claudioc/OSNote2010/datadriven.tex

\section{Data Driven Background Estimation Methods}
\label{sec:datadriven}
We have developed two data-driven methods to 
estimate the background in the signal region.
The first one explouts the fact that 
\met and \met$/\sqrt{\rm SumJetPt}$ are nearly 
uncorrelated for the $t\bar{t}$ background 
(Section~\ref{sec:abcd});  the second one 
is based on the fact that in $t\bar{t}$ the
$P_T$ of the dilepton pair is on average 
nearly the same as the $P_T$ of the pair of neutrinos
from $W$-decays, which is reconstructed as \met in the
detector.

In 30 pb$^{-1}$ we expect $\approx$ 1 SM event in 
the signal region.  The expectations from the LMO
and LM1 SUSY benchmark points are 5.6 and
2.2 events respectively. 
%{\color{red} I took these
%numbers from the twiki, rescaling from 11.06 to 30/pb.
%They seem too large...are they really right?}


\subsection{ABCD method}
\label{sec:abcd}

We find that in $t\bar{t}$ events \met and 
\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated.
This is demonstrated in Figure~\ref{fig:uncor}.
Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs
sumJetPt plane to estimate the background in a data driven way.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.75\linewidth]{uncorrelated.pdf}
\caption{\label{fig:uncor}\protect Distributions of SumJetPt 
in MC $t\bar{t}$ events for different intervals of 
MET$/\sqrt{\rm SumJetPt}$.}
\end{center}
\end{figure}

\begin{figure}[bt]
\begin{center}
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf}
\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt 
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo.  Here we also
show our choice of ABCD regions.}
\end{center}
\end{figure}


Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
The signal region is region D.  The expected number of events 
in the four regions for the SM Monte Carlo, as well as the BG 
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated
luminosity of 30 pb$^{-1}$.  The ABCD method is accurate 
to about 10\%. {\color{red} Avi wants some statement about stability 
wrt changes in regions.  I am not sure that we have done it and 
I am not sure it is necessary (Claudio).}

\begin{table}[htb]
\begin{center}
\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for 
30 pb$^{-1}$ in the ABCD regions.}
\begin{tabular}{|l|c|c|c|c||c|}
\hline
Sample   & A   & B    & C   & D   & AC/D \\ \hline
ttdil    & 6.9 & 28.6 & 4.2 & 1.0 & 1.0  \\
Zjets    & 0.0 & 1.3  & 0.1 & 0.1 & 0.0  \\
Other SM & 0.5 & 2.0  & 0.1 & 0.1 & 0.0  \\ \hline
total MC & 7.4 & 31.9 & 4.4 & 1.2 & 1.0 \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{Dilepton $P_T$ method}
\label{sec:victory}
This method is based on a suggestion by V. Pavlunin\cite{ref:victory},
and was investigated by our group in 2009\cite{ref:ourvictory}.
The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos
from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization 
effects).  One can then use the observed 
$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which 
is identified with the \met.

Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a 
selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead.
In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection
to account for the fact that any dilepton selection must include a 
moderate \met cut in order to reduce Drell Yan backgrounds.  This 
is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met
cut of 50 GeV, the rescaling factor is obtained from the data as

\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
\begin{center}
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
\end{center}


Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
depending on selection details.

There are several effects that spoil the correspondance between \met and
$P_T(\ell\ell)$: 
\begin{itemize}
\item $Ws$ in top events are polarized.  Neutrinos are emitted preferentially
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
than the $P_T(\ell\ell)$ distribution for top dilepton events.
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
leptons that have no simple correspondance to the neutrino requirements.
\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and
neutrinos which is only partially compensated by the $K$ factor above.
\item The \met resolution is much worse than the dilepton $P_T$ resolution.
When convoluted with a falling spectrum in the tails of \met, this result
in a harder spectrum for \met than the original $P_T(\nu\nu)$.
\item The \met response in CMS is not exactly 1.  This causes a distortion
in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution.
\item The $t\bar{t} \to$ dilepton signal includes contributions from 
$W \to \tau \to \ell$.  For these events the arguments about the equivalence 
of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply.
\item A dilepton selection will include SM events from non $t\bar{t}$ 
sources.  These events can affect the background prediction.  Particularly 
dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50 
GeV selection.  They will tend to push the data-driven background prediction up.
\end{itemize}

We have studied these effects in SM Monte Carlo, using a mixture of generator and
reconstruction level studies, putting the various effects in one at a time.
For each configuration, we apply the data-driven method and report as figure
of merit the ratio of observed and predicted events in the signal region.
The results are summarized in Table~\ref{tab:victorybad}.

\begin{table}[htb]
\begin{center}
\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo 
under different assumptions.  See text for details.}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
\hline
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & Z veto & \met $>$ 50& obs/pred \\
& included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &  \\ \hline
1&Y                        &     N          &   N      &  GEN    &   N             &   N    & N          & 1.90  \\
2&Y                        &     N          &   N      &  GEN    &   Y             &   N    & N          & 1.64  \\
3&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & N          & 1.59  \\
4&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & Y          & 1.55  \\
5&Y                        &     N          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.51  \\
6&Y                        &     Y          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.58  \\
7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.18  \\
\hline
\end{tabular}
\end{center}
\end{table}


The largest discrepancy between prediction and observation occurs on the first 
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
cuts.  We have verified that this effect is due to the polarization of
the $W$ (we remove the polarization by reweighting the events and we get
good agreement between prediction and observation).  The kinematical 
requirements (lines 2,3,4) compensate somewhat for the effect of W polarization. 
Going from GEN to RECOSIM, the change in observed/predicted is small.  
% We have tracked this down to the fact that tcMET underestimates the true \met
% by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1
%for each 1.5\% change in \met response.}.  
Finally, contamination from non $t\bar{t}$
events can have a significant impact on the BG prediction.  The changes between 
lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3
Drell Yan events that pass the \met selection in Monte Carlo (thus the effect
is statistically not well quantified).

An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does
not include effects of spin correlations between the two top quarks.  
We have studied this effect at the generator level using Alpgen.  We find
that the bias is a the few percent level.

Based on the results of Table~\ref{tab:victorybad}, we conclude that the 
naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to 
be corrected by a factor of {\color{red} $1.2 \pm 0.3$ (We need to talk 
about this)} . The quoted 
uncertainty is based on the stability of the Monte Carlo tests under 
variations of event selections, choices of \met algorithm, etc.


\subsection{Signal Contamination}
\label{sec:sigcont}

All data-driven methods are in principle subject to signal contaminations
in the control regions, and the methods described in 
Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions.
Signal contamination tends to dilute the significance of a signal
present in the data by inflating the background prediction.

It is hard to quantify how important these effects are because we 
do not know what signal may be hiding in the data.  Having two
independent methods (in addition to Monte Carlo ``dead-reckoning'')
adds redundancy because signal contamination can have different effects
in the different control regions for the two methods.
For example, in the extreme case of a
new physics signal 
with $P_T(\ell \ell) = \met$, an excess of events would be seen 
in the ABCD method but not in the $P_T(\ell \ell)$ method.


The LM points are benchmarks for SUSY analyses at CMS.  The effects
of signal contaminations for a couple such points are summarized
in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}. 
Signal contamination is definitely an important
effect for these two LM points, but it does not totally hide the
presence of the signal.


\begin{table}[htb]
\begin{center}
\caption{\label{tab:sigcontABCD} Effects of signal contamination 
for the background predictions of the ABCD method including LM0 or 
LM1.  Results
are normalized to 30 pb$^{-1}$.}
\begin{tabular}{|c||c|c||c|c|}
\hline
SM         & LM0         & BG Prediction & LM1          & BG Prediction \\
Background & Contribution& Including LM0 & Contribution & Including LM1  \\ \hline
1.2        & 5.6         & 3.7           & 2.2          & 1.3 \\ 
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\begin{center}
\caption{\label{tab:sigcontPT} Effects of signal contamination 
for the background predictions of the $P_T(\ell\ell)$ method including LM0 or 
LM1.  Results
are normalized to 30 pb$^{-1}$. {\color{red} Does this BG prediction include
the fudge factor of 1.4 or watever because the method is not perfect.}}
\begin{tabular}{|c||c|c||c|c|}
\hline
SM         & LM0         & BG Prediction & LM1          & BG Prediction \\
Background & Contribution& Including LM0 & Contribution & Including LM1  \\ \hline
1.2        & 5.6         & 2.2           & 2.2          & 1.5 \\ 
\hline
\end{tabular}
\end{center}
\end{table}

Revision:	1.6
Committed:	Wed Nov 3 23:05:16 2010 UTC (14 years, 6 months ago) by claudioc
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.5:	+33 -27 lines
Log Message:	new
#	User	Rev	Content
1	claudioc	1.1	\section{Data Driven Background Estimation Methods}
2			\label{sec:datadriven}
3			We have developed two data-driven methods to
4			estimate the background in the signal region.
5			The first one explouts the fact that
6			\met and \met$/\sqrt{\rm SumJetPt}$ are nearly
7			uncorrelated for the $t\bar{t}$ background
8			(Section~\ref{sec:abcd}); the second one
9			is based on the fact that in $t\bar{t}$ the
10			$P_T$ of the dilepton pair is on average
11			nearly the same as the $P_T$ of the pair of neutrinos
12			from $W$-decays, which is reconstructed as \met in the
13			detector.
14
15	claudioc	1.3	In 30 pb$^{-1}$ we expect $\approx$ 1 SM event in
16	claudioc	1.1	the signal region. The expectations from the LMO
17	dbarge	1.5	and LM1 SUSY benchmark points are 5.6 and
18	claudioc	1.6	2.2 events respectively.
19			%{\color{red} I took these
20			%numbers from the twiki, rescaling from 11.06 to 30/pb.
21			%They seem too large...are they really right?}
22	claudioc	1.1
23
24			\subsection{ABCD method}
25			\label{sec:abcd}
26
27			We find that in $t\bar{t}$ events \met and
28			\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated.
29			This is demonstrated in Figure~\ref{fig:uncor}.
30			Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs
31			sumJetPt plane to estimate the background in a data driven way.
32
33	claudioc	1.2	\begin{figure}[tb]
34	claudioc	1.1	\begin{center}
35			\includegraphics[width=0.75\linewidth]{uncorrelated.pdf}
36			\caption{\label{fig:uncor}\protect Distributions of SumJetPt
37			in MC $t\bar{t}$ events for different intervals of
38			MET$/\sqrt{\rm SumJetPt}$.}
39			\end{center}
40			\end{figure}
41
42	claudioc	1.2	\begin{figure}[bt]
43	claudioc	1.1	\begin{center}
44	claudioc	1.3	\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf}
45	claudioc	1.1	\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt
46			vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also
47	dbarge	1.5	show our choice of ABCD regions.}
48	claudioc	1.1	\end{center}
49			\end{figure}
50
51
52			Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
53			The signal region is region D. The expected number of events
54			in the four regions for the SM Monte Carlo, as well as the BG
55	claudioc	1.2	prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated
56	claudioc	1.1	luminosity of 30 pb$^{-1}$. The ABCD method is accurate
57	claudioc	1.4	to about 10\%. {\color{red} Avi wants some statement about stability
58			wrt changes in regions. I am not sure that we have done it and
59			I am not sure it is necessary (Claudio).}
60	claudioc	1.1
61			\begin{table}[htb]
62			\begin{center}
63			\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for
64			30 pb$^{-1}$ in the ABCD regions.}
65			\begin{tabular}{\|l\|c\|c\|c\|c\|\|c\|}
66			\hline
67			Sample & A & B & C & D & AC/D \\ \hline
68	claudioc	1.3	ttdil & 6.9 & 28.6 & 4.2 & 1.0 & 1.0 \\
69			Zjets & 0.0 & 1.3 & 0.1 & 0.1 & 0.0 \\
70			Other SM & 0.5 & 2.0 & 0.1 & 0.1 & 0.0 \\ \hline
71			total MC & 7.4 & 31.9 & 4.4 & 1.2 & 1.0 \\ \hline
72	claudioc	1.1	\end{tabular}
73			\end{center}
74			\end{table}
75
76	claudioc	1.2	\subsection{Dilepton $P_T$ method}
77			\label{sec:victory}
78			This method is based on a suggestion by V. Pavlunin\cite{ref:victory},
79			and was investigated by our group in 2009\cite{ref:ourvictory}.
80			The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos
81			from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization
82			effects). One can then use the observed
83			$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which
84			is identified with the \met.
85
86			Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a
87			selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead.
88			In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection
89			to account for the fact that any dilepton selection must include a
90			moderate \met cut in order to reduce Drell Yan backgrounds. This
91			is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met
92			cut of 50 GeV, the rescaling factor is obtained from the data as
93
94			\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
95			\begin{center}
96			$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
97			\end{center}
98
99
100			Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
101			depending on selection details.
102
103			There are several effects that spoil the correspondance between \met and
104			$P_T(\ell\ell)$:
105			\begin{itemize}
106			\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially
107			forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
108			than the $P_T(\ell\ell)$ distribution for top dilepton events.
109			\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
110			leptons that have no simple correspondance to the neutrino requirements.
111			\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and
112			neutrinos which is only partially compensated by the $K$ factor above.
113			\item The \met resolution is much worse than the dilepton $P_T$ resolution.
114			When convoluted with a falling spectrum in the tails of \met, this result
115			in a harder spectrum for \met than the original $P_T(\nu\nu)$.
116			\item The \met response in CMS is not exactly 1. This causes a distortion
117			in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution.
118			\item The $t\bar{t} \to$ dilepton signal includes contributions from
119			$W \to \tau \to \ell$. For these events the arguments about the equivalence
120			of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply.
121			\item A dilepton selection will include SM events from non $t\bar{t}$
122			sources. These events can affect the background prediction. Particularly
123			dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50
124			GeV selection. They will tend to push the data-driven background prediction up.
125			\end{itemize}
126
127			We have studied these effects in SM Monte Carlo, using a mixture of generator and
128			reconstruction level studies, putting the various effects in one at a time.
129			For each configuration, we apply the data-driven method and report as figure
130			of merit the ratio of observed and predicted events in the signal region.
131			The results are summarized in Table~\ref{tab:victorybad}.
132
133			\begin{table}[htb]
134			\begin{center}
135			\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
136			under different assumptions. See text for details.}
137	claudioc	1.6	\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|c\|}
138	claudioc	1.2	\hline
139	claudioc	1.6	& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & Z veto & \met $>$ 50& obs/pred \\
140			& included & included & included & RECOSIM & and $\eta$ cuts & & & \\ \hline
141			1&Y & N & N & GEN & N & N & N & 1.90 \\
142			2&Y & N & N & GEN & Y & N & N & 1.64 \\
143			3&Y & N & N & GEN & Y & Y & N & 1.59 \\
144			4&Y & N & N & GEN & Y & Y & Y & 1.55 \\
145			5&Y & N & N & RECOSIM & Y & Y & Y & 1.51 \\
146			6&Y & Y & N & RECOSIM & Y & Y & Y & 1.58 \\
147			7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.18 \\
148	claudioc	1.2	\hline
149			\end{tabular}
150			\end{center}
151			\end{table}
152
153
154			The largest discrepancy between prediction and observation occurs on the first
155			line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
156			cuts. We have verified that this effect is due to the polarization of
157			the $W$ (we remove the polarization by reweighting the events and we get
158			good agreement between prediction and observation). The kinematical
159	claudioc	1.6	requirements (lines 2,3,4) compensate somewhat for the effect of W polarization.
160			Going from GEN to RECOSIM, the change in observed/predicted is small.
161			% We have tracked this down to the fact that tcMET underestimates the true \met
162			% by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1
163			%for each 1.5\% change in \met response.}.
164			Finally, contamination from non $t\bar{t}$
165	claudioc	1.2	events can have a significant impact on the BG prediction. The changes between
166	claudioc	1.6	lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3
167			Drell Yan events that pass the \met selection in Monte Carlo (thus the effect
168			is statistically not well quantified).
169	claudioc	1.2
170			An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does
171			not include effects of spin correlations between the two top quarks.
172			We have studied this effect at the generator level using Alpgen. We find
173			that the bias is a the few percent level.
174
175			Based on the results of Table~\ref{tab:victorybad}, we conclude that the
176	claudioc	1.6	naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
177			be corrected by a factor of {\color{red} $1.2 \pm 0.3$ (We need to talk
178			about this)} . The quoted
179	claudioc	1.2	uncertainty is based on the stability of the Monte Carlo tests under
180			variations of event selections, choices of \met algorithm, etc.
181
182
183	claudioc	1.6
184	claudioc	1.2	\subsection{Signal Contamination}
185			\label{sec:sigcont}
186
187	claudioc	1.6	All data-driven methods are in principle subject to signal contaminations
188	claudioc	1.2	in the control regions, and the methods described in
189			Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions.
190			Signal contamination tends to dilute the significance of a signal
191			present in the data by inflating the background prediction.
192
193			It is hard to quantify how important these effects are because we
194			do not know what signal may be hiding in the data. Having two
195			independent methods (in addition to Monte Carlo ``dead-reckoning'')
196			adds redundancy because signal contamination can have different effects
197			in the different control regions for the two methods.
198			For example, in the extreme case of a
199			new physics signal
200	claudioc	1.6	with $P_T(\ell \ell) = \met$, an excess of events would be seen
201	claudioc	1.2	in the ABCD method but not in the $P_T(\ell \ell)$ method.
202
203	claudioc	1.4
204	claudioc	1.2	The LM points are benchmarks for SUSY analyses at CMS. The effects
205			of signal contaminations for a couple such points are summarized
206			in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}.
207			Signal contamination is definitely an important
208			effect for these two LM points, but it does not totally hide the
209			presence of the signal.
210	claudioc	1.1
211
212	claudioc	1.2	\begin{table}[htb]
213			\begin{center}
214			\caption{\label{tab:sigcontABCD} Effects of signal contamination
215			for the background predictions of the ABCD method including LM0 or
216			LM1. Results
217			are normalized to 30 pb$^{-1}$.}
218			\begin{tabular}{\|c\|\|c\|c\|\|c\|c\|}
219			\hline
220			SM & LM0 & BG Prediction & LM1 & BG Prediction \\
221			Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline
222	claudioc	1.6	1.2 & 5.6 & 3.7 & 2.2 & 1.3 \\
223	claudioc	1.2	\hline
224			\end{tabular}
225			\end{center}
226			\end{table}
227
228			\begin{table}[htb]
229			\begin{center}
230			\caption{\label{tab:sigcontPT} Effects of signal contamination
231			for the background predictions of the $P_T(\ell\ell)$ method including LM0 or
232			LM1. Results
233	claudioc	1.6	are normalized to 30 pb$^{-1}$. {\color{red} Does this BG prediction include
234			the fudge factor of 1.4 or watever because the method is not perfect.}}
235	claudioc	1.2	\begin{tabular}{\|c\|\|c\|c\|\|c\|c\|}
236			\hline
237			SM & LM0 & BG Prediction & LM1 & BG Prediction \\
238			Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline
239	claudioc	1.6	1.2 & 5.6 & 2.2 & 2.2 & 1.5 \\
240	claudioc	1.2	\hline
241			\end{tabular}
242			\end{center}
243			\end{table}
244	claudioc	1.1