Annotation of ttbar/p20_taujets_note/Systematics.tex, revision 1.1
1.1 ! uid12904 1: \newpage
! 2: \section{Systematic uncertainties}
! 3:
! 4: Several factors contribute to systematic uncertainties in the measurement. Here we describe such uncertainties.
! 5:
! 6: \subsection{JES}
! 7:
! 8: \noindent The jet energy scale (JES) systematic is determined by shifiting the jet energy scale
! 9: by $\pm 1 \sigma$ in all MC samples.
! 10:
! 11:
! 12: \subsection{TES}
! 13:
! 14: \noindent The tau energy scale (TES) systematic is determined by shifiting the tau energy scale
! 15: by its uncertainty as given in \cite{tes_sys}.
! 16:
! 17:
! 18: \subsection{Jet Energy Resolution and Jet ID}
! 19:
! 20: \noindent The jet energy resolution (JER) systematic is determined by shifiting the jet energy
! 21: resolution by $\pm 1 \sigma$ in all MC samples.
! 22:
! 23: \subsection{Trigger}
! 24: \noindent Each event was corrected by the ratio of the actual and predicted trigger result as a function of $H_{T}$, which was
! 25: used based on the fact that the agreement varies as function of it.
! 26:
! 27:
! 28: \subsection{b-quark fragmentation}
! 29: \noindent This uncertainty is estimated using the standard procedure described in \cite{bfrag} by reweighting $t\bar{t}$ events
! 30: using different fragmentation functions.
! 31:
! 32: \subsection{\boldmath $b$-tagging}
! 33:
! 34: \noindent b-tagging uncertainty effects are taken into account by varying the
! 35: systematic and statistical errors on the MC tagging weights.
! 36:
! 37: These errors (which are computed using standard D\O\ b ID group tools) arise form several independent sources \cite{bID-p20}:
! 38:
! 39: \begin{itemize}
! 40: \item B-jet tagging parameterization.
! 41: \item C-jet tagging parameterization.
! 42: \item Light jet tagging parameterization (negative tag rate).
! 43: %\item Systematic uncertainties on the scale factors $SF_{hf}$ and $SF_{ll}$
! 44: %are derived from the statistical error due to finite MC statistics.
! 45: \item Semi-leptonic b-tagging efficiency parameterization in MC and in data
! 46: (System 8).
! 47: \item Taggability. This includes the statistical error due to finite statistic
! 48: in the samples from which it had been derived and systematic, reflecting
! 49: the (neglected) taggability dependence on the jet multiplicity.
! 50: \end{itemize}
! 51:
! 52:
! 53: \subsection{\boldmath $\tau$ ID systematics}
! 54:
! 55: \noindent Here we include systematics associated to the NN cut (NN $>$ 0.90 for taus types 1 and 2 and NN $>$ 0.95 for taus type 3)
! 56: applied to select hadronic taus. As recommended by the $\tau $-ID group
! 57: these systematics are 9.5\%, 3.5\% and 5.0\% for taus type 1, 2 and 3 respectively. However in this analysis we chose
! 58: treat taus types 1 and 2 together. This led us to combine their uncertainties in the following way
! 59:
! 60: \begin{center}
! 61: \begin{equation}
! 62: sys_{12} = \displaystyle \sqrt{\epsilon_{1}^{2}*f_{1}^{2} + \epsilon_{2}^{2}*f_{2}^{2}}
! 63: \end{equation}
! 64: \end{center}
! 65:
! 66: \noindent where $\epsilon_{1}$ and $\epsilon_{2}$ are the $\tau$ ID efficiencies for taus types 1 and 2 respectively and
! 67: $f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively.
! 68:
! 69:
! 70: \subsection{\label{sub:qcd_syst}QCD systematics}
! 71: As explained in the section \ref{sub:Variables} we use the control (b-veto) data set to
! 72: validate our method of modeling the multijet background. Therefore we have to
! 73: use the same sample to evaluate the associated uncertainties. The way it was
! 74: done is by reweighting topological event NN for QCD template
! 75: (``loose-tight'' $\tau$), so that it matches the one for ``tight'' $\tau$ data exactly
! 76: (electroweak beckgrounds were subtracted).
! 77: %Figure \ref{fig:qcd_reweight} shows that this scaling is close to 1, as it should be, since QCD template
! 78: %models the QCD-dominated data very well.
! 79:
! 80: \subsection{W and Z scale factors}
! 81: We apply a ascale factor of 1.47 to both W + bb and W + cc events with an uncertainty of 15\%. At the same time a scales factors
! 82: of 1.52 and 1.67 are applied to Z + bb and Z + cc events, both with an uncertainty of 20\%.
! 83:
! 84:
! 85: \subsection{Template statistics}
! 86: When we performed the template fit to data (Section \ref{sub:NN}) the QCD template had limited statistics
! 87: (1132 events for taus types 1 and 2 and 4487 events for taus type 3). We have to take the
! 88: statistical uncertainty in this histogram as one of the cross section systematics. It was calculated by
! 89: varying the content of each bin of the QCD template NN distribution within its uncertainty and observing
! 90: how the cross section result changed.
! 91:
! 92: \subsection{$t\bar{t}$ contamination in the loose-tight sample}
! 93: When measuring the cross-section we had to take into account the signal contamination in the loose-tight
! 94: sample we use to model QCD in the high NN region. The systematic uncertainty in this case
! 95: is calculated by varying the final assumed cross section by $\pm 1 \sigma$, re-estimating the signal contamination
! 96: and finally measuring the up and down values of the cross section.
! 97:
! 98: \subsection{PDF}
! 99: Systematics on Parton Distribution Functions (PDF) are estimated by reweighting signal $t\bar{t}$ MC from
! 100: CTEQ6L1 to CTEQ6.1m and its twenty error PDF's. The reweighting of the PDF's is done by using {\tt caf\_pdfreweight}
! 101: package tool on Pythia $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with Pythia on the Alpgen
! 102: $t\bar{t}$ MC.
! 103:
! 104: \subsection{Luminosity}
! 105: Here we take the D\O\ standard measured uncertainty on luminosity of 6.1$\%$ .
! 106:
! 107:
! 108: Tables \ref{cap:Syst1} and \ref{cap:Syst2} summarize all of these uncertainty sources and shows how the resulting cross section shifts.
! 109:
! 110: %\clearpage
! 111: %
! 112:
! 113: %\section{Summary \label{sec:summary}}
! 114:
! 115:
! 116: %
! 117:
! 118: %\section{Summary \label{sec:summary}}
! 119:
! 120: \begin{table}[h]
! 121: \caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) for NNelec $>$ 0.9.}
! 122: %\begin{ruledtabular}
! 123: {\footnotesize }\begin{tabular}{cccc}
! 124: \hline
! 125: Channel&
! 126: {\footnotesize $\tau$+jets types 1 and 2 }&
! 127: {\footnotesize $\tau$+jets type 3 }&
! 128: {\footnotesize Combined }\\
! 129: {\footnotesize Tau Energy Scale }&
! 130: {\footnotesize $_{+0.068, -0.102}$ }&
! 131: {\footnotesize $_{+0.340, -0.306}$ }&
! 132: {\footnotesize $_{+0.136, -0.136}$ }\\
! 133: {\footnotesize Jet Energy Scale }&
! 134: {\footnotesize $_{+0.051, -0.034}$ }&
! 135: {\footnotesize $_{+0.051, -0.085}$ }&
! 136: {\footnotesize $_{+0.051, -0.000}$ }\\
! 137: {\footnotesize Jet Energy Resolution }&
! 138: {\footnotesize $_{+0.102, -0.051}$ }&
! 139: {\footnotesize $_{+0.204, -0.034}$ }&
! 140: {\footnotesize $_{+0.119, -0.052}$ }\\
! 141: {\footnotesize Jet ID }&
! 142: {\footnotesize $_{+0.204, -0.204}$ }&
! 143: {\footnotesize $_{+0.153, -0.153}$ }&
! 144: {\footnotesize $_{+0.204, -0.204}$ }\\
! 145: {\footnotesize b-tag }&
! 146: {\footnotesize $_{+0.562, -0.493}$ }&
! 147: {\footnotesize $_{+0.493, -0.426}$ }&
! 148: {\footnotesize $_{+0.544, -0.477}$ }\\
! 149: {\footnotesize b-fragmentation }&
! 150: {\footnotesize $_{+0.102, -0.102}$ }&
! 151: {\footnotesize $_{+0.068, -0.068}$ }&
! 152: {\footnotesize $_{+0.085, -0.085}$ }\\
! 153: {\footnotesize QCD Modeling }&
! 154: {\footnotesize $_{+0.340, -0.340}$ }&
! 155: {\footnotesize $_{+0.221, -0.221}$ }&
! 156: {\footnotesize $_{+0.324, -0.305}$ }\\
! 157: {\footnotesize $\tau$ ID }&
! 158: {\footnotesize $_{+0.272, -0.272}$ }&
! 159: {\footnotesize $_{+0.306, -0.306}$ }&
! 160: {\footnotesize $_{+0.290, -0.290}$ }\\
! 161: {\footnotesize Trigger }&
! 162: {\footnotesize $_{+0.256, -0.256}$ }&
! 163: {\footnotesize $_{+0.238, -0.238}$ }&
! 164: {\footnotesize $_{+0.256, -0.256}$ }\\
! 165: %{\footnotesize $\tau$ triggering }&
! 166: %{\footnotesize $_{+xxxx, -xxxx}$ }&
! 167: %{\footnotesize $_{+xxxx, -xxxx}$ }&
! 168: %{\footnotesize $_{+xxxx, -xxxx}$ }\\
! 169: {\footnotesize W Scale Factor }&
! 170: {\footnotesize $_{+0.034, -0.034}$ }&
! 171: {\footnotesize $_{+0.034, -0.034}$ }&
! 172: {\footnotesize $_{+0.034, -0.034}$ }\\
! 173: {\footnotesize Z Scale Factor }&
! 174: {\footnotesize $_{+0.072, -0.072}$ }&
! 175: {\footnotesize $_{+0.072, -0.072}$ }&
! 176: {\footnotesize $_{+0.048, -0.048}$ }\\
! 177: {\footnotesize Template statistics }&
! 178: {\footnotesize $_{+0.156, -0.156}$ }&
! 179: {\footnotesize $_{+0.204, -0.204}$ }&
! 180: {\footnotesize $_{+0.168, -0.168}$ }\\
! 181: {\footnotesize Signal contamination}&
! 182: {\footnotesize $_{+0.153, -0.153}$ }&
! 183: {\footnotesize $_{+0.255, -0.272}$ }&
! 184: {\footnotesize $_{+0.188, -0.170}$ }\\
! 185: {\footnotesize PDF }&
! 186: {\footnotesize $_{+0.097, -0.084}$ }&
! 187: {\footnotesize $_{+0.188, -0.198}$ }&
! 188: {\footnotesize $_{+0.092, -0.081}$ }\\
! 189:
! 190: \end{tabular}{\footnotesize \par}
! 191: %\end{ruledtabular}
! 192: \label{cap:Syst1}
! 193: \end{table}
! 194:
! 195:
! 196: \begin{table}[h]
! 197: \caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) when no NNelec cut is applied.}
! 198: %\begin{ruledtabular}
! 199: {\footnotesize }\begin{tabular}{cccc}
! 200: \hline
! 201: Channel&
! 202: {\footnotesize $\tau$+jets types 1 and 2 }&
! 203: {\footnotesize $\tau$+jets type 3 }&
! 204: {\footnotesize Combined }\\
! 205: {\footnotesize Tau Energy Scale }&
! 206: {\footnotesize $_{+0.101, -0.002}$ }&
! 207: {\footnotesize $_{+0.238, -0.255}$ }&
! 208: {\footnotesize $_{+0.102, -0.017}$ }\\
! 209: {\footnotesize Jet Energy Scale }&
! 210: {\footnotesize $_{+0.016, -0.001}$ }&
! 211: {\footnotesize $_{+0.017, -0.000}$ }&
! 212: {\footnotesize $_{+0.016, -0.000}$ }\\
! 213: {\footnotesize Jet Energy Resolution }&
! 214: {\footnotesize $_{+0.084, -0.086}$ }&
! 215: {\footnotesize $_{+0.017, -0.034}$ }&
! 216: {\footnotesize $_{+0.068, -0.085}$ }\\
! 217: {\footnotesize Jet ID }&
! 218: {\footnotesize $_{+0.169, -0.169}$ }&
! 219: {\footnotesize $_{+0.017, -0.017}$ }&
! 220: {\footnotesize $_{+0.153, -0.153}$ }\\
! 221: {\footnotesize b-tag }&
! 222: {\footnotesize $_{+0.424, -0.375}$ }&
! 223: {\footnotesize $_{+0.358, -0.306}$ }&
! 224: {\footnotesize $_{+0.425, -0.375}$ }\\
! 225: {\footnotesize b-fragmentation }&
! 226: {\footnotesize $_{+0.069, -0.069}$ }&
! 227: {\footnotesize $_{+0.102, -0.102}$ }&
! 228: {\footnotesize $_{+0.068, -0.068}$ }\\
! 229: {\footnotesize QCD Modeling }&
! 230: {\footnotesize $_{+0.271, -0.273}$ }&
! 231: {\footnotesize $_{+0.153, -0.136}$ }&
! 232: {\footnotesize $_{+0.225, -0.256}$ }\\
! 233: {\footnotesize $\tau$ ID }&
! 234: {\footnotesize $_{+0.220, -0.220}$ }&
! 235: {\footnotesize $_{+0.204, -0.204}$ }&
! 236: {\footnotesize $_{+0.221, -0.221}$ }\\
! 237: {\footnotesize Trigger }&
! 238: {\footnotesize $_{+0.204, -0.204}$ }&
! 239: {\footnotesize $_{+0.170, -0.170}$ }&
! 240: {\footnotesize $_{+0.204, -0.204}$ }\\
! 241: %{\footnotesize $\tau$ triggering }&
! 242: %{\footnotesize $_{+xxxx, -xxxx}$ }&
! 243: %{\footnotesize $_{+xxxx, -xxxx}$ }&
! 244: %{\footnotesize $_{+xxxx, -xxxx}$ }\\
! 245: {\footnotesize W Scale Factor }&
! 246: {\footnotesize $_{+0.034, -0.034}$ }&
! 247: {\footnotesize $_{+0.034, -0.034}$ }&
! 248: {\footnotesize $_{+0.034, -0.034}$ }\\
! 249: {\footnotesize Z Scale Factor }&
! 250: {\footnotesize $_{+0.072, -0.072}$ }&
! 251: {\footnotesize $_{+0.072, -0.072}$ }&
! 252: {\footnotesize $_{+0.048, -0.048}$ }\\
! 253: {\footnotesize Template statistics }&
! 254: {\footnotesize $_{+0.118, -0.118}$ }&
! 255: {\footnotesize $_{+0.170, -0.170}$ }&
! 256: {\footnotesize $_{+0.102, -0.102}$ }\\
! 257: {\footnotesize Signal contamination}&
! 258: {\footnotesize $_{+0.050, -0.052}$ }&
! 259: {\footnotesize $_{+0.136, -0.187}$ }&
! 260: {\footnotesize $_{+0.051, -0.051}$ }\\
! 261: {\footnotesize PDF }&
! 262: {\footnotesize $_{+0.097, -0.084}$ }&
! 263: {\footnotesize $_{+0.188, -0.198}$ }&
! 264: {\footnotesize $_{+0.092, -0.081}$ }\\
! 265:
! 266: \end{tabular}{\footnotesize \par}
! 267: %\end{ruledtabular}
! 268: \label{cap:Syst2}
! 269: \end{table}
! 270:
! 271:
! 272:
! 273: \clearpage
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