claudioc/SSbPAS2012/models.tex

\section{Models of new physics}
\label{sec:models}
We use the search results to constrain specific models of new physics.
For each model
considered, we base our limits on the signal region 
which is expected to give the most 
stringent limit on the cross section at a given point 
in model parameter space.  
As described in Ref.~\cite{Chatrchyan:2012qka},
the event
selection efficiency for a given model is 
obtained from Monte Carlo simulation, and the limits are
calculated including systematic uncertainties on lepton efficiency 
(5\% per lepton), luminosity (2.2\%), jet energy scale and 
b-tag uncertainty.  The latter two uncertainties are 
evaluated at each point in parameter space.

\subsection{Same sign top production}
\label{sec:sstt}
In Ref.~\cite{Chatrchyan:2012qka} we used the results
of SR2 to set limits on the cross-section for same-sign 
top quark production $\sigma(pp \to tt)$ and on the 
parameter space of two models that naturally give rise 
to this final state~\cite{fcnczprime,mxflv1}. (Note that 
SR2 requires two positive leptons, thus it is sensitive
to $pp \to tt$ but not $pp \to \bar{t}\bar{t}$; the latter
process would be suppressed because of the proton parton 
distribution functions).

The model of Ref.~\cite{fcnczprime} was proposed
to explain the forward-backward \ttbar asymmetry observed at the 
Tevatron~\cite{cdf:fwtop1,cdf:fwtop2,d0:fwtop}.  Our results 
from Ref.~\cite{Chatrchyan:2012qka} have excluded this model
by a considerable margin.  Thus,
here we simply set a limit on $\sigma(pp \to tt)$.

The limit is calculated using $pp \to \ttbar$ as 
an acceptance model.  We find that the acceptance,
including branching fractions, is xx $\pm$ yy\%; this
results in an upper limit of xx pb at 95\% CL.

\subsection{Models with four top quarks and two LSPs from gluino pair production and decay via real or virtual top squarks}
\label{sec:stop}


\begin{figure}[htb]
\begin{center}
\includegraphics[height=0.33\linewidth]{FDT1tttt.pdf}
\hspace{2 cm}
\includegraphics[height=0.33\linewidth]{FDGlstop.pdf}
\caption{Diagrams for models A1 (left) and 
A2 (right).
\label{fig:stopFD}}
\end{center}
\end{figure}

Here we consider two SUSY models of gluino pair 
production that result in $tt\bar{t}\bar{t} \chi_1^0 \chi^0_1$
final states, see 
Fig.~\ref{fig:stopFD}~\cite{stopVirtual,stopVirtualPRD,T1tttt,wacker,naturalness4}.  In model A1, the gluino would undergo a three-body decay
into \ttbar$\chi_1^0$ mediated by an off-shell stop quark; in model 
A2, the gluino decays to antitop-stop, and the on-shell 
stop further decays into top-neutralino.  

These would be the 
most dominant decay modes of the gluino if the
top squark was the lightest supersymmetric quark.  Such models
have gained in popularity since a light stop is required 
to preserve naturalness, and all other squarks (if they exist!)
are likely to be very heavy since they have escaped detection
in the 7 TeV searches at the LHC~\cite{naturalness4}.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.49\linewidth]{T1tttt_SmoothLimitsOnWhite.pdf}
\includegraphics[width=0.49\linewidth]{GlStop_cheeseWedge.pdf}
\caption{Results from the 2011 7 TeV CMS run of Ref.~\cite{Chatrchyan:2012qka}.
Left plot: exclusion (95 \% CL) in the 
% $m(\chiz_1)-m(\sGlu)$ 
$m(\tilde{\chi}^0_1)-m(\tilde{g})$ 
plane for model A1 (gluino decay via virtual top squarks).
Right plot: exclusion (95\% CL) in the
% $m(\sTop_1)-m(\sGlu)$ 
$m(\tilde{t}_1)-m(\tilde{g})$
plane for model A2 
(gluino decay to on-shell top squarks).
The lines represent the kinematic boundaries of the models.  
The regions to the left of the bands, and within the kinematic boundaries,
are excluded; the thicknesses of the bands represent the theoretical 
uncertainties on the gluino pair production cross section from scale 
and parton distribution functions (pdf) variations.
In the case of model A2 
we show results for 
% $m(\chiz_1)=50$ 
$m(m(\tilde{\chi}^0_1)=50$
GeV (red, with dashed lines for the 
kinematic boundaries) and 
% $m(\chiz_1)=150$ 
$m(m(\tilde{\chi}^0_1)=150$
GeV (blue, with solid line
for the kinematic boundary).
\label{fig:stop7tev}}
\end{center}
\end{figure}

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.49\linewidth]{T1tttt_SmoothLimitsOnWhite.pdf}
\includegraphics[width=0.49\linewidth]{GlStop_cheeseWedge.pdf}
\caption{Same as Fig.~\ref{fig:stop7tev}, but for 
8 TeV data.  THIS IS A PLACEHOLDER FOR NOW.
\label{fig:stop8tev}}
\end{center}
\end{figure}


The exclusion from our 7 TeV search of Ref.~\cite{Chatrchyan:2012qka}
is shown in Fig.~\ref{fig:stop7tev}.  The equivalent results from this 
analysis at 8 TeV are shown in 
Fig.~\ref{fig:stop8tev}.

WILL ADD SOME COMMENTS HERE ONCE WE SEE WHAT THE NEW PLOTS LOOK LIKE. 


\subsection{Models with multiple top quarks and W-bosons from decays of bottom squarks}
\label{sec:sbottom}


\begin{figure}[h]
\begin{center}
\includegraphics[width=0.49\linewidth]{FDsbpair.pdf}
\includegraphics[width=0.49\linewidth]{FDGlsb.pdf}
\caption{Diagrams for models B1 (left) and 
B2 (right).  
\label{fig:sbFD}}
\end{center}
\end{figure}

In this Section we consider 
% Here we study 
possible SUSY signals with pairs of
bottom squarks decaying as 
% $\sBot_1 \to \PQt \chim_1$ and $\chim_1 \to \PWm \chiz_1$.
$\tilde{b}_1 \to t \tilde{\chi}^-_1$ followed by 
$\tilde{\chi}^-_1 \to W^- \tilde{\chi}^0_1$,
see Fig.~\ref{fig:sbFD}.

Model B1 is a model of sbottom pair production, followed 
by one of the most likely decay modes of the sbottom; model B2
would be the favorite gluino mode
if the sbottom was the lightest squark.  

The exclusion from our 7 TeV search of Ref.~\cite{Chatrchyan:2012qka}
is shown in Fig.~\ref{fig:sbottom7tev}.  The equivalent results from this 
analysis at 8 TeV are shown in 
Fig.~\ref{fig:sbottom8tev}.

WILL ADD SOME COMMENTS HERE ONCE WE SEE WHAT THE NEW PLOTS LOOK LIKE. 

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.49\linewidth]{B1_LimitsOnWhite.pdf}
\includegraphics[width=0.49\linewidth]{B2_CheeseWedge.pdf}
\end{center}
\caption{Results from the 2011 7 TeV CMS run of Ref.~\cite{Chatrchyan:2012qka}.
Left plot: exclusion (95\% CL) in the 
% $m(\chipm_1) - m(\sBot_1)$ 
$m(\tilde{\chi}^{\pm}_1 - m(\tilde{b}_1)$ 
plane for model B1 (sbottom pair production); 
Right plot: exclusion (95\% CL) in the 
% $m(\sBot_1)-m(\sGlu)$
$m(\tilde{b}_1) - m(\tilde{g})$ 
plane for model B2 (sbottom production from gluino decay).
The lines represent the kinematic boundaries of the models.  
The regions to the left of the bands, and within the kinematic boundaries,
are excluded; the thicknesses of the bands represent the theoretical 
uncertainties on the gluino and sbottom pair production cross section from 
scale and parton distribution functions (pdf) variations.
In the case of model B2 
we show results for 
% $m(\chipm_1)=150$ 
$m(\tilde{\chi}^{\pm}_1)=150$ 
GeV (red, with dashed
line for the kinematic boundary) and 
% $m(\chipm_1)=300$ 
$m(\tilde{\chi}^{\pm}_1)=300$ 
GeV (blue, with
solid line for the kinematic boundary).
\label{fig:sbottom7tev}}
\end{figure}


\begin{figure}[bht]
\begin{center}
\includegraphics[width=0.49\linewidth]{B1_LimitsOnWhite.pdf}
\includegraphics[width=0.49\linewidth]{B2_CheeseWedge.pdf}
\end{center}
\caption{
Same as Fig.~\ref{fig:sbottom7tev}, but for 
8 TeV data.  THIS IS A PLACEHOLDER FOR NOW.}
\label{fig:sbottom8tev}
\end{figure}


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#	Content
1	\section{Models of new physics}
2	\label{sec:models}
3	We use the search results to constrain specific models of new physics.
4	For each model
5	considered, we base our limits on the signal region
6	which is expected to give the most
7	stringent limit on the cross section at a given point
8	in model parameter space.
9	As described in Ref.~\cite{Chatrchyan:2012qka},
10	the event
11	selection efficiency for a given model is
12	obtained from Monte Carlo simulation, and the limits are
13	calculated including systematic uncertainties on lepton efficiency
14	(5\% per lepton), luminosity (2.2\%), jet energy scale and
15	b-tag uncertainty. The latter two uncertainties are
16	evaluated at each point in parameter space.
17
18	\subsection{Same sign top production}
19	\label{sec:sstt}
20	In Ref.~\cite{Chatrchyan:2012qka} we used the results
21	of SR2 to set limits on the cross-section for same-sign
22	top quark production $\sigma(pp \to tt)$ and on the
23	parameter space of two models that naturally give rise
24	to this final state~\cite{fcnczprime,mxflv1}. (Note that
25	SR2 requires two positive leptons, thus it is sensitive
26	to $pp \to tt$ but not $pp \to \bar{t}\bar{t}$; the latter
27	process would be suppressed because of the proton parton
28	distribution functions).
29
30	The model of Ref.~\cite{fcnczprime} was proposed
31	to explain the forward-backward \ttbar asymmetry observed at the
32	Tevatron~\cite{cdf:fwtop1,cdf:fwtop2,d0:fwtop}. Our results
33	from Ref.~\cite{Chatrchyan:2012qka} have excluded this model
34	by a considerable margin. Thus,
35	here we simply set a limit on $\sigma(pp \to tt)$.
36
37	The limit is calculated using $pp \to \ttbar$ as
38	an acceptance model. We find that the acceptance,
39	including branching fractions, is xx $\pm$ yy\%; this
40	results in an upper limit of xx pb at 95\% CL.
41
42	\subsection{Models with four top quarks and two LSPs from gluino pair production and decay via real or virtual top squarks}
43	\label{sec:stop}
44
45
46	\begin{figure}[htb]
47	\begin{center}
48	\includegraphics[height=0.33\linewidth]{FDT1tttt.pdf}
49	\hspace{2 cm}
50	\includegraphics[height=0.33\linewidth]{FDGlstop.pdf}
51	\caption{Diagrams for models A1 (left) and
52	A2 (right).
53	\label{fig:stopFD}}
54	\end{center}
55	\end{figure}
56
57	Here we consider two SUSY models of gluino pair
58	production that result in $tt\bar{t}\bar{t} \chi_1^0 \chi^0_1$
59	final states, see
60	Fig.~\ref{fig:stopFD}~\cite{stopVirtual,stopVirtualPRD,T1tttt,wacker,naturalness4}. In model A1, the gluino would undergo a three-body decay
61	into \ttbar$\chi_1^0$ mediated by an off-shell stop quark; in model
62	A2, the gluino decays to antitop-stop, and the on-shell
63	stop further decays into top-neutralino.
64
65	These would be the
66	most dominant decay modes of the gluino if the
67	top squark was the lightest supersymmetric quark. Such models
68	have gained in popularity since a light stop is required
69	to preserve naturalness, and all other squarks (if they exist!)
70	are likely to be very heavy since they have escaped detection
71	in the 7 TeV searches at the LHC~\cite{naturalness4}.
72
73	\begin{figure}[htb]
74	\begin{center}
75	\includegraphics[width=0.49\linewidth]{T1tttt_SmoothLimitsOnWhite.pdf}
76	\includegraphics[width=0.49\linewidth]{GlStop_cheeseWedge.pdf}
77	\caption{Results from the 2011 7 TeV CMS run of Ref.~\cite{Chatrchyan:2012qka}.
78	Left plot: exclusion (95 \% CL) in the
79	% $m(\chiz_1)-m(\sGlu)$
80	$m(\tilde{\chi}^0_1)-m(\tilde{g})$
81	plane for model A1 (gluino decay via virtual top squarks).
82	Right plot: exclusion (95\% CL) in the
83	% $m(\sTop_1)-m(\sGlu)$
84	$m(\tilde{t}_1)-m(\tilde{g})$
85	plane for model A2
86	(gluino decay to on-shell top squarks).
87	The lines represent the kinematic boundaries of the models.
88	The regions to the left of the bands, and within the kinematic boundaries,
89	are excluded; the thicknesses of the bands represent the theoretical
90	uncertainties on the gluino pair production cross section from scale
91	and parton distribution functions (pdf) variations.
92	In the case of model A2
93	we show results for
94	% $m(\chiz_1)=50$
95	$m(m(\tilde{\chi}^0_1)=50$
96	GeV (red, with dashed lines for the
97	kinematic boundaries) and
98	% $m(\chiz_1)=150$
99	$m(m(\tilde{\chi}^0_1)=150$
100	GeV (blue, with solid line
101	for the kinematic boundary).
102	\label{fig:stop7tev}}
103	\end{center}
104	\end{figure}
105
106	\begin{figure}[htb]
107	\begin{center}
108	\includegraphics[width=0.49\linewidth]{T1tttt_SmoothLimitsOnWhite.pdf}
109	\includegraphics[width=0.49\linewidth]{GlStop_cheeseWedge.pdf}
110	\caption{Same as Fig.~\ref{fig:stop7tev}, but for
111	8 TeV data. THIS IS A PLACEHOLDER FOR NOW.
112	\label{fig:stop8tev}}
113	\end{center}
114	\end{figure}
115
116
117
118	The exclusion from our 7 TeV search of Ref.~\cite{Chatrchyan:2012qka}
119	is shown in Fig.~\ref{fig:stop7tev}. The equivalent results from this
120	analysis at 8 TeV are shown in
121	Fig.~\ref{fig:stop8tev}.
122
123	WILL ADD SOME COMMENTS HERE ONCE WE SEE WHAT THE NEW PLOTS LOOK LIKE.
124
125
126	\subsection{Models with multiple top quarks and W-bosons from decays of bottom squarks}
127	\label{sec:sbottom}
128
129
130	\begin{figure}[h]
131	\begin{center}
132	\includegraphics[width=0.49\linewidth]{FDsbpair.pdf}
133	\includegraphics[width=0.49\linewidth]{FDGlsb.pdf}
134	\caption{Diagrams for models B1 (left) and
135	B2 (right).
136	\label{fig:sbFD}}
137	\end{center}
138	\end{figure}
139
140	In this Section we consider
141	% Here we study
142	possible SUSY signals with pairs of
143	bottom squarks decaying as
144	% $\sBot_1 \to \PQt \chim_1$ and $\chim_1 \to \PWm \chiz_1$.
145	$\tilde{b}_1 \to t \tilde{\chi}^-_1$ followed by
146	$\tilde{\chi}^-_1 \to W^- \tilde{\chi}^0_1$,
147	see Fig.~\ref{fig:sbFD}.
148
149	Model B1 is a model of sbottom pair production, followed
150	by one of the most likely decay modes of the sbottom; model B2
151	would be the favorite gluino mode
152	if the sbottom was the lightest squark.
153
154	The exclusion from our 7 TeV search of Ref.~\cite{Chatrchyan:2012qka}
155	is shown in Fig.~\ref{fig:sbottom7tev}. The equivalent results from this
156	analysis at 8 TeV are shown in
157	Fig.~\ref{fig:sbottom8tev}.
158
159	WILL ADD SOME COMMENTS HERE ONCE WE SEE WHAT THE NEW PLOTS LOOK LIKE.
160
161	\begin{figure}[h]
162	\begin{center}
163	\includegraphics[width=0.49\linewidth]{B1_LimitsOnWhite.pdf}
164	\includegraphics[width=0.49\linewidth]{B2_CheeseWedge.pdf}
165	\end{center}
166	\caption{Results from the 2011 7 TeV CMS run of Ref.~\cite{Chatrchyan:2012qka}.
167	Left plot: exclusion (95\% CL) in the
168	% $m(\chipm_1) - m(\sBot_1)$
169	$m(\tilde{\chi}^{\pm}_1 - m(\tilde{b}_1)$
170	plane for model B1 (sbottom pair production);
171	Right plot: exclusion (95\% CL) in the
172	% $m(\sBot_1)-m(\sGlu)$
173	$m(\tilde{b}_1) - m(\tilde{g})$
174	plane for model B2 (sbottom production from gluino decay).
175	The lines represent the kinematic boundaries of the models.
176	The regions to the left of the bands, and within the kinematic boundaries,
177	are excluded; the thicknesses of the bands represent the theoretical
178	uncertainties on the gluino and sbottom pair production cross section from
179	scale and parton distribution functions (pdf) variations.
180	In the case of model B2
181	we show results for
182	% $m(\chipm_1)=150$
183	$m(\tilde{\chi}^{\pm}_1)=150$
184	GeV (red, with dashed
185	line for the kinematic boundary) and
186	% $m(\chipm_1)=300$
187	$m(\tilde{\chi}^{\pm}_1)=300$
188	GeV (blue, with
189	solid line for the kinematic boundary).
190	\label{fig:sbottom7tev}}
191	\end{figure}
192
193
194	\begin{figure}[bht]
195	\begin{center}
196	\includegraphics[width=0.49\linewidth]{B1_LimitsOnWhite.pdf}
197	\includegraphics[width=0.49\linewidth]{B2_CheeseWedge.pdf}
198	\end{center}
199	\caption{
200	Same as Fig.~\ref{fig:sbottom7tev}, but for
201	8 TeV data. THIS IS A PLACEHOLDER FOR NOW.}
202	\label{fig:sbottom8tev}
203	\end{figure}
204
205
206
207
208