Annotation of ttbar/p20_taujets_note/TriggParam.tex, revision 1.2
1.2 ! uid12904 1: \section{Trigger modeling\label{sec:trig_param}}
1.1 uid12904 2:
3: As aforementioned the trigger used in this analysis is JT2$\_$3JT15L$\_$IP$\_$VX.
1.2 ! uid12904 4: For both the v15 and v16 trigger versions, this trigger has four terms at level 2. Three
! 5: of these, the L2 $H_{T}$, missing $E_{T}$ ($\not\!\! E_{T}$) and
! 6: sphericity based branches have been modelled for the $h \rightarrow b\bar{b}$ analysis \cite{bIDH_note}. We
! 7: use those in this analysis. The missing term is the acoplanarity term, namely,
1.1 uid12904 8: L2JET(1,20,2.4) L2HT(35,6) MJT(20,10) L2ACOP(168.75), which is the same in both
1.2 ! uid12904 9: v15 and v16 trigger lists.
1.1 uid12904 10:
11:
12: Table \ref{tabtrigcond} shows the L1, L2 and L3 requirements of the trigger.
13:
14:
1.2 ! uid12904 15: In its work, the $h \rightarrow b\bar{b}$ group has parametrized the trigger in three instantaneous luminosity
! 16: ($10^{32}$) bins: low ($L_{int} <$ 77 ), medium ( 77 $\leq L_{int} <$ 124 ) and
! 17: high ( $L_{int} \geq 124$ ). To model the trigger efficiency
! 18: we take into account both the trigger probabilities and the b-tag probabilities. Thus, the trigger
! 19: probabilities for 0, 1, 2 and 3 or more b-tagged jets are multiplied by the probabilities
! 20: of 0, 1, 2 and 3 or more jets being tagged, respectively, which are themselves derived from the TRF's,
! 21: as described in section \ref{sec:nntag}.
1.1 uid12904 22:
23: The trigger efficiency is computed as a probability ({\it TrigWeight}) which we associate to each
1.2 ! uid12904 24: MC event as follows:
1.1 uid12904 25:
26: \begin{center}
27: \begin{equation}
1.2 ! uid12904 28: P \displaystyle = P_{t0}\cdot P_{0b} + P_{t1}\cdot P_{1b} + P_{t2}\cdot P_{2b} + P_{t\geq 3}\cdot P_{b\geq 3}
1.1 uid12904 29: \end{equation}
30: \end{center}
31:
32: \noindent where $P_{ti}$ is the trigger probability for the event if it has $i$ b-tags and $P_{bi}$ is in turn
1.2 ! uid12904 33: the probability of having $i$ b-tags in the offline event reconstruction.\\
1.1 uid12904 34:
1.2 ! uid12904 35: We now give a brief description of how the trigger probabilities at each level were calculated. Single-object
! 36: turn-on curves were determined using muon-triggered events from the TOPJETTRIG skim.
1.1 uid12904 37: Some turn-on curves are found in Appendix \ref{app:turnon}. A more complete description can be found in \cite{bIDH_note}.
38:
39: \clearpage
40:
41:
42: \begin{table}[h]
43: \begin{small}
44: \begin{center}
45: %\subtable[v15]{
46: \begin{tabular}{l c}
47: \hline\hline
48: Level & v15 \\
49: \hline
50: L1 & CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4) \\
51: L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) OR\\
52: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(10,10) OR \\
53: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(100,6) \\
1.2 ! uid12904 54: L3 & L3JET(3,15,3.6) L3JET(2,25,3.6) ${|z_{\mbox{PV}}|< 35\;cm}$ BTAG(0.4) \\
1.1 uid12904 55: \hline
56: Name & JT2$\_$3JT15L$\_$IP$\_$VX \\
57: \hline\hline
58: \end{tabular}
59:
60: \begin{tabular}{l c}
61: \hline\hline
62: Level & v16 \\
63: \hline
64: L1 & CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4) \\
65: L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) STTIP(1,5.5,3) OR\\
66: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(20,10) OR \\
67: & L2JET(1,30,2.4) L2JET(2,15,2.4) L2JET(3,8,2.4) L2HT(75,6) STTIP(1,5.5,3)\\
1.2 ! uid12904 68: L3 & L3JET(3,15,3.6) JT(2,25,3.6) ${|z_{\mbox{PV}}|< 35\;cm}$ BTAG(0.4) \\
1.1 uid12904 69: \hline
70: Name & JT2$\_$3JT15L$\_$IP$\_$VX \\
71: \hline\hline
72: \end{tabular}
73: %}
74: \end{center}
75: \caption{\small Level-by-level description of trigger JT2$\_$3JT15L$\_$IP$\_$VX. The
76: CSWJT(x,y,z) term corresponds to x L1 jets above y~GeV and within
77: $\mathrm{|\eta| < z}$. The JT(x,y,z) term corresponds to x jets
78: reconstructed at L2 or L3 with $p_T > y$ GeV and $\mathrm{|\eta|<z}$. The HT(x,y) term is used only at
79: L2 and requires that the sum of the transverse momenta of L2 jets with $p_T > y$ GeV is above x~GeV.
80: The SPHER(0.1) term requires the event sphericity calculated from L2 jets to be greater than 0.1.
81: The MJT(x,y) term corresponds to a missing transverse energy $>$ x~GeV calculated from jets
82: with $E_{T} >$ y~GeV. The STTIP(1,5.5,3) term requires one L2STT track with an impact parameter
83: significance greater than or equal to three and a $\chi^{2} < 5.5$.
84: The $\mathrm{|z_{PV}|< 35\;cm}$ term requires the primary vertex reconstructed
85: at L3 to be within 35 cm of the center of the detector and the BTAG(0.4) term is used
86: only at L3 and corresponds to a cut of 0.4 on the probability for the event to not contain a $b$-quark.}
87: \label{tabtrigcond}
88: \end{small}
89: \end{table}
90:
91:
92: \subsection{\label{sub:trig_paramL1}\boldmath Level 1}
93:
1.2 ! uid12904 94: \noindent Level 1 consists of jet terms only: One jet with $E_{T} >$ 30 GeV and $|\eta| < 2.4$, a second jet
1.1 uid12904 95: with $E_{T} >$ 15 GeV and $|\eta| < 2.4$
96: and a third jet with $E_{T} >$ 8 GeV and $|\eta| < 3.2$. The total L1 probability is given by
97:
98: \begin{equation}
99: \begin{split}
1.2 ! uid12904 100: P(L1) &= [P(\geq 3 \hspace{0.2cm} \mbox{jets}) + P(= 2 \hspace{0.2cm} \mbox{jets})*P(\geq 1 \hspace{0.2cm} \mbox{noise jet}) + P(= 1 \hspace{0.2cm} \mbox{jet})*P(\geq 2 \hspace{0.2cm} \mbox{noise jets}) + P(= 0 \hspace{0.2cm} \mbox{jets})*P(\geq 3 \hspace{0.2cm} \mbox{noise jets})]\\
! 101: &* [P(\geq 2 \hspace{0.2cm} \mbox{jets}) + P(= 1 \hspace{0.2cm} \mbox{jet})*P(\geq 1 \hspace{0.2cm} \mbox{noise jet}) + P(= 0 \hspace{0.2cm} \mbox{jets})*P(\geq 2 \hspace{0.2cm} \mbox{noise jets})] \\
! 102: &* [P(\geq 1 \hspace{0.2cm} \mbox{jet}) + P(= 0 \hspace{0.2cm} \mbox{jets})*P(\geq 1 \hspace{0.2cm} \mbox{noise jet})]
1.1 uid12904 103: \end{split}
104: \end{equation}
105:
106: \noindent where $P(\geq x jets)$ is the probability of having $x$ or more jets present in the event and $P(= x jets)$ is
107: the probability of having exactly $x$ jets in the event. The term {\it noise jets} refers to all
108: those L1 jets that didn't match to an offline jet within $\Delta R < 0.5$. In the equation above the first line
109: corresponds to the term CSWJT(3,8,$\mathrm{|\eta|<3.2}$), the second to the term
110: CSWJT(2,15,$\mathrm{|\eta|<2.4}$) and the third to the term CSWJT(1,30,$\mathrm{|\eta|<2.4}$).
111: L1 jets that matched offline ones had their turn-on curves parametrized as functions of
112: offline jet $p{T}$'s. The number of noise jets per event was parametrized as a function
113: of offline $H_{T}$. All L1 turn-on curves are found in Appendix \ref{app:jetturnon_L1}.
114:
115: \subsection{\label{sub:trig_paramL2}\boldmath Level 2}
116:
1.2 ! uid12904 117: \noindent The Level 2 part of this trigger consists of an OR of three terms (here classified as
1.1 uid12904 118: {\it top}, {\it hbb} and {\it mjt}), each with a variation for v15 and v16:
119:
120: \begin{description}
121: \item[v15 top:] 3 jets with $p_{T} >$8 GeV, 2 with $p_{T} >$15~GeV, 1 with $p_{T} >$30~GeV and $H_{T} >$100~GeV
122: \item[v16 top:] 3 jets with $p_{T} >$8 GeV, 2 with $p_{T} >$15~GeV, 1 with $p_{T} >$30~GeV, $H_{T} >$75~GeV and STT IP with IPSIG $\geq$ 3 and $\chi^{2} < 5.5$.
123: \item[v15 hbb:] 3 jets with $p_{T} >$6 GeV, $H_{T} >$75~GeV and sphericity $>$ 0.1
124: \item[v16 hbb:] 3 jets with $p_{T} >$6 GeV, $H_{T} >$75~GeV, sphericity $>$ 0.1 and STT IP with IPSIG $\geq$ 3 and $\chi^{2} < 5.5$.
1.2 ! uid12904 125: \item[v15 mjt:] 3 jets with $p_{T} >$8 GeV, 2 jets $p_{T} >$15~GeV, 1 jet with $p_{T} >$30~GeV, $H_{T} >$75~GeV and $\not\!\!E_{T}$ $>$ 10~GeV.
! 126: \item[v16 mjt:] 3 jets with $p_{T} >$8 GeV, 2 jets $p_{T} >$15~GeV, 1 jet with $p_{T} >$30~GeV, $H_{T} >$75~GeV and $\not\!\!E_{T}$ $>$ 20~GeV.
1.1 uid12904 127: \end{description}
128:
129: For this level the net trigger probability is
130:
131: \begin{center}
132: \begin{equation}
133: \begin{split}
134: P(L2) &= P(hbb \cup mht \cup top)\\
135: &= P(top) + P(hbb) + P(mht) - P(top \cap hbb) - P(top \cap mht) - P(hbb \cap mht) + P(hbb \cap mht \cap top)
136: \end{split}
137: \end{equation}
138: \end{center}
139:
140: \noindent where P(x) corresponds to the probability of either L2, the mht, hbb or the top term firing.
141:
142:
143: \noindent {\bf Level 2 jet terms}: from Table \ref{tabtrigcond} we see that for v15 trigger
144: version, L2 jets terms are actually
145: subsets of L1. As here conditional probability is used, it means that the probability of L2 jet terms
1.2 ! uid12904 146: firing if L1 terms fired is unity. However in v16 the $p_{T}$ requirement of jets in the first trigger term
1.1 uid12904 147: was loosened from 8 to 6 GeV and $\eta$ requirement on 8 GeV jets in the third trigger term
148: was tightened from $|\eta| < 3.2$ to $|\eta| < 2.4$. As in the L1 case, all L2 jets matching offline
149: ones had their turn-on curves parametrized as functions of offline jet $p_{T}$'s, except
1.2 ! uid12904 150: for noise jets, whose number in each event which parametrized as funcions of offline $H_{t}$.
1.1 uid12904 151: Turn-on curves for these cases are found in Appendix \ref{app:jetturnon_L2}.
152:
153: \noindent {\bf Level 2 $H_{T}$ term}: this term consists of a cut of $H_{T}$ $> 75$~GeV for v15
1.2 ! uid12904 154: and $H_{T}$ $>~100$~GeV for v16. Corresponding turn-on curves are shown in Appendix \ref{app:htturnon_L2}.
1.1 uid12904 155:
156: \noindent {\bf Level 2 $\not\!\!E_{T}$ term}: the correspondent $\not\!\!E_{T}$ cuts are $> 10~$GeV and $>~20$~GeV
157: for v15 and v16 respectively. Their turn-on are shown in Appendix \ref{app:mhtturnon_L2}.
158:
159: \noindent {\bf L2 Sphericity Term}: this term requires a sphericity cut of $>$ 0.1.
160: Corresponding turn-on curves are shown in Appendix \ref{app:spherturnon_L2}.
161:
162:
163: \noindent {\bf L2 STT}: the L2STTIP efficiency was measured for events in v16 which have passed the rest of the
164: L1, L2 (L2top OR L2hbb) and L3 (except L3 b-tag)
165: trigger requirements and the offline three to five jet selection. The efficiency was measured versus
166: the invariant mass of the two
1.2 ! uid12904 167: leading jets, separately for 0, 1, 2 and 3 offline tight NN b-tagged events, in the three different luminosity bins.
1.1 uid12904 168: Appendix \ref{app:sttip_L2} shows the STTIP(1,5.5,3) efficiency versus the
1.2 ! uid12904 169: leading invariant di-jet mass in the low, medium and high luminosity range for different numbers of offline b-tags.
1.1 uid12904 170:
171: \subsection{\label{sub:trig_paramL3}\boldmath Level 3}
172:
173: \noindent L3 consists of a jet part and a b-tag one. For the jet part of L3, turn-on curves were
174: determined for events passing both L1 and L2 requirements. Corresponding probability is given the equation below
175:
176: \begin{equation}
177: \begin{split}
1.2 ! uid12904 178: P(L3) &= [P(\geq 3 \hspace{0.2cm} \mbox{jets}) + P(= 2 \hspace{0.2cm} \mbox{jets})*P(\geq 1 \hspace{0.2cm} \mbox{noise jet}) + P(= 1 \hspace{0.2cm} \mbox{jet})*P(\geq 2 \hspace{0.2cm} \mbox{noise jets}) + P(= 0 \hspace{0.2cm} \mbox{jets})*P(\geq 3 \hspace{0.2cm} \mbox{noise jets})]\\
! 179: &* [P(\geq 2 \hspace{0.2cm} \mbox{jets}) + P(= 1 \hspace{0.2cm} \mbox{jet})*P(\geq 1 \hspace{0.2cm} \mbox{noise jet}) + P(= 0 \hspace{0.2cm} \mbox{jets})*P(\geq 2 \hspace{0.2cm} \mbox{noise jets})]
1.1 uid12904 180: \end{split}
181: \end{equation}
182:
183: \noindent In the equation above the first line
184: corresponds to the term JT(3,15,$\mathrm{|\eta|<3.6}$), the second to the term
185: JT(2,25,$\mathrm{|\eta|<3.6}$). Here was applied the same treatment to L3 jets matching offline ones and to noise
186: jets as in L1 and L2 jet terms. Corresponding turn-on curves are shown in Appendix \ref{app:jetturnon_L1}.
187:
188:
1.2 ! uid12904 189: Efficiencies for the b-tag part of L3 were measured in two different ways depending on whether the trigger list was v15
! 190: or v16. In v15 case events were recorded with the JT2$\_$4JT20 and JT2$\_$3JT12L$\_$MM3$\_$V triggers,
1.1 uid12904 191: since their L1 and L2 conditions were exactly the same. Events were further required to pass the
1.2 ! uid12904 192: rest of L3 conditions of JT2$\_$3JT15L$\_$IP$\_$VX and the offline event selection. In v16 case
1.1 uid12904 193: efficiencies were measured in a similar fashion, but using
194: trigger JT4$\_$3JT15L$\_$VX (which has no L2STT or L3BTAG requirements). Events were then required
195: to have fired one of the three L2 branches of JT2$\_$3JT15L$\_$IP$\_$VX and to pass the offline
196: three to five jet selection. All turn-on curves for both trigger lists are found in Appendix \ref{app:btagturnon_L3}.
197:
198: \clearpage
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