Annotation of ttbar/p20_taujets_note/Systematics.tex, revision 1.1.1.1
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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