Annotation of ttbar/p20_taujets_note/Systematics.tex, revision 1.2
1.1 uid12904 1: \newpage
2: \section{Systematic uncertainties}
3:
1.2 ! uid12904 4: The following components are added in quadrature to estimate the total systematic uncertainty.
1.1 uid12904 5:
1.2 ! uid12904 6: \subsection{Jet Energy Scale}
1.1 uid12904 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:
1.2 ! uid12904 12: \subsection{Tau Energy Scale}
1.1 uid12904 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}
1.2 ! uid12904 24: \noindent For this systematics, the level of agreement (as a function of $H_T$) when applying the trigger
! 25: turn-on curves to 4-jet data events was measured. We then used the ratio between the predicted and the
! 26: actual trigger decision as a function of $H_T$ to assign a error due to the trigger modeling. All MC events
! 27: were re-weighted by this ratio as a function of $H_T$, which was
1.1 uid12904 28: used based on the fact that the agreement varies as function of it.
29:
30:
31: \subsection{b-quark fragmentation}
32: \noindent This uncertainty is estimated using the standard procedure described in \cite{bfrag} by reweighting $t\bar{t}$ events
33: using different fragmentation functions.
34:
35: \subsection{\boldmath $b$-tagging}
36:
37: \noindent b-tagging uncertainty effects are taken into account by varying the
1.2 ! uid12904 38: systematic and statistical uncertainties on the MC tagging weights.
1.1 uid12904 39:
1.2 ! uid12904 40: These uncertainties (which are computed using standard D0 b ID group tools) arise form several independent sources \cite{bID-p20}:
1.1 uid12904 41:
42: \begin{itemize}
43: \item B-jet tagging parameterization.
44: \item C-jet tagging parameterization.
45: \item Light jet tagging parameterization (negative tag rate).
46: %\item Systematic uncertainties on the scale factors $SF_{hf}$ and $SF_{ll}$
47: %are derived from the statistical error due to finite MC statistics.
48: \item Semi-leptonic b-tagging efficiency parameterization in MC and in data
49: (System 8).
1.2 ! uid12904 50: \item Taggability. This includes the statistical uncertainty due to finite statistic
1.1 uid12904 51: in the samples from which it had been derived and systematic, reflecting
52: the (neglected) taggability dependence on the jet multiplicity.
53: \end{itemize}
54:
55:
1.2 ! uid12904 56: \subsection{\boldmath $\tau$ identification}
1.1 uid12904 57:
58: \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)
59: applied to select hadronic taus. As recommended by the $\tau $-ID group
60: these systematics are 9.5\%, 3.5\% and 5.0\% for taus type 1, 2 and 3 respectively. However in this analysis we chose
1.2 ! uid12904 61: to treat taus types 1 and 2 together. This led us to combine their uncertainties in the following way
1.1 uid12904 62:
63: \begin{center}
64: \begin{equation}
1.2 ! uid12904 65: sys_{12} = \displaystyle \sqrt{\epsilon_{1}^{2} \cdot f_{1}^{2} + \epsilon_{2}^{2} \cdot f_{2}^{2}}
1.1 uid12904 66: \end{equation}
67: \end{center}
68:
69: \noindent where $\epsilon_{1}$ and $\epsilon_{2}$ are the $\tau$ ID efficiencies for taus types 1 and 2 respectively and
70: $f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively.
71:
72:
1.2 ! uid12904 73: \subsection{\label{sub:qcd_syst}QCD modeling}
! 74: As explained in the section \ref{sub:Variables} we use the control (b-veto) sample to
1.1 uid12904 75: validate our method of modeling the multijet background. Therefore we have to
1.2 ! uid12904 76: use the same sample to evaluate the associated uncertainties. We did this
! 77: by reweighting topological event NN for QCD template
1.1 uid12904 78: (``loose-tight'' $\tau$), so that it matches the one for ``tight'' $\tau$ data exactly
1.2 ! uid12904 79: (electroweak backgrounds were subtracted).
1.1 uid12904 80: %Figure \ref{fig:qcd_reweight} shows that this scaling is close to 1, as it should be, since QCD template
81: %models the QCD-dominated data very well.
82:
1.2 ! uid12904 83: \subsection{$W$ and $Z$ scale factors}
! 84: We apply a scale factor of 1.47 to both $Wbb$ and $Wcc$ events with an uncertainty of 15\%. At the same time a scales factors
! 85: of 1.52 and 1.67 are applied to $Zbb$ and $Zcc$ events, both with an uncertainty of 20\%.
1.1 uid12904 86:
87:
88: \subsection{Template statistics}
89: When we performed the template fit to data (Section \ref{sub:NN}) the QCD template had limited statistics
90: (1132 events for taus types 1 and 2 and 4487 events for taus type 3). We have to take the
91: statistical uncertainty in this histogram as one of the cross section systematics. It was calculated by
92: varying the content of each bin of the QCD template NN distribution within its uncertainty and observing
93: how the cross section result changed.
94:
95: \subsection{$t\bar{t}$ contamination in the loose-tight sample}
1.2 ! uid12904 96: When measuring the cross section we had to take into account the signal contamination in the loose-tight
1.1 uid12904 97: sample we use to model QCD in the high NN region. The systematic uncertainty in this case
98: is calculated by varying the final assumed cross section by $\pm 1 \sigma$, re-estimating the signal contamination
99: and finally measuring the up and down values of the cross section.
100:
101: \subsection{PDF}
102: Systematics on Parton Distribution Functions (PDF) are estimated by reweighting signal $t\bar{t}$ MC from
103: CTEQ6L1 to CTEQ6.1m and its twenty error PDF's. The reweighting of the PDF's is done by using {\tt caf\_pdfreweight}
1.2 ! uid12904 104: package tool on {\sc PYTHIA} $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with {\sc PYTHIA}
! 105: on the {\sc ALPGEN} $t\bar{t}$ MC.
1.1 uid12904 106:
107: \subsection{Luminosity}
1.2 ! uid12904 108: Here we take the D0 standard measured uncertainty on luminosity of 6.1$\%$ .
1.1 uid12904 109:
110:
111: Tables \ref{cap:Syst1} and \ref{cap:Syst2} summarize all of these uncertainty sources and shows how the resulting cross section shifts.
112:
113: %\clearpage
114: %
115:
116: %\section{Summary \label{sec:summary}}
117:
118:
119: %
120:
121: %\section{Summary \label{sec:summary}}
122:
123: \begin{table}[h]
124: \caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) for NNelec $>$ 0.9.}
125: %\begin{ruledtabular}
126: {\footnotesize }\begin{tabular}{cccc}
127: \hline
128: Channel&
129: {\footnotesize $\tau$+jets types 1 and 2 }&
130: {\footnotesize $\tau$+jets type 3 }&
131: {\footnotesize Combined }\\
132: {\footnotesize Tau Energy Scale }&
133: {\footnotesize $_{+0.068, -0.102}$ }&
134: {\footnotesize $_{+0.340, -0.306}$ }&
135: {\footnotesize $_{+0.136, -0.136}$ }\\
136: {\footnotesize Jet Energy Scale }&
137: {\footnotesize $_{+0.051, -0.034}$ }&
138: {\footnotesize $_{+0.051, -0.085}$ }&
139: {\footnotesize $_{+0.051, -0.000}$ }\\
140: {\footnotesize Jet Energy Resolution }&
141: {\footnotesize $_{+0.102, -0.051}$ }&
142: {\footnotesize $_{+0.204, -0.034}$ }&
143: {\footnotesize $_{+0.119, -0.052}$ }\\
144: {\footnotesize Jet ID }&
145: {\footnotesize $_{+0.204, -0.204}$ }&
146: {\footnotesize $_{+0.153, -0.153}$ }&
147: {\footnotesize $_{+0.204, -0.204}$ }\\
148: {\footnotesize b-tag }&
149: {\footnotesize $_{+0.562, -0.493}$ }&
150: {\footnotesize $_{+0.493, -0.426}$ }&
151: {\footnotesize $_{+0.544, -0.477}$ }\\
152: {\footnotesize b-fragmentation }&
153: {\footnotesize $_{+0.102, -0.102}$ }&
154: {\footnotesize $_{+0.068, -0.068}$ }&
155: {\footnotesize $_{+0.085, -0.085}$ }\\
156: {\footnotesize QCD Modeling }&
157: {\footnotesize $_{+0.340, -0.340}$ }&
158: {\footnotesize $_{+0.221, -0.221}$ }&
159: {\footnotesize $_{+0.324, -0.305}$ }\\
160: {\footnotesize $\tau$ ID }&
161: {\footnotesize $_{+0.272, -0.272}$ }&
162: {\footnotesize $_{+0.306, -0.306}$ }&
163: {\footnotesize $_{+0.290, -0.290}$ }\\
164: {\footnotesize Trigger }&
165: {\footnotesize $_{+0.256, -0.256}$ }&
166: {\footnotesize $_{+0.238, -0.238}$ }&
167: {\footnotesize $_{+0.256, -0.256}$ }\\
168: %{\footnotesize $\tau$ triggering }&
169: %{\footnotesize $_{+xxxx, -xxxx}$ }&
170: %{\footnotesize $_{+xxxx, -xxxx}$ }&
171: %{\footnotesize $_{+xxxx, -xxxx}$ }\\
172: {\footnotesize W Scale Factor }&
173: {\footnotesize $_{+0.034, -0.034}$ }&
174: {\footnotesize $_{+0.034, -0.034}$ }&
175: {\footnotesize $_{+0.034, -0.034}$ }\\
176: {\footnotesize Z Scale Factor }&
177: {\footnotesize $_{+0.072, -0.072}$ }&
178: {\footnotesize $_{+0.072, -0.072}$ }&
179: {\footnotesize $_{+0.048, -0.048}$ }\\
180: {\footnotesize Template statistics }&
181: {\footnotesize $_{+0.156, -0.156}$ }&
182: {\footnotesize $_{+0.204, -0.204}$ }&
183: {\footnotesize $_{+0.168, -0.168}$ }\\
184: {\footnotesize Signal contamination}&
185: {\footnotesize $_{+0.153, -0.153}$ }&
186: {\footnotesize $_{+0.255, -0.272}$ }&
187: {\footnotesize $_{+0.188, -0.170}$ }\\
188: {\footnotesize PDF }&
189: {\footnotesize $_{+0.097, -0.084}$ }&
190: {\footnotesize $_{+0.188, -0.198}$ }&
191: {\footnotesize $_{+0.092, -0.081}$ }\\
1.2 ! uid12904 192: \hline
! 193: {\footnotesize TOTAL }&
! 194: {\footnotesize $_{+0.839, -0.791}$ }&
! 195: {\footnotesize $_{+0.882, -0.820}$ }&
! 196: {\footnotesize $_{+0.843, -0.779}$ }\\
1.1 uid12904 197:
198: \end{tabular}{\footnotesize \par}
199: %\end{ruledtabular}
200: \label{cap:Syst1}
201: \end{table}
202:
203:
204: \begin{table}[h]
205: \caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) when no NNelec cut is applied.}
206: %\begin{ruledtabular}
207: {\footnotesize }\begin{tabular}{cccc}
208: \hline
209: Channel&
210: {\footnotesize $\tau$+jets types 1 and 2 }&
211: {\footnotesize $\tau$+jets type 3 }&
212: {\footnotesize Combined }\\
213: {\footnotesize Tau Energy Scale }&
214: {\footnotesize $_{+0.101, -0.002}$ }&
215: {\footnotesize $_{+0.238, -0.255}$ }&
216: {\footnotesize $_{+0.102, -0.017}$ }\\
217: {\footnotesize Jet Energy Scale }&
218: {\footnotesize $_{+0.016, -0.001}$ }&
219: {\footnotesize $_{+0.017, -0.000}$ }&
220: {\footnotesize $_{+0.016, -0.000}$ }\\
221: {\footnotesize Jet Energy Resolution }&
222: {\footnotesize $_{+0.084, -0.086}$ }&
223: {\footnotesize $_{+0.017, -0.034}$ }&
224: {\footnotesize $_{+0.068, -0.085}$ }\\
225: {\footnotesize Jet ID }&
226: {\footnotesize $_{+0.169, -0.169}$ }&
227: {\footnotesize $_{+0.017, -0.017}$ }&
228: {\footnotesize $_{+0.153, -0.153}$ }\\
229: {\footnotesize b-tag }&
230: {\footnotesize $_{+0.424, -0.375}$ }&
231: {\footnotesize $_{+0.358, -0.306}$ }&
232: {\footnotesize $_{+0.425, -0.375}$ }\\
233: {\footnotesize b-fragmentation }&
234: {\footnotesize $_{+0.069, -0.069}$ }&
235: {\footnotesize $_{+0.102, -0.102}$ }&
236: {\footnotesize $_{+0.068, -0.068}$ }\\
237: {\footnotesize QCD Modeling }&
238: {\footnotesize $_{+0.271, -0.273}$ }&
239: {\footnotesize $_{+0.153, -0.136}$ }&
240: {\footnotesize $_{+0.225, -0.256}$ }\\
241: {\footnotesize $\tau$ ID }&
242: {\footnotesize $_{+0.220, -0.220}$ }&
243: {\footnotesize $_{+0.204, -0.204}$ }&
244: {\footnotesize $_{+0.221, -0.221}$ }\\
245: {\footnotesize Trigger }&
246: {\footnotesize $_{+0.204, -0.204}$ }&
247: {\footnotesize $_{+0.170, -0.170}$ }&
248: {\footnotesize $_{+0.204, -0.204}$ }\\
249: %{\footnotesize $\tau$ triggering }&
250: %{\footnotesize $_{+xxxx, -xxxx}$ }&
251: %{\footnotesize $_{+xxxx, -xxxx}$ }&
252: %{\footnotesize $_{+xxxx, -xxxx}$ }\\
253: {\footnotesize W Scale Factor }&
254: {\footnotesize $_{+0.034, -0.034}$ }&
255: {\footnotesize $_{+0.034, -0.034}$ }&
256: {\footnotesize $_{+0.034, -0.034}$ }\\
257: {\footnotesize Z Scale Factor }&
258: {\footnotesize $_{+0.072, -0.072}$ }&
259: {\footnotesize $_{+0.072, -0.072}$ }&
260: {\footnotesize $_{+0.048, -0.048}$ }\\
261: {\footnotesize Template statistics }&
262: {\footnotesize $_{+0.118, -0.118}$ }&
263: {\footnotesize $_{+0.170, -0.170}$ }&
264: {\footnotesize $_{+0.102, -0.102}$ }\\
265: {\footnotesize Signal contamination}&
266: {\footnotesize $_{+0.050, -0.052}$ }&
267: {\footnotesize $_{+0.136, -0.187}$ }&
268: {\footnotesize $_{+0.051, -0.051}$ }\\
269: {\footnotesize PDF }&
270: {\footnotesize $_{+0.097, -0.084}$ }&
271: {\footnotesize $_{+0.188, -0.198}$ }&
272: {\footnotesize $_{+0.092, -0.081}$ }\\
1.2 ! uid12904 273: \hline
! 274: {\footnotesize TOTAL }&
! 275: {\footnotesize $_{+0.653, -0.613}$ }&
! 276: {\footnotesize $_{+0.616, -0.607}$ }&
! 277: {\footnotesize $_{+0.624, -0.596}$ }\\
1.1 uid12904 278:
279: \end{tabular}{\footnotesize \par}
280: %\end{ruledtabular}
281: \label{cap:Syst2}
282: \end{table}
283:
284:
285:
286: \clearpage
1.2 ! uid12904 287: \section{Conclusion}
! 288:
! 289: In this analysis we presented of the $\sigma_{t\bar{t}}$ in the tau + jets channel using 4951.86 pb$^{-1}$
! 290: of integrated luminosity. This cross section was $8.46\;\;_{-1.33}^{+1.38}\;\;({\textrm{stat}})$.
! 291:
! 292: \clearpage
! 293:
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