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\begin{document}
\input{phys_defs.tex}
\pagewiselinenumbers
\title{\bf Search for the new physics in the exclusive $\gamma + \mett$ final state.}
\preprint{FERMILAB-PUB-06/yyy-E}

\date{\today}

\begin{abstract}
We present the results of a search for physics beyond the Standard Model 
in a sample of exclusive \photon +\mett\ events in $p{\bar p}$ collisions 
at $\sqrt{s}=1.96$~TeV at CDF Run II.
Using a sample of 1996~\invpb\ of collision data we observe 280 events, consistent
with the background estimate of 264.8$\pm$16.8 events for photon with transverse 
energy $E_{\rm T} > 50$~GeV. We optimize the search for the best sensitivity to the
Large Extra Dimensions model and find 40 event, consistent
with the background estimate of 42.4$\pm$2.9 events for photons with 
$E_{\rm T} > 90$~GeV.
We combine this search with the updated exclusive jet +\mett\ analysis and set
the best Tevatron limits on the Large Extra Dimensions model.

\end{abstract}


\pacs{...}
% PACS, the Physics and Astronomy Classification Scheme.

\maketitle
\newcounter{myctr}

Since the Standard Model (SM) is known to be 
incomplete~\cite{super}, there is a world-wide program to look for hints of new 
physics. Many popular models such as Large Extra Dimensions (ADD)~\cite{matchev}, 
Gauge Mediated Supersymmetry Breaking (GMSB)~\cite{gmsb}, Seesaw models~\cite{rhn}
and others predict a production of invisible particles in association with a photon. In general, 
a photon (\photon) plus missing transverse energy (\mett) signature is sensitive to 
any mechanism that can produce a photon and 
an exotic particle that escapes the detection. Often these exotic invisible particles
are good candidates for the dark matter. In these types of models the exotic signal
would appear as an excess over Standard Model (SM) at the tail of the photon transverse energy 
(\Et) spectrum. On the other hand, \photon + \mett\ signature is also sensitive to
any heavy resonance that decays to a photon and undetectable particle, or even to 
two photons because a significant portion of photons is lost in the detector.
In such a case the excess would look like peak on top the SM background.
For example, 140~GeV heavy particle decaying to two photons
would produce via $\gamma + \gamma \rightarrow \gamma + \mett$ 
an excess at photon $E_{\rm T} \sim 70$~GeV.

In this Letter we present an {\it a priori} model-independent search for 
new physics in the exclusive $\gamma +\mett$ channel using the CDF Run II detector~\cite{CDFII} 
at the Fermilab Tevatron. The data corresponds to 1996$\pm$120~\invpb\ of $p{\bar p}$ collisions 
at $\sqrt{s}=1.96$~TeV. We optimize the cut on photon transverse energy for the
best sensitivity to ADD model. At the end we combine the result with the updated 
search in the exclusive jet+\mett\ channel, also sensitive to the ADD model.
While other experiments have searched in $\gamma + \mett$ channel~\cite{d0gamma}, 
the CDF experiment is in unique position to look into this signature
because at high instantaneous luminosities at LHC this signature could be spoiled by
a large number of extra-collisions. Reducing cosmic background is crucial for this analysis, 
and the recently installed photon timing system at CDF ~\cite{nim} allows us to effectively reduce it.

We briefly describe the ADD model we use~\cite{matchev}.
In this model the photon is produced via $q\bar q \rightarrow \gamma G_{KK}$.
Extra spatial dimensions are assumed to be compactified with radius $R$. The model introduces the 
fundamental mass scale $M_D$. The two parameters, $M_D$ and $R$, are related
to the Newton's constant and the number of extra dimensions by 
$G_N^{-1} = 8\pi R^n M_D^{2+n}$.  The SM fields propagate only on the normal 
3+1 dimensional plane, while gravitons propagate in the bulk, and would 
appear to us as massive states of the graviton, or, said differently,
as massive minimally-interacting particles. Large values of $R$ result in a 
large phase space for graviton production, canceling the weakness of the coupling 
to standard model fields.  For a given number of extra dimensions the 
production cross section scales as $1/M_D^{n+2}$. It turns out that 
the kinematics are independent of $M_D$ for a given $n$.

A full description of the CDF 
Run II detector can be found elsewhere~\cite{CDFII}. Here we briefly describe 
the aspects of the detector relevant to this analysis. The magnetic 
spectrometer consists of tracking devices inside a \mbox{3-m} diameter, 5-m long 
superconducting solenoid magnet that operates at 1.4~T. A 3.1-m long drift 
chamber (COT) with 96 layers of sense wires is used to determine the momenta of 
charged particles, the $z$ position of the $\pbarp$ interaction, and the time of 
the interaction. Muons from collisions and 
cosmic rays are identified with a system of planar drift chambers situated 
outside the calorimeters in the region with rapidity $|\eta|<1.0$~\cite{rapdef}.
The calorimeter, constructed of projective 
towers, each with an electromagnetic and hadronic compartment, is divided into a 
central barrel that surrounds the solenoid coil (\mbox{$|\eta|<1.1$}) and a pair 
of plug barrels that cover the region $1.1<|\eta|<3.6$. Both are used  to identify and measure 
photons, electrons, jets and \mett. The electromagnetic compartments of the central and plug
calorimeters were recently instrumented with a new system, EMTiming, 
to provide a measurement of the arrival time of the 
energy in each tower~\cite{nim}. The timing system is used to fight background induced 
by cosmic rays.

The analysis selection cuts and cut efficiencies, all estimated from data,
 are summarized in Table~\ref{tab:select}. 
The selection begins with events passing online 
the CDF three-level trigger by virtue of having a high energy 
EM cluster in the region $|\eta|<$1.1 with \ett$>25$~GeV (presumably from the photon) and 
\mett$>$25~GeV. The trigger is 100\% efficient for the final \photon\ and \mett\ energy 
requirements. Offline, the highest \ett\ photon candidate in the fiducial 
region of the calorimeter is required to pass the standard photon 
identification (ID) cuts~\cite{photons,ggmet}. 
We require at least one central photon with $|\eta| < 1.1$ and $E_{\rm T} > 50$~GeV.
We also ask that the missing transverse energy is greater than 50~GeV. 
We veto events with jets above 15 GeV or tracks above 10 GeV. 
To reduce non-collision backgrounds we ask for at least 
3 COT tracks, the photon timing has to be consistent with coming from a collision and
to pass the discriminant that separates collision photons from 
look-alike cosmic ray candidates. For the discriminant we use Relevance Vector
Machine~\cite{rvmmach} (RVM) that is trained on data to distinguish
between collision and cosmic photon candidates.

\scriptsize
\begin{table}
  \begin{center}
    \begin{tabular}{ll}
      \hline \hline
      {\bf Quality Cuts} & $\epsilon(\%)$ \\
      \ \  Photon ID ($E_{\rm T}^{\gamma} > 50$ GeV) \\
      \ \ \ \ $\mett > 50$~GeV & 68\\
      \bf{Non-collision Rejection} & \\
      \ \  Cosmics Rejection & \\
      \ \ \ \ Timing & 99 \\ 
      \ \ \ \ RVM & 92 \\
      \ \ \ \ at least 3 COT tracks & 79 \\
       \ \  Beam Halo Rejection & 99 \\
      \bf{High $E_{\rm T}$ objects from extra collisions} & 98\\
      \ \ \ \ No jets with $E_{\rm T} > 15$~GeV \\
      \ \ \ \ No tracks with $P_{\rm T} > 10$~GeV \\
      \hline \hline
    \end{tabular}
  \end{center}
  \caption{The data selection criteria and the efficiency 
  for central photons with rapidity $|\eta|<$1.1. All efficiency are estimated
  from data and should be model-independent. The lower set 
  of cuts are model-dependent. The overall efficiency for photons with $|\eta|<1.1$ 
  is $45.5 \pm 4.7 \%$.}
    \label{tab:select}
    \end{table}
\normalsize

%\mysect{Backgrounds}

Table~\ref{tab:backs} shows the breakdown of various backgrounds.
There are two major sources: collision and 
non-collision photon candidates. Collision photons are presumed to be from the 
SM interactions such as irreducible $Z\gamma\rightarrow\gamma\nu\bar{\nu}$ electroweak 
process, $W\rightarrow l\nu$ production where lepton fakes the photon, $W\gamma$ and 
$\gamma\gamma$ events when the second lepton or photon is lost.
All of the above backgrounds, except for irreducible $Z\gamma$ and cosmics, are important 
at low energies, but die out fast as photon energy increases. $Z\gamma$ and 
$W\rightarrow \mu/\tau\rightarrow\gamma$ are estimated from Monte Carlo, for the
rest the data is used.

At low energies the dominant background is $W\rightarrow l\rightarrow\gamma$.
To understand this background we rely on Monte Carlo to find the 
\Et\ dependence of the fake rate. The data sample of $e\gamma$ events
is used to normalize the fake rate. The sample is selected to 
have no \mett\ and mass of the electron-photon pair to be consistent with  $Z$ peak.
For the electroweak $W\gamma$ and QCD $\gamma\gamma$ backgrounds
we use similar approach. The rate at which only a single photon would be left
in the detector is determined from Monte Carlo, but the data is used for the
absolute normalisation. For example, to estimate $\gamma\gamma$ the ratio of the 
events with single photon to events with 2 photons is found from Monte Carlo,
and multiplied by the number of events with 2 photon in the data. 
In this way the additional contribution from $\gamma + \pi$ QCD process, where a photon is lost 
and jet fakes a photon, production is naturally accounted for.

As we look at photons with higher energies, the $Z\gamma\rightarrow \nu\nu\gamma$ background
becomes dominant. To estimate this background we use Monte Carlo with only Leading
Order contributions to the cross-section which adequately describes the production cross-section 
in the presence of jet veto cut~\cite{baur}.
 
\scriptsize
\begin{table}
\begin{center}
\begin{tabular}{|l| l l|}
\hline
Channel & $E_{\rm T}^{\gamma} > 50$~GeV & $E_{\rm T}^{\gamma} > 90$~GeV \\ \hline
$W\rightarrow e\rightarrow\gamma$              & 47.3 $\pm$ 5.1 & 2.6 $\pm$0.4 \\
$W\rightarrow \mu/\tau\rightarrow\gamma$        & 19.1 $\pm$ 4.2 & 1.0 $\pm$ 0.2 \\
$W\gamma\rightarrow\mu\gamma\rightarrow\gamma$ & 33.1 $\pm$ 10.2& 1.7 $\pm$1.2 \\
$W\gamma\rightarrow e\gamma\rightarrow\gamma$  & 8.0  $\pm$ 3.0 & 0.8 $\pm$0.7 \\
$W\gamma\rightarrow\tau\gamma\rightarrow\gamma$& 17.6 $\pm$ 1.6 & 2.5 $\pm$0.2 \\
$\gamma\gamma\rightarrow\gamma$               & 18.9 $\pm$ 2.3 & 2.3 $\pm$0.6 \\
cosmics                                            & 36.4 $\pm$ 2.5 & 9.8 $\pm$    1.3 \\
%                                                  & 180.4$\pm$ 13.1& 21.5$\pm$ 2.1 \\
$Z\gamma\rightarrow \nu\nu\gamma$              & 84.4 $\pm$ 8.0 & 20.9$\pm$
 2.0 \\ \hline
Total & 264.8 $\pm$ 14.8 & 42.4 $\pm$ 2.9 \\ \hline\hline
Data  & 280  & 40 \\ \hline
\end{tabular}
\end{center}
 \caption{The table shows the background estimates for photons with $E_{\rm T} > 50$~GeV
 and $E_{\rm T} > 90$~GeV.}
\label{tab:backs}
\end{table}
\normalsize
 
Non-collision backgrounds come from cosmic rays and beam effects which produce fake 
photons and \mett. Beam halo photon candidates are 
produced by muons that originate upstream of the detector and fly
parallel to the beam line. Those muons produce fake photon candidates as 
they interact with the calorimeter. Beam halo muons normally leave a trail of 
the calorimeter towers with some energy deposited in the same wedge with the 
photon. We use this fact to develop highly efficient rejection cuts that 
completely eliminates this background.

We rely heavily on the recently installed calorimeter timing system
to fight the cosmics ray background. 
Photon candidates from cosmic rays are not correlated in time with collisions, 
and therefore their timing shape is roughly flat in time.
The timing for the collision photons has Gaussian shape with the mean at zero and 
RMS of 1.6 ns~\cite{nim}. We select photon candidates with timing above 20~ns to predict the level of 
the background in the prompt window. We also use photon candidates to select a sample of pure 
cosmic photons to train
the discriminant to separate collision photons from cosmic ones. At the end we are able to reduce
the cosmic background by $\sim 600$ times. Still, it remains to be the dominant background
at hight $E_{T}$ region where we are most sensitive to the new physics.

\begin{figure}[h]
  \centering%
  \includegraphics[width=0.8\linewidth]{../Plots/phoEt_data_wled_log.eps}
  \includegraphics[width=0.8\linewidth]{../Plots/phoEt_data.eps}
  \caption[Photon \Et\ and \mett\ distributions]
	  {The figure shows photon \Et\ distrribution on the log and linear scales. 
	  The backgrounds are stacked on top of each other. The top plot also shows the 
	  signal from ADD model stacked on top of SM backgrounds.}
	  \label{fig:phoMet}
\end{figure} 


Figure~\ref{fig:phoMet} and Table~\ref{tab:backs} 
show the comparison between data and background prediction.
We note that the data is in a good agreement at low and high regions of the photon \Et\ 
spectrum. There is an excess in the data around photon $E_{\rm T} \sim 70$~GeV. 
The probability for the background fluctuation is 0.68\% which is eqvivalent to
the less than 3$\sigma$ significance. It would be interesting to see if the excess 
fades away as more data is analyzed in the future.

To estimate our sensitivity to ADD model we simulate the signal with the {\small PYTHIA} 
Monte Carlo~\cite{pythia} along with the standard {\small GEANT}~\cite{geant} based
detector simulation. For each extra-dimension we simulate the the samples for $M_{D}$ 
in the range between 0.7 and 2~TeV.
The final kinematic selection requirements defining the final data sample are 
determined by optimizing the expected cross section limit without looking at the data. 
To compute the expected 95\% confidence level (C.L.) cross section upper limit 
we combine the predicted ADD signal and background estimates with the systematic 
uncertainties using a Bayesian method with a flat prior~\cite{Conway}. 
The expected limits are computed as a function of photon \Et. 
The  acceptance, the ratio of simulated events that pass 
all the requirements in Table~\ref{tab:select} to all events produced, is found to be 
almost independent  within 2\% of the mass $M_{D}$.
The total sysematic uncertainity on the signal
is $5.7\%$. The major contributions to the systematic error are from  initial/final state 
radiation convoluted with jet veto cut (4.8\%), uncertainty on the $Q^2$ scale (2\%), 
and uncertainty in parton distribution functions (1\%).

The optimization shows that the maximum 
sensitivity is reached at photon \Et$ > 90 $~GeV independent of the number of extra dimensions. 
The data yields 40 events above 90 GeV, in good agreement with the predicted background of 
42.3 events. Figure~\ref{fig:phoMet}
shows the total number of events including the estimated signal from ADD.

\scriptsize
\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c||c|c||c|}
\hline
 & \multicolumn{3}{|c||}{$\gamma+\mett$ } & \multicolumn{2}{|c||}{$Jet+\mett$ } & \\ \hline
 N LED&\ \  $\alpha$\ \ &\ \ $\sigma_{obs}^{95}$\ \ & $M_D^{obs}$ &\ \ $\alpha$\ \ &  
  $M_D^{obs}$  & $M_D^{comb}$\\ \hline
2& 7.1 & 99.2 & 1040& 9.9  & 1310 & 1400\\
3& 7.1 & 99.0 & 970 & 11.1 & 1080 & 1150\\
4& 7.4 & 93.9 & 940 & 12.6 & 980 & 1040\\
5& 7.2 & 96.8 & 900 & 12.1 & 910 & 980\\
6& 7.1 & 98.6 & 880 & 12.3 & 880 & 940\\
\hline
\end{tabular}
\label{tab:model}
\caption{The table shows the limits on the ADD model for different numbers of
extra-dimensions.}
\end{center}
\end{table}
\normalsize


\begin{figure}
  \centering%
  \includegraphics[width=0.8\linewidth]{../Plots/LEDcomp.eps}
  \caption[ADD exclusion limits]
	  {The figure shows exclusion limits for the ADD model.}
	  \label{fig:led}
\end{figure} 

In conclusion, the CDF experiment has recently completed a search for new physics in the
exclusive $\gamma + \mett$ channel that decay to photons using 1996 \invpb of data. 
While the current data is consistent with the
background expectations, limits on the ADD model are among the worlds most sensitive for 
these types of new particle production. 
As the experiment collects more and more data, this search becomes more sensitive for 
the potential discovery.
The next couple of years are equally exciting as the analysis
is expected to triple the dataset and to further improve the sensitivity for discovery.


%\mysect{acknowledgments}
\begin{acknowledgments}
We thank the Fermilab staff and the technical staffs of the
participating institutions for their vital contributions. This
work was supported by the U.S. Department of Energy and National
Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare;
the Ministry of Education, Culture, Sports, Science and Technology of
Japan; the Natural Sciences and Engineering Research Council of
Canada; the National Science Council of the Republic of China; the
Swiss National Science Foundation; the A.P. Sloan Foundation; the
Bundesministerium f\"ur Bildung und Forschung, Germany; the Korean
Science and Engineering Foundation and the Korean Research Foundation;
the Particle Physics and Astronomy Research Council and the Royal
Society, UK; the Russian Foundation for Basic Research; the Comisi\'on
Interministerial de Ciencia y Tecnolog\'{\i}a, Spain; in part by the
European Community's Human Potential Programme under contract
HPRN-CT-2002-00292; and the Academy of Finland.
\end{acknowledgments}

%====YOUAREHERE===============================\\
%\clearpage
%\newpage

\begin{thebibliography}{99}

\bibitem{super} S.~P.~Martin arXiv:hep-ph/9709356.

%\bibitem{gmsb} See for example S. Ambrosanio, G.~L.~Kane, G.~D.~Kribs,
%  S.~P.~Martin and S.~Mrenna, Phys.~Rev. D\textbf{~54}, 5395 (1996) or
%  C.~H.~Chen and J.~F.~Gunion, Phys.~Rev. D\textbf{~58}, 075005 (1998).

\bibitem{matchev} N.~Arkani-Hamed, S.~Dimopoulos,
  and G.~Dvali, Phys. Lett. B {\bf 429}, 263 (1998).

\bibitem{gmsb}
S.~Ambrosanio {\it et al.}, Phys.~Rev. D\textbf{~54}, 5395 (1996);\\
C.~H.~Chen and J.~F.~Gunion, Phys.~Rev. D\textbf{~58}, 075005 (1998).

\bibitem{rhn}
  M.~L.~Graesser,
  %``Experimental constraints on Higgs boson decays to TeV-scale right-handed
  %neutrinos,''
  arXiv:0705.2190 [hep-ph].
  %%CITATION = ARXIV:0705.2190;%%

\bibitem{llpho}
  A.~Abulencia {\it et al.}  [CDF Collaboration],
  %``Search for heavy, long-lived particles that decay to photons at CDF II,''
  Phys.\ Rev.\ Lett.\  {\bf 99}, 121801 (2007)
  [arXiv:0704.0760 [hep-ex]].
  %%CITATION = PRLTA,99,121801;%%

\bibitem{CDFII} 
CDF Collaboration, D.~Acosta {\it et al.}, Phys. Rev. D \textbf{71}, 032001 (2005).

\bibitem{d0gamma} Phys.\ Rev.\ Lett.\  {\bf 90}, 251802 (2003)

\bibitem{nim} M.~Goncharov {\it at al.}, Nucl.Instrum.Meth. A563, 543 (2006) 

%\bibitem{feng} 
%  J.~L.~Feng, A.~Rajaraman, and F.~Takayama arXiv:hep-ph/0306024.\\ 
%J.~L.~Feng {\it et al.}, Phys.Rev.Lett.91:011302,2003; \\
%arXiv:hep-ph/0302215;\\
%J.~L.~Feng {\it et al.}, Phys.Rev.D68:063504,2003;\\
% arXiv:hep-ph/0306024;\\
%M.~J.~Strassler and K.~M.~Zurek, arXiv:hep-ph/0605193.

%\bibitem{ggmet}
%CDF Collaboration, D.~Acosta {\it et al.}, Phys. Rev. D 71, 031104(R) (2005).

%\bibitem{lumi}
%CDF Collaboration, D.~Acosta {\it et al.}, Nucl. Instrum. Meth. A {\bf 494}, 57 (2002).

%\bibitem{lep} ALEPH Collaboration, A. Heister {\it et al.},
%  Eur.~Phys.~J. C\textbf{~25}, 339 (2002).

%\bibitem{prospects} D.~Toback and P.~Wagner, \Journal{\PRD}{70}{2004}{114032}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\bibitem{zvtime}
%  The $z$ distribution of the $\pbarp$ collisions has an RMS of 30~cm.
%  The time variation has an RMS of 1.3~ns~\cite{nim}.

\bibitem{rapdef}
$\eta = -{\rm ln~tan}(\theta/2)$, and $\theta$ is the angle from the beam line.

\bibitem{photons}
See \mbox{F. Abe {\it et al.},} \Journal{\PRD}{52}{1995}{4784}
for a detailed description of the definition of an electromagnetic cluster
and the analysis variables used to identify photons.
Ref.~\protect\cite{ggmet} contains a description of the standard photon
identification requirements. In this analysis, we note that in this analysis
the standard $\chi^2_{CES}<20$ requirement has be removed because 
there is evidence that it is inefficient for photons from that arrive with
large incident angles relative to the face of the detector, as would be
expected in this case. 

\bibitem{rvmmach} Chih-Chung Chang and Chih-Jen Lin, 
``{LIBSVM}: a library for support vector machines'', 2001.

\bibitem{pythia}
  T.~Sj\"{o}strand {\it et al.}, \Journal{Comput. Phys. Commun.}{135}{238}{2001}. 

\bibitem{geant} R.~Brun \etal, CERN-DD/EE/84-1 (1987).

\bibitem{Conway}
J.~Conway, CERN Yellow Book Report No. CERN 2000-005, 2000, p. 247. 


\bibitem{Boos}
E.~Boos, A.~Vologdin, D.~Toback, and J.~Gaspard, Phys. Rev. D 66, 013011 (2002).

\bibitem{ggmet}
CDF Collaboration, F. Abe {\it et al.},Phys. Rev. Lett. {\bf 81}, 1791 (1998);
%Phys. Rev. D {\bf 59}, 092002 (1999).

%\bibitem{phomumet}
%A.~Abulencia {\it et al.} (CDF Collaboration), 
%Phys. Rev. Lett. \textbf{97}, 031801 (2006); arXiv:hep-ex/0605097

\bibitem{baur}
U.~Baur, T.~Han, J.~Ohnemus, Phys. Rev. D 57, 2823 (1998).


\end{thebibliography}

\end{document}