Annotation of ttbar/p20_taujets_note/TriggParam.tex, revision 1.1.1.1
1.1 uid12904 1: \section{Trigger Parametrization \label{sec:trig_param}}
2:
3: As aforementioned the trigger used in this analysis is JT2$\_$3JT15L$\_$IP$\_$VX.
4: In both v15 and v16 trigger versions, this trigger has 4 terms at level 2. Currently, only
5: three of these, the L2 $H_{T}$, missing $E_{T}$ ($\not\!\! E_{T}$) and
6: sphericity based branches have been modelled by the $hbb$ group \cite{bIDH_note}. Therefore
7: these are the ones used in this analysis. The missing term is the acoplanarity term, namely,
8: L2JET(1,20,2.4) L2HT(35,6) MJT(20,10) L2ACOP(168.75), which is the same in both
9: v15 and v15 trigger lists.
10:
11:
12: Table \ref{tabtrigcond} shows the L1, L2 and L3 requirements of the trigger.
13:
14:
15: In its work, the $hbb$ group has parametrized the trigger in three instantaneous luminosity
16: ($10^{32}$)regions: low ($L_{int} <$ 77 ), medium ( 77 $\leq L_{int} <$ 124 ) and
17: high ( $L_{int} \geq 124$ ). The final goal is to measure the total trigger efficiency for our events. In order to
18: do so 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 then multiplied by the probabilities
20: of 0, 1, 2 and 3 or more jets being tagged, which are themselves got from TRF's, as described in section \ref{sec:nntag}.
21:
22: The trigger efficiency is computed as a probability ({\it TrigWeight}) which we associate to each
23: MC event with:
24:
25: \begin{center}
26: \begin{equation}
27: P \displaystyle = P_{t0}*P_{b0} + P_{t1}*P_{b1} + P_{t2}*P_{b2} + P_{t\geq 3}*P_{b\geq 3}
28: \end{equation}
29: \end{center}
30:
31: \noindent where $P_{ti}$ is the trigger probability for the event if it has $i$ b-tags and $P_{bi}$ is in turn
32: the probability of having $i$ b-tags in the event offline reconstruction.\\
33:
34: What follows is a brief description of how the trigger probabilities at each level were calculated. Single-object
35: turn-on curves were determined using muon triggered events from the TOPJETTRIG skim.
36: Some turn-on curves are found in Appendix \ref{app:turnon}. A more complete description can be found in \cite{bIDH_note}.
37:
38: \clearpage
39:
40:
41: \begin{table}[h]
42: \begin{small}
43: \begin{center}
44: %\subtable[v15]{
45: \begin{tabular}{l c}
46: \hline\hline
47: Level & v15 \\
48: \hline
49: L1 & CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4) \\
50: L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) OR\\
51: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(10,10) OR \\
52: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(100,6) \\
53: L3 & L3JET(3,15,3.6) L3JET(2,25,3.6) $\mathrm{|z_{PV}|< 35\;cm}$ BTAG(0.4) \\
54: \hline
55: Name & JT2$\_$3JT15L$\_$IP$\_$VX \\
56: \hline\hline
57: \end{tabular}
58:
59: \begin{tabular}{l c}
60: \hline\hline
61: Level & v16 \\
62: \hline
63: L1 & CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4) \\
64: L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) STTIP(1,5.5,3) OR\\
65: & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(20,10) OR \\
66: & L2JET(1,30,2.4) L2JET(2,15,2.4) L2JET(3,8,2.4) L2HT(75,6) STTIP(1,5.5,3)\\
67: L3 & L3JET(3,15,3.6) JT(2,25,3.6) $\mathrm{|z_{PV}|< 35\;cm}$ BTAG(0.4) \\
68: \hline
69: Name & JT2$\_$3JT15L$\_$IP$\_$VX \\
70: \hline\hline
71: \end{tabular}
72: %}
73: \end{center}
74: \caption{\small Level-by-level description of trigger JT2$\_$3JT15L$\_$IP$\_$VX. The
75: CSWJT(x,y,z) term corresponds to x L1 jets above y~GeV and within
76: $\mathrm{|\eta| < z}$. The JT(x,y,z) term corresponds to x jets
77: reconstructed at L2 or L3 with $p_T > y$ GeV and $\mathrm{|\eta|<z}$. The HT(x,y) term is used only at
78: L2 and requires that the sum of the transverse momenta of L2 jets with $p_T > y$ GeV is above x~GeV.
79: The SPHER(0.1) term requires the event sphericity calculated from L2 jets to be greater than 0.1.
80: The MJT(x,y) term corresponds to a missing transverse energy $>$ x~GeV calculated from jets
81: with $E_{T} >$ y~GeV. The STTIP(1,5.5,3) term requires one L2STT track with an impact parameter
82: significance greater than or equal to three and a $\chi^{2} < 5.5$.
83: The $\mathrm{|z_{PV}|< 35\;cm}$ term requires the primary vertex reconstructed
84: at L3 to be within 35 cm of the center of the detector and the BTAG(0.4) term is used
85: only at L3 and corresponds to a cut of 0.4 on the probability for the event to not contain a $b$-quark.}
86: \label{tabtrigcond}
87: \end{small}
88: \end{table}
89:
90:
91: \subsection{\label{sub:trig_paramL1}\boldmath Level 1}
92:
93: \noindent Level 1 consists of jet terms only: 1 jet with $E_{T} >$ 30 GeV and $|\eta| < 2.4$, a second jet
94: with $E_{T} >$ 15 GeV and $|\eta| < 2.4$
95: and a third jet with $E_{T} >$ 8 GeV and $|\eta| < 3.2$. The total L1 probability is given by
96:
97: \begin{equation}
98: \begin{split}
99: P(L1) &= [P(\geq 3 \mbox{jets}) + P(= 2 \mbox{jets})*P(\geq 1 \mbox{noise jet}) + P(= 1 \mbox{jet})*P(\geq 2 \mbox{noise jets}) + P(= 0 \mbox{jets})*P(\geq 3 \mbox{noise jets})]\\
100: &* [P(\geq 2 \mbox{jets}) + P(= 1 \mbox{jet})*P(\geq 1 \mbox{noise jet}) + P(= 0 \mbox{jets})*P(\geq 2 \mbox{noise jets})] \\
101: &* [P(\geq 1 \mbox{jet}) + P(= 0 \mbox{jets})*P(\geq 1 \mbox{noise jet})]
102: \end{split}
103: \end{equation}
104:
105: \noindent where $P(\geq x jets)$ is the probability of having $x$ or more jets present in the event and $P(= x jets)$ is
106: the probability of having exactly $x$ jets in the event. The term {\it noise jets} refers to all
107: those L1 jets that didn't match to an offline jet within $\Delta R < 0.5$. In the equation above the first line
108: corresponds to the term CSWJT(3,8,$\mathrm{|\eta|<3.2}$), the second to the term
109: CSWJT(2,15,$\mathrm{|\eta|<2.4}$) and the third to the term CSWJT(1,30,$\mathrm{|\eta|<2.4}$).
110: L1 jets that matched offline ones had their turn-on curves parametrized as functions of
111: offline jet $p{T}$'s. The number of noise jets per event was parametrized as a function
112: of offline $H_{T}$. All L1 turn-on curves are found in Appendix \ref{app:jetturnon_L1}.
113:
114: \subsection{\label{sub:trig_paramL2}\boldmath Level 2}
115:
116: \noindent Level 2 part of this trigger consists of an OR of three terms (here classified as
117: {\it top}, {\it hbb} and {\it mjt}), each with a variation for v15 and v16:
118:
119: \begin{description}
120: \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
121: \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 $\chi^{2} < 5.5$.
122: \item[v15 hbb:] 3 jets with $p_{T} >$6 GeV, $H_{T} >$75~GeV and sphericity $>$ 0.1
123: \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 $\chi^{2} < 5.5$.
124: \item[v15 mjt:] 3 jets with $p_{T} >$8 GeV, 2 jets with $p_{T} >$15~GeV, 1 jet with $p_{T} >$30~GeV, $H_{T} >$75~GeV and $\not\!\!E_{T}$ $>$ 10~GeV.
125: \item[v16 mjt:] 3 jets with $p_{T} >$8 GeV, 2 jets with $p_{T} >$15~GeV, 1 jet with $p_{T} >$30~GeV, $H_{T} >$75~GeV and $\not\!\!E_{T}$ $>$ 20~GeV.
126: \end{description}
127:
128: For this level the net trigger probability is
129:
130: \begin{center}
131: \begin{equation}
132: \begin{split}
133: P(L2) &= P(hbb \cup mht \cup top)\\
134: &= P(top) + P(hbb) + P(mht) - P(top \cap hbb) - P(top \cap mht) - P(hbb \cap mht) + P(hbb \cap mht \cap top)
135: \end{split}
136: \end{equation}
137: \end{center}
138:
139: \noindent where P(x) corresponds to the probability of either L2, the mht, hbb or the top term firing.
140:
141:
142: \noindent {\bf Level 2 jet terms}: from Table \ref{tabtrigcond} we see that for v15 trigger
143: version, L2 jets terms are actually
144: subsets of L1. As here conditional probability is used, it means that the probability of L2 jet terms
145: firing if L1 terms fired is unity. However in v16 the Pt requirement of jets in the first trigger term
146: was loosened from 8 to 6 GeV and $\eta$ requirement on 8 GeV jets in the third trigger term
147: was tightened from $|\eta| < 3.2$ to $|\eta| < 2.4$. As in the L1 case, all L2 jets matching offline
148: ones had their turn-on curves parametrized as functions of offline jet $p_{T}$'s, except
149: for noise jets, whose number in each event which paratrized as funcions of offline $H_{t}$.
150: Turn-on curves for these cases are found in Appendix \ref{app:jetturnon_L2}.
151:
152: \noindent {\bf Level 2 $H_{T}$ term}: this term consists of a cut of $H_{T}$ $> 75$~GeV for v15
153: and $H_{T}$ $>~100$~GeV for v16). Correspondent turn-on curves are shown in Appendix \ref{app:htturnon_L2}.
154:
155: \noindent {\bf Level 2 $\not\!\!E_{T}$ term}: the correspondent $\not\!\!E_{T}$ cuts are $> 10~$GeV and $>~20$~GeV
156: for v15 and v16 respectively. Their turn-on are shown in Appendix \ref{app:mhtturnon_L2}.
157:
158: \noindent {\bf L2 Sphericity Term}: this term requires a sphericity cut of $>$ 0.1.
159: Corresponding turn-on curves are shown in Appendix \ref{app:spherturnon_L2}.
160:
161:
162: \noindent {\bf L2 STT}: the L2STTIP efficiency was measured for events in v16 which have passed the rest of the
163: L1, L2 (L2top OR L2hbb) and L3 (except L3 b-tag)
164: trigger requirements and the offline three to five jet selection. The efficiency was measured versus
165: the invariant mass of the two
166: leading jets, separately for 0, 1, 2 and 3 offline tight NN b-tagged events, in the three different luminosity regions.
167: Appendix \ref{app:sttip_L2} shows the STTIP(1,5.5,3) efficiency versus the
168: leading invariant di-jet mass in the low, medium and high luminosity range for different number of offline b-tags.
169:
170: \subsection{\label{sub:trig_paramL3}\boldmath Level 3}
171:
172: \noindent L3 consists of a jet part and a b-tag one. For the jet part of L3, turn-on curves were
173: determined for events passing both L1 and L2 requirements. Corresponding probability is given the equation below
174:
175: \begin{equation}
176: \begin{split}
177: P(L3) &= [P(\geq 3 \mbox{jets}) + P(= 2 \mbox{jets})*P(\geq 1 \mbox{noise jet}) + P(= 1 \mbox{jet})*P(\geq 2 \mbox{noise jets}) + P(= 0 \mbox{jets})*P(\geq 3 \mbox{noise jets})]\\
178: &* [P(\geq 2 \mbox{jets}) + P(= 1 \mbox{jet})*P(\geq 1 \mbox{noise jet}) + P(= 0 \mbox{jets})*P(\geq 2 \mbox{noise jets})]
179: \end{split}
180: \end{equation}
181:
182: \noindent In the equation above the first line
183: corresponds to the term JT(3,15,$\mathrm{|\eta|<3.6}$), the second to the term
184: JT(2,25,$\mathrm{|\eta|<3.6}$). Here was applied the same treatment to L3 jets matching offline ones and to noise
185: jets as in L1 and L2 jet terms. Corresponding turn-on curves are shown in Appendix \ref{app:jetturnon_L1}.
186:
187:
188: Efficiencies for the b-tag part of L3 were measured in two different ways depending whether the trigger list was v15
189: or v16. In the v15 case events were recorded with the JT2$\_$4JT20 and JT2$\_$3JT12L$\_$MM3$\_$V triggers,
190: since their L1 and L2 conditions were exactly the same. Events were further required to pass the
191: rest of L3 conditions of JT2$\_$3JT15L$\_$IP$\_$VX and the offline event selection. In the v16 case
192: efficiencies were measured in a similar fashion, but using
193: trigger JT4$\_$3JT15L$\_$VX (which has no L2STT or L3BTAG requirements). Events were then required
194: to have fired one of the three L2 branches of JT2$\_$3JT15L$\_$IP$\_$VX and to pass the offline
195: three to five jet selection. All turn-on curves for both trigger lists are found in Appendix \ref{app:btagturnon_L3}.
196:
197: \clearpage
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