Indirect search for top squarks using dilepton mass distribustions at the 8 TeV LHC
Andres G. Delannoy$^{2}$
Vector boson fusion (VBF) processes at the Large Hadron Collider (LHC) provide a unique opportunity to search for new physics with electroweak couplings. A feasibility study for the search of supersymmetric dark matter in the final state of two VBF jets and large missing transverse energy is presented at 14 TeV. Prospects for determining the dark matter relic density are studied for the cases of Wino and Bino-Higgsino dark matter. The LHC could probe Wino dark matter with mass up to approximately $600$ GeV with a luminosity of $1000$ fb$^{-1}$. %The results are applicable for dark matter with electroweak couplings in other paradigms. %Vector boson fusion (VBF) processes are a promising avenue to study Wino, Higgsino, and Bino-Higgsino dark matter in supersymmetric extensions of the Standard Model at the LHC. A feasibility study for searching for the nearly-degenerate neutral and charged Wino and Higgsino system, and the neutral Bin-Higgsino system is presented. Tagged jets are utilized to trigger VBF events and kinematic selections are developed to search for signals of these supersymmetric states above Standard Model backgrounds in $\geq 2j \, + \met$ final states at $\sqrt{s} = 8,14$ TeV.
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\begin{document}

%
%\vspace*{2cm}
%\title{Indirect search for top squarks using dilepton mass distribustions at the 8 TeV LHC}
%\title{Top Squark Searches through Decays to Neutralinos and Charginos at the LHC}
\title{Probing Dark Matter at the LHC using Vector Boson Fusion Processes}

%Searching for Top Squarks Decaying to Neutralinos and Charginos Using Dilepton and Trijet Invariant Mass at the LHC}

\author{Andres G. Delannoy$^{2}$}
\author{Bhaskar Dutta$^{1}$}
\author{Alfredo Gurrola$^{2}$}
\author{Will Johns$^{2}$}
\author{Teruki Kamon$^{1,3}$}
\author{Eduardo Luiggi$^{4}$}
\author{Andrew Melo$^{2}$}
\author{Paul Sheldon$^{2}$}
\author{Kuver Sinha$^{1}$}
\author{Kechen Wang$^{1}$}
\author{Sean Wu$^{1}$}

\affiliation{$^{1}$~Mitchell Institute for Fundamental Physics and Astronomy, \\
Department of Physics and Astronomy, Texas A\&M University, College Station, TX 77843-4242, USA \\
$^{2}$~Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, 37235, USA \\
$^{3}$~Department of Physics, Kyungpook National University, Daegu 702-701, South Korea \\
$^{4}$~Department of Physics, University of Colorado, Boulder, CO 80309-0390, USA 
}

\begin{abstract}

Vector boson fusion (VBF) processes at the Large Hadron Collider (LHC) provide a unique opportunity to search for new physics with electroweak couplings. A feasibility study for the search of supersymmetric dark matter in the final state of two VBF jets and large missing transverse energy is presented at 14 TeV. Prospects for determining the dark matter relic density are studied for the cases of Wino and Bino-Higgsino dark matter. The LHC could probe Wino dark matter with mass up to approximately $600$ GeV with a luminosity of $1000$ fb$^{-1}$. %The results are applicable for dark matter with electroweak couplings in other paradigms.

%Vector boson fusion (VBF) processes are a promising avenue to study Wino, Higgsino, and Bino-Higgsino dark matter in supersymmetric extensions of the Standard Model at the LHC. A feasibility study for searching for the nearly-degenerate neutral and charged Wino and Higgsino system, and the neutral Bin-Higgsino system is presented. Tagged jets are utilized to trigger VBF events and kinematic selections are developed to search for signals of these supersymmetric states above Standard Model backgrounds in $\geq 2j \, + \met$ final states at $\sqrt{s} = 8,14$ TeV.  

\end{abstract}
MIFPA-13-15
\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%


Nearly $80\%$ of the matter of the Universe is dark matter (DM) \cite{WMAP}. The identity of DM is one of the most profound questions at the interface of particle physics and cosmology. Weakly interacting massive particles (WIMPs) are particularly promising DM candidates that can explain the observed relic density and are under investigation in a variety of direct and indirect searches. Within the context of $R$-parity conserving supersymmetric extensions of the standard model (SM), the WIMP DM candidate is the lightest supersymmetric particle (LSP), typically the lightest neutralino ($\neu{1}$), which is a mixture of Bino, Wino, and Higgsino states. 

The DM relic density is typically determined by its annihilation cross section at the time of thermal freeze-out. For supersymmetric WIMP DM, the annihilation cross section depends on the mass of $\neu{1}$ and its couplings to various SM final states, for which a detailed knowledge of the composition of $\neu{1}$ in gaugino/Higgsino states is required. Moreover, other states in the electroweak sector, such as sleptons, staus, or charginos can enter the relic density calculation. 

It is important to probe the electroweak sector of supersymmetric models directly in order to study their DM connection.  The main challenge to a direct probe of the electroweak sector at the Large Hadron Collider (LHC) is the small production cross section of neutralinos, charginos, and sleptons \cite{ATLASneutchargino}. 

%At the Large Hadron Collider (LHC), supersymmetric DM is expected to manifest itself as an excess of events above the SM background showing an imbalance in momentum conservation as the DM candidate escapes the collider. The purpose of 

In this Letter we explore supersymmetric DM produced directly at the LHC using vector boson fusion (VBF) processes \cite{Cahn:1983ip, Bjorken:1992er}. This appears particularly promising since some of the present authors recently showed that VBF production is quite effective in probing the chargino-neutralino system \cite{Dutta:2012xe}. It has also been suggested that VBF processes might be useful in both Higgs boson and supersymmetry studies \cite{Rainwater:1998kj, Choudhury:2003hq,cho,datta, Giudice:2010wb}. VBF production is characterized by the presence of two tagging jets with large dijet invariant mass in the forward region in opposite hemispheres. As shown in \cite{Dutta:2012xe}, the requirement of tagging jets along with missing transverse energy ($\met$) is very efficient in reducing SM background.%\footnote{We note that there are alternative approaches to study the electroweak sector, for example by exploiting existing multi-lepton channels to search for extended Higgs sectors \cite{Craig:2012pu}.}.

We also show in this Letter that information about production cross sections in VBF processes and the distribution of $\met$ in the final state can be used to solve for the mass and composition of $\neu{1}$, and hence the DM relic density. The cases of pure Wino or Higgsino $\neu{1}$, as well as the case of a mixed Bino-Higgsino $\neu{1}$ are studied. 

We note that the production of squarks ($\tilde{q}$) or gluinos ($\tilde{g}$) through gluon fusion, followed by cascade decay ending in the production of DM, is the classic setting for DM searches in final states with appreciable missing energy, multiple jets and leptons. However, determining the content of the neutralino and the masses of the superpartners without any color charges requires specific model dependent correlation between masses of colored and non-colored superpartners. In very specific settings, it is possible to determine the composition of $\neu{1}$ \cite{content}, as well as the mass of light staus or sleptons \cite{relic}. In general, the combinatoric background poses a major problem for such attempts. 

Recently, experiments at the 8-TeV LHC (LHC8) have put lower bounds on the masses of the $\tilde{g}$ and $\tilde{q}$. For comparable masses, the exclusion limits are approximately $1.5$ TeV at $95\%$ CL with $13$ fb$^{-1}$ of integrated luminosity \cite{:2012rz, Aad:2012hm, :2012mfa}. There are also active searches for the lightest top squark ($\tilde{t}$), and exclusion limits in the $m_{\st}$-$m_{\neu{1}}$ plane have been obtained in certain decay modes  \cite{ATLASStop1, ATLASStop2}. 

A direct probe of the electroweak sector using VBF processes is complementary to such searches. A variety of possibilities exist for the colored sector (compressed spectra, mildly fine-tuned split scenarios \cite{squarkheavy}, non-minimal supersymmetric extensions, etc.) with varying implications for existing and future searches. Experimental constraints (e.g. triggering) significantly affect the ability to probe supersymmetric DM in some of the above scenarios, for example those with compressed spectra. The important point to note is that \textit{a direct probe of the electroweak sector is largely agnostic about the fate of the colored sector} and provides a direct window to DM physics. 

The strategy pursued in this Letter will be to investigate direct DM production by VBF processes in events with $2j \, + \, \met$ in the final state. Such an approach has several advantages. The $2j \, + \, \met$ final state configuration provides a search strategy that is free from trigger bias. This is reinforced as the $p_T$ thresholds for triggering objects are raised by ATLAS and CMS experiments.
 
% A sample diagram of DM production from VBF processes is shown in Figure \ref{VBFWinoDiagram}.


%\begin{figure}[!htp]
%\centering
%\includegraphics[width=2.0in]{VBFWinoDiagram}
%\caption{Feynman diagram of production of Wino DM by VBF processes.}
%\label{VBFWinoDiagram}
%\end{figure}

%The plan of the paper is as follows. In Section \ref{results} the search strategy and results are presented. We end with our Conclusions.


%\section{Strategy and Results} \label{results}


In order to probe DM directly, the following processes are investigated:
%
%We are interested in VBF production of the lightest chargino and \neu{2}
%
\be
pp \rightarrow \neu{1} \, \neu{1} \, jj, \,\,\, \chpm{1} \, \chmp{1} \, jj , \,\,\, \chpm{1} \, \neu{1} \, jj \,\,\,\,.
\ee
%
The main sources of SM background are: $(i)$ \,\, $pp \rightarrow Z jj \rightarrow \nu \nu j j $ and $(ii)$ \,\, $pp \rightarrow W jj \rightarrow l \nu j j $. The former is an irreducible background with the same topology as the signal. The $\met$ comes from the neutrinos. The latter arises from events which survive a lepton veto; $(iii)$ \,\, $pp \rightarrow t\tbar + $jets: This background may be reduced by vetoing $b$-jets, light leptons, $\tau$ leptons and light-quark/gluon jets.

The search strategy relies on requiring the tagged VBF jets, vetoes for $b$-jets, light leptons, $\tau$ leptons and light-quark/gluon jets, and requiring large $\met$ in the event. Signal and background events are generated with \madgraph \,\, \cite{Alwall:2011uj}. The detector simulation code used here is \pgs \, \cite{pgs}. 

Distributions of $\pT(j_1), \pT(j_2), M_{j_1j_2}$, and $\met$ for background as well as VBF pair production of DM are studied at $\sqrt{s}=8$ TeV and 14 TeV. In the case of pure Wino or Higgsino DM, $\chpm{1}$ is taken to be outside the exclusion limits for ATLAS' disappearing track analysis \cite{chargedtrack} and thus VBF production of $\chpm{1} \chpm{1}$, $\chpm{1} \chmp{1}$, and $\chpm{1} \neu{1}$ also contribute. The $\neu{1}$ masses chosen for this study are in the range 100 GeV to 1 TeV. The colored sector is assumed to be much heavier. There is no contribution to the neutralino production from cascade decays of colored particles. %The pure Wino or Higgsino benchmark points are taken outside the bounds coming from \cite{chargedtrack}.



Events are preselected by requiring $\met > 50$ GeV and the two leading jets ($j_{1}$,$j_{2}$) each satisfying $p_{T} \geq 30$ GeV with $|\Delta \eta(j_{1},j_{2})| > 4.2$ and $\eta_{j_{1}}\eta_{j_{2}} < 0$. The preselected events are used to optimize the final selections to achieve maximal signal significance ($S / \sqrt{S + B}$). For the final selections, the following cuts are employed: $(i)$ The tagged jets are required to have $p_{T} > 50$ GeV and $M_{j_{1} j_{2}} > 1500$ GeV; $(ii)$ Events with loosely identified leptons ($l = e,\mu,\tau_{h}$) and $b$-quark jets are rejected, reducing the $t \tbar$ and $Wjj \rightarrow l\nu jj$ backgrounds by approximately $10^{-2}$ and $10^{-1}$, respectively, while achieving $99\%$ efficiency for signal events. The $b$-jet tagging efficiency used in this study is $70\%$ with a misidentification probability of $1.5\%$, following Ref. \cite{Chatrchyan:2012jua}. Events with a third jet (with $p_{T} > 50$ GeV) residing between $\eta_{j_{1}}$ and $\eta_{j_{2}}$ are also rejected; $(iii)$ The $\met$ cut is optimized for each different value of the DM mass. For $m_{\neu{1}} = 100$ GeV ($1$ TeV), $\met \geq 200$ GeV ($450$ GeV) is chosen, reducing the $Wjj\rightarrow l\nu jj$ background by approximately $10^{-3} \, (10^{-4})$. %The $\met$ cut is taken to be between $200-450$ GeV for $m_{\neu{1}}$ between $100$ GeV to $1$ TeV.

The production cross section as a function of $m_{\neu{1}}$ after requiring $|\Delta \eta (j_1, j_2)| > 4.2$ is displayed in Fig. \ref{xsectionColor}. The left and right panels show the cross sections for LHC8 and LHC14, respectively. For the pure Wino and Higgsino cases, inclusive $\neu{1} \neu{1}$,  $\chpm{1} \chpm{1}$, $\chpm{1} \chmp{1}$, and $\chpm{1} \neu{1}$ production cross sections are displayed. The green (solid) curve corresponds to the case where $\neu{1}$ is $99\%$ Wino. The inclusive production cross section is $\sim 40$ fb for a $100$ GeV Wino at LHC14, and falls steadily with increasing mass. The cross section is approximately $5-10$ times smaller for the pure Higgsino case, represented by the green (dashed) curve. As the Higgsino fraction in $\neu{1}$ decreases for a given mass, the cross section drops. For $20\%$ Higgsino fraction in $\neu{1}$, the cross section is $ \sim 10^{-2}$ fb for $m_{\neu{1}} = 100$ GeV at LHC14.

\begin{figure}[!htp]
\centering
\includegraphics[width=3.5in]{xsectionColor}
\caption{Production cross section as a function of $m_{\neu{1}}$ after requiring $|\Delta \eta (j_1, j_2)| > 4.2$, at LHC8 and LHC14. For the pure Wino and Higgsino cases, inclusive $\neu{1} \neu{1}$,  $\chpm{1} \chpm{1}$, $\chpm{1} \chmp{1}$, and $\chpm{1} \neu{1}$ production cross sections are displayed.}
\label{xsectionColor}
\end{figure}

Figure \ref{DiJetMass_VBFDM} shows the dijet invariant mass distribution $M_{j_1j_2}$ for the tagging jet pair $(j_1,j_2)$ and main sources of background, after the pre-selection cuts and requiring $p_T > 50$ GeV for the tagging jets at LHC14. The dashed black curves show the distribution for the case of a pure Wino DM, with $m_{\neu{1}} = 50$ and $100$ GeV.  The dijet invariant mass distribution for $W+$ jets, $Z+$ jets, and $t \bar{t} +$ jets background are also displayed. Clearly, requiring $M_{j_1j_2} > 1500$ GeV is effective in rejecting background events, resulting in a reduction rate between $10^{-4}$ and $10^{-2}$ for the backgrounds of interest.

\begin{figure}[!htp]
\centering
\includegraphics[width=3.5in]{DiJetMass_VBFDM}
\caption{Distribution of the dijet invariant mass $M_{j_1j_2}$ normalized to unity for the tagging jet pair $(j_1,j_2)$ and main sources of background after pre-selection cuts and requiring $p_T > 50$ GeV for the tagging jets at LHC14. The dashed black curves show the distribution for the case where $\neu{1}$ is a nearly pure Wino with $m_{\neu{1}} = 50$ and $100$ GeV. Inclusive $\neu{1} \neu{1}$,  $\chpm{1} \chpm{1}$, $\chpm{1} \chmp{1}$, and $\chpm{1} \neu{1}$ production is considered.}
\label{DiJetMass_VBFDM}
\end{figure}



Figure \ref{Met_VBFDM_versionB} shows the $\met$ distribution for an integrated luminosity of 500 fb$^{-1}$ at LHC14  after all final selections except the $\met$ requirement. There is a significant enhancement of signal events in the high $\met$ region.

%Figure \ref{Met_VBFDM_versionB} shows the number of events as a function of $\met$ for inclusive $\neu{1} \neu{1}, \chpm{1} \chmp{1},$ and $ \chpm{1} \, \neu{1}$ pair production by VBF processes in the $\geq 2j + \met$ final state at $\sqrt{s} = 8$ TeV, for $m_{\neu{1}} = 50,100$ GeV and the $W+$ jets and $Z+$ jets background with $500$ fb$^{-1}$ of integrated luminosity at LHC14. Clearly, there is a nice enhancement of events in the high $\met$ region.

\begin{figure}[!htp]
\centering
\includegraphics[width=3.5in]{Met_VBFDM_versionB}
\caption{The $\met$ distributions for Wino DM (50 GeV and 100 GeV) compared to $W+$ jets and $Z+$ jets events with $500$ fb$^{-1}$ integrated luminosity at LHC14. The distributions are after all selections except the $\met$ cut. Inclusive $\neu{1} \neu{1}$,  $\chpm{1} \chpm{1}$, $\chpm{1} \chmp{1}$, and $\chpm{1} \neu{1}$ production is considered.}
\label{Met_VBFDM_versionB}
\end{figure}

The significance as a function of $\neu{1}$ mass is plotted in Fig. \ref{SignificanceVsMassVsLumi_versionD} for different luminosities at LHC14. %In Table \ref{significancetable}, the significance is shown for different masses of $\neu{1}$. 
The blue, red, and black curves correspond to luminosities of $1000, 500,$ and $100$ fb$^{-1}$, respectively. At $1000$ fb$^{-1}$, a significance of $5\sigma$ can be obtained up to a Wino mass of approximately $600$ GeV.  

\begin{figure}[!htp]
\centering
\includegraphics[width=3.5in]{SignificanceVsMassVsLumi_versionD}
\caption{Significance curves for the case where $\neu{1}$ is $99\%$ Wino as a function of $m_{\neu{1}}$ mass for different luminosities at LHC14. The green lines correspond to $3\sigma$ and $5\sigma$ significances.}
\label{SignificanceVsMassVsLumi_versionD}
\end{figure}



%\subsection{DM Mass, Composition, and Relic Density}

%Using $\neu{1}$ as the DM candidate that gives the observed relic density of the Universe, it is imperative to obtain the quantities that determine its annihilation cross-section into Standard Model particles. 


 %like mass and composition in terms of the gaugino/Higgsino eigenstates .

Determining the composition of $\neu{1}$ for a given mass is very important in order to understand early universe cosmology. For example, if $\neu{1}$ has a large Higgsino or Wino component, the annihilation cross section is too large to fit the observed relic density for $m_{\neu{1}}$ mass less than $\sim 1$ TeV for Higgsinos \cite{Allahverdi:2012wb} and $\sim 2.5$ TeV for Winos. On the other hand if $\neu{1}$ is mostly Bino, the annihilation cross section is too small. In the first case one has under-abundance whereas in the second case one has over-abundance of DM. Both problems can be solved if the DM is non-thermal \cite{Allahverdi:2012gk} (in the case of thermal DM, addressing the over abundance  problem requires addition effects like resonance, coannihilation etc. in the cross section, while the under-abundance problem can be addressed by having multi-component DM \cite{Baer:2012cf}). If  $\neu{1}$ is a suitable mixture of Bino and Higgsino, the observed DM relic density can be satisfied.   

From Figs. \ref{xsectionColor} and \ref{Met_VBFDM_versionB}, it is clear that varying of the rate and the shape of the $\met$ distribution can be used to solve for the mass of $\neu{1}$ as well as its composition in gaugino/Higgsino eigenstates. The VBF study described in this work was performed over a grid of input points on the $F - m_{\neu{1}}$ plane (where $F$ is the Wino or Higgsino percentage in $\neu{1}$). The $\met$ cut was optimized over the grid, and the $\met$ shape and observed rate of data were used to extract $F$ and $m_{\neu{1}}$ which was then used to determine the DM relic density. 

% filling out a surface on the ${\rm rate} - \met$ plane. The information on the ${\rm rate} - \met$ plane was used to solve for $F\%$ and $m_{\neu{1}}$ which was then used to determine the DM relic density. 

%By carefully optimizing the $\met$ cut for a given $m_{\neu{1}}$, one can simultaneously fit the $\met$ shape and observed rate in data to extract the mass and composition of $\neu{1}$

In Fig. \ref{OmegaVsMLSP_WinoAndHiggsino_versionD}, the case of $99\%$ Higgsino and $99\%$ Wino were chosen, and $1\sigma$ contour plots drawn on the relic density-$m_{\neu{1}}$ plane for $500$ fb$^{-1}$ luminosity at LHC14. The relic density was normalized to a benchmark value $\Omega_{\rm benchmark}$, which is the relic density for $m_{\neu{1}} = 100$ GeV.  For the Wino case, the relic density can be determined within $\sim 20\%$, while for the Higgsino case it can be determined within $\sim 40\%$. For higher values of $m_{\neu{1}}$, higher luminosities would be required to achieve these results. We note we have not evaluated the impact of any degradation in $\met$ scale, linearity and resolution due to large pile-up events. Our results represent the best case scenario and it will be crucial to revisit with the expected performance of upgraded ATLAS and CMS detectors. 

\begin{figure}[!htp]
\centering
\includegraphics[width=3.5in]{OmegaVsMLSP_WinoAndHiggsino_versionD}
\caption{Contour lines in the relic density-$m_{\neu{1}}$ plane for $99\%$ Wino (blue dashed) and $99\%$ Higgsino (grey dotted) DMs expected with $500$ fb$^{-1}$ of luminosity at LHC14. The relic density is normalized to its value at $m_{\neu{1}} = 100$ GeV.}
%vertical axis shows values of $\Omega/\Omega_{{\rm benchmark}}$} where $\Omega_{{\rm benchmark}}h^2$ is the relic density for $m_{\neu{1}}$.
%on the $\Omega - m_{\neu{1}}$ plane for $500$ fb$^{-1}$ luminosity at LHC14, for the case of $99/%$ Higgsino and $99\%$ Wino.}
\label{OmegaVsMLSP_WinoAndHiggsino_versionD}
\end{figure}

In conclusion, this Letter has investigated the direct production of supersymmetric DM by VBF processes at the LHC. The cases of pure Wino, pure Higgsino, and mixed Bino-Higgsino DM have been studied in the $2j + \met$ final state at 14 TeV. The presence of the energetic VBF jets with large dijet invariant mass as well as the large $\met$ due to DM production have been used to reduce SM background. It has been shown that broad enhancements in the $\met$ and VBF dijet mass distributions provide a smoking gun signature for VBF production of supersymmetric DM. By optimizing the $\met$ cut for a given $m_{\neu{1}}$, one can simultaneously fit the $\met$ shape and observed rate in data to extract the mass and composition of $\neu{1}$, and hence solve for the DM relic density. At an integrated luminosity of $1000$ fb$^{-1}$, a significance of $5\sigma$ can be obtained up to a Wino mass of approximately $600$ GeV. The relic density can be determined to within $20\% \, (40\%)$ for the case of a pure Wino (Higgsino) for $500$ fb$^{-1}$ at LHC14, for $m_{\neu{1}} = 100$ GeV. We note that our study does not include the effect of large multiple interactions at high luminosity operations at the LHC. This is a very important subject, but outside the scope of the present work, because the final performance will depend on the planned upgrade of ATLAS and CMS detectors.

%\section{Conclusions}



% \section{Acknowledgements}

This work is supported in part by DOE Grant No. DE-FG02-95ER40917 and DE-FG02-04ER41290, NSF Award PHY-1206044, and
by the World Class University (WCU) project through the National Research Foundation (NRF) of Korea funded by the Ministry of Education, Science, and Technology (Grant No. R32-2008-000-20001-0). K.S. would like to thank Nathaniel Craig for helpful discussions.



\begin{thebibliography}{99}

\bibitem{WMAP}
Planck Collaboration, arXiv:1303.5076 [astro-ph.CO]; 
WMAP Collaboration,   arXiv:1212.5226 [astro-ph.CO].

\bibitem{ATLASneutchargino}
ATLAS Collaboration, 
%``Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in $13.0$ fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector," 
ATLAS-CONF-2012-154. 
%``Search for electroweak production of supersymmetric particles in final states with at least two hadronically decaying taus and missing transverse momentum with the ATLAS detector in proton-proton collisions at $\sqrt{s} = 8$ TeV," 
ATLAS-CONF-2013-028.


  %\cite{Cahn:1983ip}
\bibitem{Cahn:1983ip} 
  R.~N.~Cahn and S.~Dawson,
%  ``Production of Very Massive Higgs Bosons,''  
  Phys.\ Lett.\ B {\bf 136}, 196 (1984)  [Erratum-ibid.\ B {\bf 138}, 464 (1984)].  %%CITATION = PHLTA,B136,196;%%
  
  %\cite{Bjorken:1992er}
\bibitem{Bjorken:1992er} 
  J.~D.~Bjorken,
%  ``Rapidity gaps and jets as a new physics signature in very high-energy hadron hadron collisions,''  
  Phys.\ Rev.\ D {\bf 47}, 101 (1993).  %%CITATION = PHRVA,D47,101;%%


  
 %\cite{Dutta:2012xe}
\bibitem{Dutta:2012xe} 
  B.~Dutta, A.~Gurrola, W.~Johns, T.~Kamon, P.~Sheldon and K.~Sinha,
  Phys.\ Rev.\ D {\bf 87}, 035029 (2013)  arXiv:1210.0964 [hep-ph].
  %``Vector Boson Fusion Processes as a Probe of Supersymmetric Electroweak Sectors at the LHC,''  arXiv:1210.0964 [hep-ph].  %%CITATION = ARXIV:1210.0964;%%  %2 citations counted in INSPIRE as of 17 Apr 2013



%\cite{Rainwater:1998kj}
\bibitem{Rainwater:1998kj} 
  D.~L.~Rainwater, D.~Zeppenfeld and K.~Hagiwara,
%  ``Searching for $H\to\tau^+\tau^-$ in weak boson fusion at the CERN LHC,''  
  Phys.\ Rev.\ D {\bf 59}, 014037 (1998)  [hep-ph/9808468].  %%CITATION = HEP-PH/9808468;%%

%\cite{Choudhury:2003hq}
\bibitem{Choudhury:2003hq} 
  D.~Choudhury, A.~Datta, K.~Huitu, P.~Konar, S.~Moretti and B.~Mukhopadhyaya,
%  ``Slepton production from gauge boson fusion,''  
  Phys.\ Rev.\ D {\bf 68}, 075007 (2003)  [hep-ph/0304192].  %%CITATION = HEP-PH/0304192;%%
    %\cite{Datta:2002vy}
%\bibitem{Datta:2002vy} 
  A.~Datta and K.~Huitu,
%  ``Characteristic slepton signal in anomaly mediated SUSY breaking models via gauge boson fusion at the CERN LHC,''  
  Phys.\ Rev.\ D {\bf 67}, 115006 (2003)  [hep-ph/0211319].  %%CITATION = HEP-PH/0211319;%%
\bibitem{cho}G.~-C.~Cho, K.~Hagiwara, J.~Kanzaki, T.~Plehn, D.~Rainwater and T.~Stelzer,
%  ``Weak boson fusion production of supersymmetric particles at the CERN LHC,''
  Phys.\ Rev.\ D {\bf 73}, 054002 (2006)
  [hep-ph/0601063].
\bibitem{datta}A.~Datta, P.~Konar and B.~Mukhopadhyaya,
 % ``Signals of neutralinos and charginos from gauge boson fusion at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 65}, 055008 (2002) [hep-ph/0109071]; 
  %``Invisible charginos and neutralinos from gauge boson fusion: A Way to explore anomaly mediation?,''
  Phys.\ Rev.\ Lett.\  {\bf 88}, 181802 (2002)
  [hep-ph/0111012]; P.~Konar and B.~Mukhopadhyaya,
  %``Gauge boson fusion as a probe of inverted hierarchies in supersymmetry,''
  Phys.\ Rev.\ D {\bf 70}, 115011 (2004)
  [hep-ph/0311347]; R.~C.~Cotta, J.~L.~Hewett, M.~P.~Le and T.~G.~Rizzo,
  %``Bounds on Dark Matter Interactions with Electroweak Gauge Bosons,''
  arXiv:1210.0525 [hep-ph].
  %%CITATION = ARXIV:1210.0525;%%

%\cite{Giudice:2010wb}
\bibitem{Giudice:2010wb} 
  G.~F.~Giudice, T.~Han, K.~Wang and L.~-T.~Wang,
  %``Nearly Degenerate Gauginos and Dark Matter at the LHC,''  
  Phys.\ Rev.\ D {\bf 81}, 115011 (2010)  [arXiv:1004.4902 [hep-ph]].  %%CITATION = ARXIV:1004.4902;%%  %21 citations counted in INSPIRE as of 18 Apr 2013



\bibitem{content}B.~Dutta, T.~Kamon, N.~Kolev, K.~Sinha, K.~Wang and S.~Wu,
  %``Top Squark Searches Using Dilepton Invariant Mass Distributions and Bino-Higgsino Dark Matter at the LHC,''
  arXiv:1302.3231 [hep-ph].  %%CITATION = ARXIV:1302.3231;%%
  


\bibitem{relic}R.~L.~Arnowitt, B.~Dutta, A.~Gurrola, T.~Kamon, A.~Krislock and D.~Toback,
  %``Determining the Dark Matter Relic Density in the mSUGRA (~X0(1))-~tau Co-Annhiliation Region at the LHC,''
  Phys.\ Rev.\ Lett.\  {\bf 100}, 231802 (2008);  B.~Dutta, A.~Gurrola, T.~Kamon, A.~Krislock, A.~B.~Lahanas, N.~E.~Mavromatos and D.~V.~Nanopoulos,
  %``Supersymmetry Signals of Supercritical String Cosmology at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 79}, 055002 (2009); B.~Dutta, T.~Kamon, A.~Krislock, N.~Kolev and Y.~Oh,
  %``Determination of Non-Universal Supergravity Models at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 82}, 115009 (2010); B.~Dutta, T.~Kamon, A.~Krislock, K.~Sinha and K.~Wang,
  %``Diagnosis of Supersymmetry Breaking Mediation Schemes by Mass Reconstruction at the LHC,''
  Phys.\ Rev.\ D {\bf 85}, 115007 (2012).  

%\cite{:2012rz}
\bibitem{:2012rz} 
  ATLAS Collaboration,
%  ``Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using $4.7$ fb$^{-1}$ of $\sqrt{s} = 7$ TeV proton-proton collision data,''  
  arXiv:1208.0949 [hep-ex].  %%CITATION = ARXIV:1208.0949;%%

%\cite{Aad:2012hm}
\bibitem{Aad:2012hm} 
  ATLAS Collaboration,
%  ``Hunt for new phenomena using large jet multiplicities and missing transverse momentum with ATLAS in $4.7$ fb$^{-1}$ of $\sqrt{s} = 7$ TeV proton-proton collisions,''  
  J. High Energy Phys. {\bf 07}, 167 (2012)  [arXiv:1206.1760 [hep-ex]].  %%CITATION = ARXIV:1206.1760;%%
  
  %\cite{:2012mfa}
\bibitem{:2012mfa} 
  CMS Collaboration,
%  ``Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at $\sqrt{s} = 7$ TeV,''  
arXiv:1207.1898 [hep-ex].  %%CITATION = ARXIV:1207.1898;%%


\bibitem{ATLASStop1}  
ATLAS Collaboration,
%``Search for direct top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in $\sqrt{s} = 8$ TeV $pp$ collisions using $13$ fb$^{-1}$ of ATLAS data," 
ATLAS-CONF-2012-166.

\bibitem{ATLASStop2}  
ATLAS Collaboration, 
%``Search for the charged current decay of a supersymmetric top-quark partner in final states with two leptons in $\sqrt{s} = 8$ TeV $pp$ collisions using $13$ fb$^{-1}$ of ATLAS data," 
ATLAS-CONF-2012-167.

\bibitem{squarkheavy}
N.~Arkani-Hamed, A.~Gupta, D.~E.~Kaplan, N.~Weiner and T.~Zorawski,
%  ``Simply Unnatural Supersymmetry,''  
arXiv:1212.6971 [hep-ph]. 
A.~Arvanitaki, N.~Craig, S.~Dimopoulos and G.~Villadoro,
%  ``Mini-Split,''  
arXiv:1210.0555 [hep-ph].


%\cite{Alwall:2011uj}
\bibitem{Alwall:2011uj} 
  J.~Alwall, M.~Herquet, F.~Maltoni, O.~Mattelaer and T.~Stelzer,
  %``MadGraph 5 : Going Beyond,''  
  J. High Energy Phys. {\bf 06}, 128 (2011)  [arXiv:1106.0522 [hep-ph]].  %%CITATION = ARXIV:1106.0522;%%  %522 citations counted in INSPIRE as of 17 Apr 2013


\bibitem{pgs}
\pgs\ is a parameterized detector simulator.
We use version 4
(\url{http://www.physics.ucdavis.edu/~conway/research/software/pgs/pgs4-general.htm})
in the LHC detector configuration.
%to find gluon/light quark jets and $b$ jets.
%We assume the $\tau$ identification efficiency
%with $p^{\rm vis}_T > 15$ GeV is 50\%, while
%the probability for a jet being mis-identified
%as a $\tau$ is  1\%.
%A parametrized $b$-tagging efficiency is used
%based on the CDF SECVTX $b$-tagger in
%A. Abulencia \etal, Phys. Rev. Lett. 97, 082004 (2006).
%The $b$-jet tagging efficiency in PGS is
%$\sim$42\% for $E_{\rm T} >$ 50 GeV
%and $|\eta| < 1.0$, and degrading between  $1.0 < |\eta| < 1.5$.
%The $b$-tagging fake rate for $c$ and light quarks/gluons is
%$\sim9\%$ and $2\%$, respectively.

\bibitem{chargedtrack} 
  ATLAS Collaboration,
%  ``Search for direct chargino production in anomaly-mediated supersymmetry breaking models based on a disappearing-track signature in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector,''  
  J. High Energy Phys. {\bf 01}, 131 (2013)  [arXiv:1210.2852 [hep-ex]].  %%CITATION = ARXIV:1210.2852;%%  %6 citations counted in INSPIRE as of 22 Feb 2013
%
%\cite{Heister:2002mn}
%\bibitem{Heister:2002mn} 
  ALEPH Collaboration,
 % ``Search for charginos nearly mass degenerate with the lightest neutralino in e+ e- collisions at center-of-mass energies up to 209-GeV,''  
  Phys.\ Lett.\ B {\bf 533}, 223 (2002)  [hep-ex/0203020].  %%CITATION = HEP-EX/0203020;%%  %40 citations counted in INSPIRE as of 22 Feb 2013
%\cite{Abbiendi:2002vz}
%\bibitem{Abbiendi:2002vz} 
  OPAL Collaboration,
%  ``Search for nearly mass degenerate charginos and neutralinos at LEP,''  
  Eur.\ Phys.\ J.\ C {\bf 29}, 479 (2003)  [hep-ex/0210043].  %%CITATION = HEP-EX/0210043;%%  %24 citations counted in INSPIRE as of 22 Feb 2013
%\cite{Abdallah:2003gv}
%\bibitem{Abdallah:2003gv} 
  DELPHI Collaboration,
%  ``Search for SUSY in the AMSB scenario with the DELPHI detector,''  
  Eur.\ Phys.\ J.\ C {\bf 34}, 145 (2004)  [hep-ex/0403047].  %%CITATION = HEP-EX/0403047;%%  %9 citations counted in INSPIRE as of 22 Feb 2013


%\cite{Chatrchyan:2012jua}
\bibitem{Chatrchyan:2012jua} 
  CMS Collaboration,
  %``Identification of b-quark jets with the CMS experiment,''  
  JINST {\bf 8}, P04013 (2013)  [arXiv:1211.4462 [hep-ex]].  %%CITATION = ARXIV:1211.4462;%%  %26 citations counted in INSPIRE as of 27 Apr 2013

%\cite{Allahverdi:2012wb}
\bibitem{Allahverdi:2012wb} 
  R.~Allahverdi, B.~Dutta and K.~Sinha,
  %``Non-thermal Higgsino Dark Matter: Cosmological Motivations and Implications for a 125 GeV Higgs,''  
  Phys.\ Rev.\ D {\bf 86}, 095016 (2012)  [arXiv:1208.0115 [hep-ph]].  %%CITATION = ARXIV:1208.0115;%%  %9 citations counted in INSPIRE as of 26 Apr 2013
%\cite{Baer:2013vpa}
%\bibitem{Baer:2013vpa} 
  H.~Baer, V.~Barger and D.~Mickelson,
  %``Direct and indirect detection of higgsino-like WIMPs: concluding the story of electroweak naturalness,''  
  arXiv:1303.3816 [hep-ph].  %%CITATION = ARXIV:1303.3816;%%  %2 citations counted in INSPIRE as of 26 Apr 2013


%\cite{Allahverdi:2012gk}
\bibitem{Allahverdi:2012gk} 
  R.~Allahverdi, B.~Dutta and K.~Sinha,
  %``Successful Supersymmetric Dark Matter with Thermal Over/Under-Abundance from Late Decay of a Visible Sector Scalar,''  
  arXiv:1212.6948 [hep-ph].  %%CITATION = ARXIV:1212.6948;%%  %3 citations counted in INSPIRE as of 22 Apr 2013

%\cite{Baer:2012cf}
\bibitem{Baer:2012cf} 
  H.~Baer, V.~Barger, P.~Huang, D.~Mickelson, A.~Mustafayev and X.~Tata,
  %``Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass,''  
  arXiv:1212.2655 [hep-ph].  %%CITATION = ARXIV:1212.2655;%%  %12 citations counted in INSPIRE as of 26 Apr 2013


\end{thebibliography}



\end{document}
1304.7779.extracted_bib
\begin{thebibliography}{99}

\bibitem{WMAP}
Planck Collaboration, arXiv:1303.5076 [astro-ph.CO]; 
WMAP Collaboration,   arXiv:1212.5226 [astro-ph.CO].

\bibitem{ATLASneutchargino}
ATLAS Collaboration, 
%``Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in $13.0$ fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector," 
ATLAS-CONF-2012-154. 
%``Search for electroweak production of supersymmetric particles in final states with at least two hadronically decaying taus and missing transverse momentum with the ATLAS detector in proton-proton collisions at $\sqrt{s} = 8$ TeV," 
ATLAS-CONF-2013-028.


  %\cite{Cahn:1983ip}
\bibitem{Cahn:1983ip} 
  R.~N.~Cahn and S.~Dawson,
%  ``Production of Very Massive Higgs Bosons,''  
  Phys.\ Lett.\ B {\bf 136}, 196 (1984)  [Erratum-ibid.\ B {\bf 138}, 464 (1984)].  %%CITATION = PHLTA,B136,196;%%
  
  %\cite{Bjorken:1992er}
\bibitem{Bjorken:1992er} 
  J.~D.~Bjorken,
%  ``Rapidity gaps and jets as a new physics signature in very high-energy hadron hadron collisions,''  
  Phys.\ Rev.\ D {\bf 47}, 101 (1993).  %%CITATION = PHRVA,D47,101;%%


  
 %\cite{Dutta:2012xe}
\bibitem{Dutta:2012xe} 
  B.~Dutta, A.~Gurrola, W.~Johns, T.~Kamon, P.~Sheldon and K.~Sinha,
  Phys.\ Rev.\ D {\bf 87}, 035029 (2013)  arXiv:1210.0964 [hep-ph].
  %``Vector Boson Fusion Processes as a Probe of Supersymmetric Electroweak Sectors at the LHC,''  arXiv:1210.0964 [hep-ph].  %%CITATION = ARXIV:1210.0964;%%  %2 citations counted in INSPIRE as of 17 Apr 2013



%\cite{Rainwater:1998kj}
\bibitem{Rainwater:1998kj} 
  D.~L.~Rainwater, D.~Zeppenfeld and K.~Hagiwara,
%  ``Searching for $H\to\tau^+\tau^-$ in weak boson fusion at the CERN LHC,''  
  Phys.\ Rev.\ D {\bf 59}, 014037 (1998)  [hep-ph/9808468].  %%CITATION = HEP-PH/9808468;%%

%\cite{Choudhury:2003hq}
\bibitem{Choudhury:2003hq} 
  D.~Choudhury, A.~Datta, K.~Huitu, P.~Konar, S.~Moretti and B.~Mukhopadhyaya,
%  ``Slepton production from gauge boson fusion,''  
  Phys.\ Rev.\ D {\bf 68}, 075007 (2003)  [hep-ph/0304192].  %%CITATION = HEP-PH/0304192;%%
    %\cite{Datta:2002vy}
%\bibitem{Datta:2002vy} 
  A.~Datta and K.~Huitu,
%  ``Characteristic slepton signal in anomaly mediated SUSY breaking models via gauge boson fusion at the CERN LHC,''  
  Phys.\ Rev.\ D {\bf 67}, 115006 (2003)  [hep-ph/0211319].  %%CITATION = HEP-PH/0211319;%%
\bibitem{cho}G.~-C.~Cho, K.~Hagiwara, J.~Kanzaki, T.~Plehn, D.~Rainwater and T.~Stelzer,
%  ``Weak boson fusion production of supersymmetric particles at the CERN LHC,''
  Phys.\ Rev.\ D {\bf 73}, 054002 (2006)
  [hep-ph/0601063].
\bibitem{datta}A.~Datta, P.~Konar and B.~Mukhopadhyaya,
 % ``Signals of neutralinos and charginos from gauge boson fusion at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 65}, 055008 (2002) [hep-ph/0109071]; 
  %``Invisible charginos and neutralinos from gauge boson fusion: A Way to explore anomaly mediation?,''
  Phys.\ Rev.\ Lett.\  {\bf 88}, 181802 (2002)
  [hep-ph/0111012]; P.~Konar and B.~Mukhopadhyaya,
  %``Gauge boson fusion as a probe of inverted hierarchies in supersymmetry,''
  Phys.\ Rev.\ D {\bf 70}, 115011 (2004)
  [hep-ph/0311347]; R.~C.~Cotta, J.~L.~Hewett, M.~P.~Le and T.~G.~Rizzo,
  %``Bounds on Dark Matter Interactions with Electroweak Gauge Bosons,''
  arXiv:1210.0525 [hep-ph].
  %%CITATION = ARXIV:1210.0525;%%

%\cite{Giudice:2010wb}
\bibitem{Giudice:2010wb} 
  G.~F.~Giudice, T.~Han, K.~Wang and L.~-T.~Wang,
  %``Nearly Degenerate Gauginos and Dark Matter at the LHC,''  
  Phys.\ Rev.\ D {\bf 81}, 115011 (2010)  [arXiv:1004.4902 [hep-ph]].  %%CITATION = ARXIV:1004.4902;%%  %21 citations counted in INSPIRE as of 18 Apr 2013



\bibitem{content}B.~Dutta, T.~Kamon, N.~Kolev, K.~Sinha, K.~Wang and S.~Wu,
  %``Top Squark Searches Using Dilepton Invariant Mass Distributions and Bino-Higgsino Dark Matter at the LHC,''
  arXiv:1302.3231 [hep-ph].  %%CITATION = ARXIV:1302.3231;%%
  


\bibitem{relic}R.~L.~Arnowitt, B.~Dutta, A.~Gurrola, T.~Kamon, A.~Krislock and D.~Toback,
  %``Determining the Dark Matter Relic Density in the mSUGRA (~X0(1))-~tau Co-Annhiliation Region at the LHC,''
  Phys.\ Rev.\ Lett.\  {\bf 100}, 231802 (2008);  B.~Dutta, A.~Gurrola, T.~Kamon, A.~Krislock, A.~B.~Lahanas, N.~E.~Mavromatos and D.~V.~Nanopoulos,
  %``Supersymmetry Signals of Supercritical String Cosmology at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 79}, 055002 (2009); B.~Dutta, T.~Kamon, A.~Krislock, N.~Kolev and Y.~Oh,
  %``Determination of Non-Universal Supergravity Models at the Large Hadron Collider,''
  Phys.\ Rev.\ D {\bf 82}, 115009 (2010); B.~Dutta, T.~Kamon, A.~Krislock, K.~Sinha and K.~Wang,
  %``Diagnosis of Supersymmetry Breaking Mediation Schemes by Mass Reconstruction at the LHC,''
  Phys.\ Rev.\ D {\bf 85}, 115007 (2012).  

%\cite{:2012rz}
\bibitem{:2012rz} 
  ATLAS Collaboration,
%  ``Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using $4.7$ fb$^{-1}$ of $\sqrt{s} = 7$ TeV proton-proton collision data,''  
  arXiv:1208.0949 [hep-ex].  %%CITATION = ARXIV:1208.0949;%%

%\cite{Aad:2012hm}
\bibitem{Aad:2012hm} 
  ATLAS Collaboration,
%  ``Hunt for new phenomena using large jet multiplicities and missing transverse momentum with ATLAS in $4.7$ fb$^{-1}$ of $\sqrt{s} = 7$ TeV proton-proton collisions,''  
  J. High Energy Phys. {\bf 07}, 167 (2012)  [arXiv:1206.1760 [hep-ex]].  %%CITATION = ARXIV:1206.1760;%%
  
  %\cite{:2012mfa}
\bibitem{:2012mfa} 
  CMS Collaboration,
%  ``Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at $\sqrt{s} = 7$ TeV,''  
arXiv:1207.1898 [hep-ex].  %%CITATION = ARXIV:1207.1898;%%


\bibitem{ATLASStop1}  
ATLAS Collaboration,
%``Search for direct top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in $\sqrt{s} = 8$ TeV $pp$ collisions using $13$ fb$^{-1}$ of ATLAS data," 
ATLAS-CONF-2012-166.

\bibitem{ATLASStop2}  
ATLAS Collaboration, 
%``Search for the charged current decay of a supersymmetric top-quark partner in final states with two leptons in $\sqrt{s} = 8$ TeV $pp$ collisions using $13$ fb$^{-1}$ of ATLAS data," 
ATLAS-CONF-2012-167.

\bibitem{squarkheavy}
N.~Arkani-Hamed, A.~Gupta, D.~E.~Kaplan, N.~Weiner and T.~Zorawski,
%  ``Simply Unnatural Supersymmetry,''  
arXiv:1212.6971 [hep-ph]. 
A.~Arvanitaki, N.~Craig, S.~Dimopoulos and G.~Villadoro,
%  ``Mini-Split,''  
arXiv:1210.0555 [hep-ph].


%\cite{Alwall:2011uj}
\bibitem{Alwall:2011uj} 
  J.~Alwall, M.~Herquet, F.~Maltoni, O.~Mattelaer and T.~Stelzer,
  %``MadGraph 5 : Going Beyond,''  
  J. High Energy Phys. {\bf 06}, 128 (2011)  [arXiv:1106.0522 [hep-ph]].  %%CITATION = ARXIV:1106.0522;%%  %522 citations counted in INSPIRE as of 17 Apr 2013


\bibitem{pgs}
\pgs\ is a parameterized detector simulator.
We use version 4
(\url{http://www.physics.ucdavis.edu/~conway/research/software/pgs/pgs4-general.htm})
in the LHC detector configuration.
%to find gluon/light quark jets and $b$ jets.
%We assume the $\tau$ identification efficiency
%with $p^{\rm vis}_T > 15$ GeV is 50\%, while
%the probability for a jet being mis-identified
%as a $\tau$ is  1\%.
%A parametrized $b$-tagging efficiency is used
%based on the CDF SECVTX $b$-tagger in
%A. Abulencia \etal, Phys. Rev. Lett. 97, 082004 (2006).
%The $b$-jet tagging efficiency in PGS is
%$\sim$42\% for $E_{\rm T} >$ 50 GeV
%and $|\eta| < 1.0$, and degrading between  $1.0 < |\eta| < 1.5$.
%The $b$-tagging fake rate for $c$ and light quarks/gluons is
%$\sim9\%$ and $2\%$, respectively.

\bibitem{chargedtrack} 
  ATLAS Collaboration,
%  ``Search for direct chargino production in anomaly-mediated supersymmetry breaking models based on a disappearing-track signature in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector,''  
  J. High Energy Phys. {\bf 01}, 131 (2013)  [arXiv:1210.2852 [hep-ex]].  %%CITATION = ARXIV:1210.2852;%%  %6 citations counted in INSPIRE as of 22 Feb 2013
%
%\cite{Heister:2002mn}
%\bibitem{Heister:2002mn} 
  ALEPH Collaboration,
 % ``Search for charginos nearly mass degenerate with the lightest neutralino in e+ e- collisions at center-of-mass energies up to 209-GeV,''  
  Phys.\ Lett.\ B {\bf 533}, 223 (2002)  [hep-ex/0203020].  %%CITATION = HEP-EX/0203020;%%  %40 citations counted in INSPIRE as of 22 Feb 2013
%\cite{Abbiendi:2002vz}
%\bibitem{Abbiendi:2002vz} 
  OPAL Collaboration,
%  ``Search for nearly mass degenerate charginos and neutralinos at LEP,''  
  Eur.\ Phys.\ J.\ C {\bf 29}, 479 (2003)  [hep-ex/0210043].  %%CITATION = HEP-EX/0210043;%%  %24 citations counted in INSPIRE as of 22 Feb 2013
%\cite{Abdallah:2003gv}
%\bibitem{Abdallah:2003gv} 
  DELPHI Collaboration,
%  ``Search for SUSY in the AMSB scenario with the DELPHI detector,''  
  Eur.\ Phys.\ J.\ C {\bf 34}, 145 (2004)  [hep-ex/0403047].  %%CITATION = HEP-EX/0403047;%%  %9 citations counted in INSPIRE as of 22 Feb 2013


%\cite{Chatrchyan:2012jua}
\bibitem{Chatrchyan:2012jua} 
  CMS Collaboration,
  %``Identification of b-quark jets with the CMS experiment,''  
  JINST {\bf 8}, P04013 (2013)  [arXiv:1211.4462 [hep-ex]].  %%CITATION = ARXIV:1211.4462;%%  %26 citations counted in INSPIRE as of 27 Apr 2013

%\cite{Allahverdi:2012wb}
\bibitem{Allahverdi:2012wb} 
  R.~Allahverdi, B.~Dutta and K.~Sinha,
  %``Non-thermal Higgsino Dark Matter: Cosmological Motivations and Implications for a 125 GeV Higgs,''  
  Phys.\ Rev.\ D {\bf 86}, 095016 (2012)  [arXiv:1208.0115 [hep-ph]].  %%CITATION = ARXIV:1208.0115;%%  %9 citations counted in INSPIRE as of 26 Apr 2013
%\cite{Baer:2013vpa}
%\bibitem{Baer:2013vpa} 
  H.~Baer, V.~Barger and D.~Mickelson,
  %``Direct and indirect detection of higgsino-like WIMPs: concluding the story of electroweak naturalness,''  
  arXiv:1303.3816 [hep-ph].  %%CITATION = ARXIV:1303.3816;%%  %2 citations counted in INSPIRE as of 26 Apr 2013


%\cite{Allahverdi:2012gk}
\bibitem{Allahverdi:2012gk} 
  R.~Allahverdi, B.~Dutta and K.~Sinha,
  %``Successful Supersymmetric Dark Matter with Thermal Over/Under-Abundance from Late Decay of a Visible Sector Scalar,''  
  arXiv:1212.6948 [hep-ph].  %%CITATION = ARXIV:1212.6948;%%  %3 citations counted in INSPIRE as of 22 Apr 2013

%\cite{Baer:2012cf}
\bibitem{Baer:2012cf} 
  H.~Baer, V.~Barger, P.~Huang, D.~Mickelson, A.~Mustafayev and X.~Tata,
  %``Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass,''  
  arXiv:1212.2655 [hep-ph].  %%CITATION = ARXIV:1212.2655;%%  %12 citations counted in INSPIRE as of 26 Apr 2013


\end{thebibliography}