| 23 |
|
|
| 24 |
|
We find that in $t\bar{t}$ events SumJetPt and |
| 25 |
|
\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated, |
| 26 |
< |
as demonstrated in Figure~\ref{fig:uncor}. |
| 26 |
> |
as demonstrated in Fig.~\ref{fig:uncor}. |
| 27 |
|
Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs |
| 28 |
|
sumJetPt plane to estimate the background in a data driven way. |
| 29 |
|
|
| 42 |
|
\caption{\label{fig:uncor}\protect Distributions of SumJetPt |
| 43 |
|
in MC $t\bar{t}$ events for different intervals of |
| 44 |
|
MET$/\sqrt{\rm SumJetPt}$. h1, h2, and h3 refer to the MET$/\sqrt{\rm SumJetPt}$ |
| 45 |
< |
intervals 4.5-6.5, 6.5-8.5 and $>$8.5, respectively.} |
| 45 |
> |
intervals 4.5-6.5, 6.5-8.5 and $>$8.5, respectively. } |
| 46 |
|
\end{center} |
| 47 |
|
\end{figure} |
| 48 |
|
|
| 49 |
|
\begin{figure}[tb] |
| 50 |
|
\begin{center} |
| 51 |
< |
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf} |
| 51 |
> |
\includegraphics[width=0.75\linewidth]{ttdil_uncor_38X.png} |
| 52 |
|
\caption{\label{fig:abcdMC}\protect Distributions of MET$/\sqrt{\rm SumJetPt}$ vs. |
| 53 |
< |
SumJetPt for SM Monte Carlo. Here we also show our choice of ABCD regions.} |
| 53 |
> |
SumJetPt for SM Monte Carlo. Here we also show our choice of ABCD regions. The correlation coefficient |
| 54 |
> |
${\rm corr_{XY}}$ is computed for events falling in the ABCD regions.} |
| 55 |
|
\end{center} |
| 56 |
|
\end{figure} |
| 57 |
|
|
| 58 |
|
|
| 59 |
|
Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}. |
| 60 |
|
The signal region is region D. The expected number of events |
| 61 |
< |
in the four regions for the SM Monte Carlo, as well as the BG |
| 62 |
< |
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated |
| 63 |
< |
luminosity of 35 pb$^{-1}$. The ABCD method with chosen boundaries is accurate |
| 64 |
< |
to about 20\%. As shown in Table~\ref{tab:abcdsyst}, we assess systematic uncertainties |
| 65 |
< |
by varying the boundaries by an amount consistent with the hadronic energy scale uncertainty, |
| 66 |
< |
which we take as $\pm$5\% for SumJetPt and $\pm$2.5\% for MET/$\sqrt{\rm SumJetPt}$, since the |
| 67 |
< |
uncertainty on this quantity partially cancels due to the fact that it is a ratio of correlated |
| 68 |
< |
quantities. Based on these studies we assess a correction factor $k_{ABCD} = 1.2 \pm 0.2$ to the |
| 69 |
< |
predicted yield using the ABCD method. |
| 61 |
> |
in the four regions for the SM Monte Carlo, as well as the background |
| 62 |
> |
prediction A $\times$ C / B are given in Table~\ref{tab:abcdMC} for an integrated |
| 63 |
> |
luminosity of 34.0 pb$^{-1}$. In Table~\ref{tab:abcdsyst}, we test the stability of |
| 64 |
> |
observed/predicted with respect to variations in the ABCD boundaries. |
| 65 |
> |
Based on the results in Tables~\ref{tab:abcdMC} and~\ref{tab:abcdsyst}, we assess |
| 66 |
> |
a systematic uncertainty of 20\% on the prediction of the ABCD method. |
| 67 |
> |
|
| 68 |
> |
%As shown in Table~\ref{tab:abcdsyst}, we assess systematic uncertainties |
| 69 |
> |
%by varying the boundaries by an amount consistent with the hadronic energy scale uncertainty, |
| 70 |
> |
%which we take as $\pm$5\% for SumJetPt and $\pm$2.5\% for MET/$\sqrt{\rm SumJetPt}$, since the |
| 71 |
> |
%uncertainty on this quantity partially cancels due to the fact that it is a ratio of correlated |
| 72 |
> |
%quantities. Based on these studies we assess a correction factor $k_{ABCD} = 1.2 \pm 0.2$ to the |
| 73 |
> |
%predicted yield using the ABCD method. |
| 74 |
|
|
| 75 |
|
|
| 76 |
|
%{\color{red} Avi wants some statement about stability |
| 80 |
|
\begin{table}[ht] |
| 81 |
|
\begin{center} |
| 82 |
|
\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for |
| 83 |
< |
35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
| 83 |
> |
34.0~pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
| 84 |
|
the signal region given by A $\times$ C / B. Here `SM other' is the sum |
| 85 |
|
of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$, |
| 86 |
|
$W^{\pm}Z^0$, $Z^0Z^0$ and single top.} |
| 87 |
|
\begin{tabular}{lccccc} |
| 88 |
+ |
%%%official json v3, 38X MC (D6T ttbar and DY) |
| 89 |
|
\hline |
| 90 |
< |
sample & A & B & C & D & A $\times$ C / B \\ |
| 90 |
> |
sample & A & B & C & D & PRED \\ |
| 91 |
|
\hline |
| 92 |
< |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 8.27 $\pm$ 0.18 & 32.16 $\pm$ 0.35 & 4.69 $\pm$ 0.13 & 1.05 $\pm$ 0.06 & 1.21 $\pm$ 0.04 \\ |
| 93 |
< |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.22 $\pm$ 0.11 & 1.54 $\pm$ 0.29 & 0.05 $\pm$ 0.05 & 0.16 $\pm$ 0.09 & 0.01 $\pm$ 0.01 \\ |
| 94 |
< |
SM other & 0.54 $\pm$ 0.03 & 2.28 $\pm$ 0.12 & 0.23 $\pm$ 0.03 & 0.07 $\pm$ 0.01 & 0.05 $\pm$ 0.01 \\ |
| 92 |
> |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 8.44 $\pm$ 0.18 & 32.83 $\pm$ 0.35 & 4.78 $\pm$ 0.14 & 1.07 $\pm$ 0.06 & 1.23 $\pm$ 0.05 \\ |
| 93 |
> |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.17 $\pm$ 0.08 & 1.18 $\pm$ 0.22 & 0.04 $\pm$ 0.04 & 0.12 $\pm$ 0.07 & 0.01 $\pm$ 0.01 \\ |
| 94 |
> |
SM other & 0.53 $\pm$ 0.03 & 2.26 $\pm$ 0.11 & 0.23 $\pm$ 0.03 & 0.07 $\pm$ 0.01 & 0.05 $\pm$ 0.01 \\ |
| 95 |
|
\hline |
| 96 |
< |
total SM MC & 9.03 $\pm$ 0.21 & 35.97 $\pm$ 0.46 & 4.97 $\pm$ 0.15 & 1.29 $\pm$ 0.11 & 1.25 $\pm$ 0.05 \\ |
| 96 |
> |
total SM MC & 9.14 $\pm$ 0.20 & 36.26 $\pm$ 0.43 & 5.05 $\pm$ 0.14 & 1.27 $\pm$ 0.10 & 1.27 $\pm$ 0.05 \\ |
| 97 |
|
\hline |
| 98 |
|
\end{tabular} |
| 99 |
|
\end{center} |
| 104 |
|
\begin{table}[ht] |
| 105 |
|
\begin{center} |
| 106 |
|
\caption{\label{tab:abcdsyst} |
| 101 |
– |
{\bf \color{red} Do we need this study at all? Observed/predicted is consistent within stat uncertainties as the boundaries are varied- is it enough to simply state this fact in the text??? } |
| 107 |
|
Results of the systematic study of the ABCD method by varying the boundaries |
| 108 |
|
between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and |
| 109 |
|
$x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV, |
| 114 |
|
\hline |
| 115 |
|
$x_1$ & $x_2$ & $y_1$ & $y_2$ & Observed/Predicted \\ |
| 116 |
|
\hline |
| 117 |
< |
nominal & nominal & nominal & nominal & $1.20 \pm 0.12$ \\ |
| 118 |
< |
+5\% & +5\% & +2.5\% & +2.5\% & $1.38 \pm 0.15$ \\ |
| 119 |
< |
+5\% & +5\% & nominal & nominal & $1.31 \pm 0.14$ \\ |
| 120 |
< |
nominal & nominal & +2.5\% & +2.5\% & $1.25 \pm 0.13$ \\ |
| 121 |
< |
nominal & +5\% & nominal & +2.5\% & $1.32 \pm 0.14$ \\ |
| 122 |
< |
nominal & -5\% & nominal & -2.5\% & $1.16 \pm 0.09$ \\ |
| 123 |
< |
-5\% & -5\% & +2.5\% & +2.5\% & $1.21 \pm 0.11$ \\ |
| 124 |
< |
+5\% & +5\% & -2.5\% & -2.5\% & $1.26 \pm 0.12$ \\ |
| 117 |
> |
|
| 118 |
> |
nominal & nominal & nominal & nominal & $1.00 \pm 0.08$ \\ |
| 119 |
> |
|
| 120 |
> |
+5\% & +5\% & +2.5\% & +2.5\% & $1.08 \pm 0.11$ \\ |
| 121 |
> |
|
| 122 |
> |
+5\% & +5\% & nominal & nominal & $1.04 \pm 0.10$ \\ |
| 123 |
> |
|
| 124 |
> |
nominal & nominal & +2.5\% & +2.5\% & $1.03 \pm 0.09$ \\ |
| 125 |
> |
|
| 126 |
> |
nominal & +5\% & nominal & +2.5\% & $1.05 \pm 0.10$ \\ |
| 127 |
> |
|
| 128 |
> |
nominal & -5\% & nominal & -2.5\% & $0.95 \pm 0.07$ \\ |
| 129 |
> |
|
| 130 |
> |
-5\% & -5\% & +2.5\% & +2.5\% & $1.00 \pm 0.08$ \\ |
| 131 |
> |
|
| 132 |
> |
+5\% & +5\% & -2.5\% & -2.5\% & $0.98 \pm 0.09$ \\ |
| 133 |
|
\hline |
| 134 |
|
\end{tabular} |
| 135 |
|
\end{center} |
| 155 |
|
|
| 156 |
|
\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}} |
| 157 |
|
\begin{center} |
| 158 |
< |
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$ |
| 158 |
> |
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~} = 1.5$ |
| 159 |
|
\end{center} |
| 160 |
|
|
| 161 |
|
|
| 149 |
– |
Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6, |
| 150 |
– |
depending on selection details. |
| 162 |
|
%%%TO BE REPLACED |
| 163 |
|
%Given the integrated luminosity of the |
| 164 |
|
%present dataset, the determination of $K$ in data is severely statistics |
| 206 |
|
\begin{table}[htb] |
| 207 |
|
\begin{center} |
| 208 |
|
\caption{\label{tab:victorybad} |
| 198 |
– |
{\bf \color{red} Need to either update this with 38X MC or remove it } |
| 209 |
|
Test of the data driven method in Monte Carlo |
| 210 |
< |
under different assumptions. See text for details.} |
| 210 |
> |
under different assumptions, evaluated using Spring10 MC. See text for details.} |
| 211 |
|
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} |
| 212 |
|
\hline |
| 213 |
|
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & Z veto & \met $>$ 50& obs/pred \\ |
| 228 |
|
\begin{table}[htb] |
| 229 |
|
\begin{center} |
| 230 |
|
\caption{\label{tab:victorysyst} |
| 231 |
< |
{Summary of uncertainties in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton. |
| 231 |
> |
Summary of variations in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton. |
| 232 |
|
In the first table, `up' and `down' refer to shifting the hadronic energy scale up and down by 5\%. In the second table, the quoted value |
| 233 |
|
refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds |
| 234 |
< |
other than $t\bar{t} \to$~dilepton is varied. |
| 225 |
< |
{\bf \color{ref} Should I remove `observed' and `predicted' and show only the ratio? }} |
| 226 |
< |
|
| 234 |
> |
other than $t\bar{t} \to$~dilepton is varied. } |
| 235 |
|
\begin{tabular}{ lcccc } |
| 236 |
|
\hline |
| 237 |
|
MET scale & Predicted & Observed & Obs/pred \\ |
| 238 |
|
\hline |
| 239 |
< |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 240 |
< |
up & 0.92 $ \pm $ 0.11 & 1.53 $ \pm $ 0.12 & 1.66 $ \pm $ 0.23 \\ |
| 241 |
< |
down & 0.81 $ \pm $ 0.07 & 1.08 $ \pm $ 0.11 & 1.32 $ \pm $ 0.17 \\ |
| 242 |
< |
\hline |
| 243 |
< |
|
| 244 |
< |
\hline |
| 245 |
< |
MET smearing & Predicted & Observed & Obs/pred \\ |
| 246 |
< |
\hline |
| 247 |
< |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 248 |
< |
10\% & 0.90 $ \pm $ 0.11 & 1.30 $ \pm $ 0.11 & 1.44 $ \pm $ 0.21 \\ |
| 249 |
< |
20\% & 0.84 $ \pm $ 0.07 & 1.36 $ \pm $ 0.11 & 1.61 $ \pm $ 0.19 \\ |
| 250 |
< |
30\% & 1.05 $ \pm $ 0.18 & 1.32 $ \pm $ 0.11 & 1.27 $ \pm $ 0.24 \\ |
| 251 |
< |
40\% & 0.85 $ \pm $ 0.07 & 1.37 $ \pm $ 0.11 & 1.61 $ \pm $ 0.19 \\ |
| 252 |
< |
50\% & 1.08 $ \pm $ 0.18 & 1.36 $ \pm $ 0.11 & 1.26 $ \pm $ 0.24 \\ |
| 253 |
< |
\hline |
| 254 |
< |
|
| 255 |
< |
\hline |
| 256 |
< |
non-$t\bar{t} \to$~dilepton scale factor & Predicted & Observed & Obs/pred \\ |
| 249 |
< |
\hline |
| 250 |
< |
ttdil only & 0.77 $ \pm $ 0.07 & 1.05 $ \pm $ 0.06 & 1.36 $ \pm $ 0.14 \\ |
| 251 |
< |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 252 |
< |
double non-ttdil yield & 1.06 $ \pm $ 0.18 & 1.52 $ \pm $ 0.20 & 1.43 $ \pm $ 0.30 \\ |
| 239 |
> |
nominal & 0.92 $ \pm $ 0.09 & 1.27 $ \pm $ 0.10 & 1.39 $ \pm $ 0.18 \\ |
| 240 |
> |
up & 0.90 $ \pm $ 0.09 & 1.58 $ \pm $ 0.10 & 1.75 $ \pm $ 0.21 \\ |
| 241 |
> |
down & 0.70 $ \pm $ 0.06 & 0.96 $ \pm $ 0.09 & 1.37 $ \pm $ 0.18 \\ |
| 242 |
> |
\hline |
| 243 |
> |
MET smearing & Predicted & Observed & Obs/pred \\ |
| 244 |
> |
\hline |
| 245 |
> |
nominal & 0.92 $ \pm $ 0.09 & 1.27 $ \pm $ 0.10 & 1.39 $ \pm $ 0.18 \\ |
| 246 |
> |
10\% & 0.88 $ \pm $ 0.09 & 1.28 $ \pm $ 0.10 & 1.47 $ \pm $ 0.19 \\ |
| 247 |
> |
20\% & 0.87 $ \pm $ 0.09 & 1.26 $ \pm $ 0.10 & 1.44 $ \pm $ 0.19 \\ |
| 248 |
> |
30\% & 1.03 $ \pm $ 0.17 & 1.33 $ \pm $ 0.10 & 1.29 $ \pm $ 0.23 \\ |
| 249 |
> |
40\% & 0.88 $ \pm $ 0.09 & 1.36 $ \pm $ 0.10 & 1.55 $ \pm $ 0.20 \\ |
| 250 |
> |
50\% & 0.80 $ \pm $ 0.07 & 1.39 $ \pm $ 0.10 & 1.73 $ \pm $ 0.19 \\ |
| 251 |
> |
\hline |
| 252 |
> |
non-$t\bar{t} \to$~dilepton bkg & Predicted & Observed & Obs/pred \\ |
| 253 |
> |
\hline |
| 254 |
> |
ttdil only & 0.79 $ \pm $ 0.07 & 1.07 $ \pm $ 0.06 & 1.36 $ \pm $ 0.14 \\ |
| 255 |
> |
nominal & 0.92 $ \pm $ 0.09 & 1.27 $ \pm $ 0.10 & 1.39 $ \pm $ 0.18 \\ |
| 256 |
> |
double non-ttdil yield & 1.04 $ \pm $ 0.15 & 1.47 $ \pm $ 0.16 & 1.40 $ \pm $ 0.25 \\ |
| 257 |
|
\hline |
| 258 |
|
\end{tabular} |
| 259 |
|
\end{center} |
| 260 |
|
\end{table} |
| 261 |
|
|
| 258 |
– |
|
| 259 |
– |
|
| 262 |
|
The largest discrepancy between prediction and observation occurs on the first |
| 263 |
|
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no |
| 264 |
|
cuts. We have verified that this effect is due to the polarization of |
| 281 |
|
We have studied this effect at the generator level using Alpgen. We find |
| 282 |
|
that the bias is at the few percent level. |
| 283 |
|
|
| 284 |
< |
Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 284 |
> |
Based on the results of Table~\ref{tab:victorysyst}, we conclude that the |
| 285 |
|
naive data-driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 286 |
< |
be corrected by a factor of $ K_C = 1.4 \pm 0.2(stat)$. |
| 286 |
> |
be corrected by a factor of $ K_C = 1.4 \pm 0.2({\rm stat})$. |
| 287 |
|
|
| 288 |
< |
The 2 dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds, |
| 289 |
< |
and the MET scale and resolution uncertainties. The impact of non-$t\bar{t}$-dilepton background is assessed |
| 290 |
< |
by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton, as shown in Table~\ref{table_kc}. |
| 291 |
< |
The systematic is assessed as the larger of the differences between the nominal $K_C$ value and the values |
| 288 |
> |
The dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds, |
| 289 |
> |
and the MET scale and resolution uncertainties, as summarized in Table~\ref{tab:victorysyst}. |
| 290 |
> |
The impact of non-$t\bar{t}$-dilepton background is assessed |
| 291 |
> |
by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton. |
| 292 |
> |
The uncertainty is assessed as the larger of the differences between the nominal $K_C$ value and the values |
| 293 |
|
obtained using only $t\bar{t} \to$~dilepton MC and obtained by doubling the non $t\bar{t} \to$~dilepton component, |
| 294 |
< |
giving an uncertainty of $0.04$. |
| 294 |
> |
giving an uncertainty of $0.03$. |
| 295 |
|
|
| 296 |
|
The uncertainty in $K_C$ due to the MET scale uncertainty is assessed by varying the hadronic energy scale using |
| 297 |
< |
the same method as in~\ref{} and checking how much $K_C$ changes, as summarized in Table~\ref{tab:victorysyst}. |
| 298 |
< |
This gives an uncertainty of 0.3. We also assess the impact of the MET resolution uncertainty on $K_C$ by applying |
| 299 |
< |
a random smearing to the MET. For each event, we determine the expected MET resolution based on the sumJetPt, and |
| 300 |
< |
smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%. The results show that |
| 301 |
< |
$K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty. |
| 297 |
> |
the same method as in~\cite{ref:top}, giving an uncertainty of 0.36. |
| 298 |
> |
We also assess the impact of the MET resolution |
| 299 |
> |
uncertainty on $K_C$ by applying a random smearing to the MET. For each event, we determine the expected MET resolution |
| 300 |
> |
based on the sumJetPt, and smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%. |
| 301 |
> |
The results show that $K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty. |
| 302 |
|
|
| 303 |
|
Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$. |
| 304 |
|
|
| 334 |
|
\caption{\label{tab:sigcont} Effects of signal contamination |
| 335 |
|
for the two data-driven background estimates. The three columns give |
| 336 |
|
the expected yield in the signal region and the background estimates |
| 337 |
< |
using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 35~pb$^{-1}$.} |
| 337 |
> |
using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 34.0~pb$^{-1}$.} |
| 338 |
|
\begin{tabular}{lccc} |
| 339 |
|
\hline |
| 340 |
|
& Yield & ABCD & $P_T(\ell \ell)$ \\ |
| 341 |
|
\hline |
| 342 |
< |
SM only & 1.29 & 1.25 & 0.92 \\ |
| 343 |
< |
SM + LM0 & 7.57 & 4.44 & 1.96 \\ |
| 344 |
< |
SM + LM1 & 3.85 & 1.60 & 1.43 \\ |
| 342 |
> |
SM only & 1.3 & 1.3 & 0.9 \\ |
| 343 |
> |
SM + LM0 & 7.4 & 4.4 & 1.9 \\ |
| 344 |
> |
SM + LM1 & 3.8 & 1.6 & 1.4 \\ |
| 345 |
> |
%SM only & 1.27 & 1.27 & 0.92 \\ |
| 346 |
> |
%SM + LM0 & 7.39 & 4.38 & 1.93 \\ |
| 347 |
> |
%SM + LM1 & 3.77 & 1.62 & 1.41 \\ |
| 348 |
|
\hline |
| 349 |
|
\end{tabular} |
| 350 |
|
\end{center} |
