LEPEWWG/
\bibitem{ref:cms-higgs-sensitivity}
The CMS collaboration, ``Projected sensitivity for Standard Model
Higgs boson searches at 7 and 8 TeV, and 1-10~\ifb'', 
{\tt https://twiki.cern.ch/twiki/bin/view/CMSPublic/}
{\tt PhysicsResultsHIGStandardModelProjections}
\bibitem{ref:atlas-higgs-sensitivity}
The ATLAS collaboration, ``Further investigations of ATLAS Sensitivity to Higgs Boson Production in different assumed LHC scenarios'', 
ATL-PHYS-PUB-2011-001.
\end{thebibliography}

\end{document}
