Diff for /ttbar/p20_taujets_note/TriggParam.tex between versions 1.1 and 1.2

version 1.1, 2011/05/18 21:30:39 version 1.2, 2011/06/01 01:20:54
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 \section{Trigger Parametrization \label{sec:trig_param}}  \section{Trigger modeling\label{sec:trig_param}}
   
 As aforementioned the trigger used in this analysis is JT2$\_$3JT15L$\_$IP$\_$VX.   As aforementioned the trigger used in this analysis is JT2$\_$3JT15L$\_$IP$\_$VX. 
 In both v15 and v16 trigger versions, this trigger has 4 terms at level 2. Currently, only   For both the v15 and v16 trigger versions, this trigger has four terms at level 2. Three 
 three of these, the L2 $H_{T}$, missing $E_{T}$ ($\not\!\! E_{T}$) and   of these, the L2 $H_{T}$, missing $E_{T}$ ($\not\!\! E_{T}$) and 
 sphericity based branches have been modelled by the $hbb$ group \cite{bIDH_note}. Therefore  sphericity based branches have been modelled for the $h \rightarrow b\bar{b}$ analysis \cite{bIDH_note}. We
 these are the ones used in this analysis. The missing term is the acoplanarity term, namely,  use those in this analysis. The missing term is the acoplanarity term, namely,
 L2JET(1,20,2.4) L2HT(35,6) MJT(20,10) L2ACOP(168.75), which is the same in both   L2JET(1,20,2.4) L2HT(35,6) MJT(20,10) L2ACOP(168.75), which is the same in both 
 v15 and v15 trigger lists.  v15 and v16 trigger lists.
   
   
 Table \ref{tabtrigcond} shows the L1, L2 and L3 requirements of the trigger.  Table \ref{tabtrigcond} shows the L1, L2 and L3 requirements of the trigger.
   
   
 In its work, the $hbb$ group has parametrized the trigger in three instantaneous luminosity   In its work, the $h \rightarrow b\bar{b}$ group has parametrized the trigger in three instantaneous luminosity 
 ($10^{32}$)regions: low ($L_{int} <$ 77 ), medium ( 77 $\leq L_{int} <$ 124 ) and   ($10^{32}$) bins: low ($L_{int} <$ 77 ), medium ( 77 $\leq L_{int} <$ 124 ) and 
 high ( $L_{int} \geq 124$ ). The final goal is to measure the total trigger efficiency for our events. In order to   high ( $L_{int} \geq 124$ ). To model the trigger efficiency 
 do so we take into account both the trigger probabilities and the b-tag probabilities. Thus, the trigger  we take into account both the trigger probabilities and the b-tag probabilities. Thus, the trigger
 probabilities for 0, 1, 2 and 3 or more b-tagged jets are then multiplied by the probabilities  probabilities for 0, 1, 2 and 3 or more b-tagged jets are multiplied by the probabilities
 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}.   of 0, 1, 2 and 3 or more jets being tagged, respectively, which are themselves derived from the TRF's, 
   as described in section \ref{sec:nntag}. 
   
 The trigger efficiency is computed as a probability ({\it TrigWeight}) which we associate to each  The trigger efficiency is computed as a probability ({\it TrigWeight}) which we associate to each
 MC event with:  MC event as follows:
   
 \begin{center}  \begin{center}
 \begin{equation}  \begin{equation}
 P \displaystyle = P_{t0}*P_{b0} + P_{t1}*P_{b1} + P_{t2}*P_{b2} + P_{t\geq 3}*P_{b\geq 3}  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}
 \end{equation}  \end{equation}
 \end{center}  \end{center}
   
 \noindent where $P_{ti}$ is the trigger probability for the event if it has $i$ b-tags and  $P_{bi}$ is in turn  \noindent where $P_{ti}$ is the trigger probability for the event if it has $i$ b-tags and  $P_{bi}$ is in turn
 the probability of having $i$ b-tags in the event offline reconstruction.\\  the probability of having $i$ b-tags in the offline event reconstruction.\\
   
 What follows is a brief description of how the trigger probabilities at each level were calculated. Single-object  We now give a brief description of how the trigger probabilities at each level were calculated. Single-object
 turn-on curves were determined using muon triggered events from the TOPJETTRIG skim.  turn-on curves were determined using muon-triggered events from the TOPJETTRIG skim.
 Some turn-on curves are found in Appendix \ref{app:turnon}. A more complete description can be found in \cite{bIDH_note}.  Some turn-on curves are found in Appendix \ref{app:turnon}. A more complete description can be found in \cite{bIDH_note}.
   
 \clearpage  \clearpage
Line 50  Some turn-on curves are found in Appendi Line 51  Some turn-on curves are found in Appendi
     L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) OR\\       L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) OR\\ 
   & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(10,10) OR \\    & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(10,10) OR \\
   & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(100,6) \\    & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(100,6) \\
     L3 & L3JET(3,15,3.6) L3JET(2,25,3.6) $\mathrm{|z_{PV}|< 35\;cm}$ BTAG(0.4) \\      L3 & L3JET(3,15,3.6) L3JET(2,25,3.6) ${|z_{\mbox{PV}}|< 35\;cm}$ BTAG(0.4) \\
                 \hline                  \hline
     Name & JT2$\_$3JT15L$\_$IP$\_$VX  \\      Name & JT2$\_$3JT15L$\_$IP$\_$VX  \\
     \hline\hline      \hline\hline
Line 64  Some turn-on curves are found in Appendi Line 65  Some turn-on curves are found in Appendi
     L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) STTIP(1,5.5,3) OR\\      L2 & L2JET(3,6) L2HT(75,6) SPHER(0.1) STTIP(1,5.5,3) OR\\
   & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(20,10) OR \\    & L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(20,10) OR \\
   & L2JET(1,30,2.4) L2JET(2,15,2.4) L2JET(3,8,2.4) L2HT(75,6) STTIP(1,5.5,3)\\    & L2JET(1,30,2.4) L2JET(2,15,2.4) L2JET(3,8,2.4) L2HT(75,6) STTIP(1,5.5,3)\\
     L3 & L3JET(3,15,3.6) JT(2,25,3.6) $\mathrm{|z_{PV}|< 35\;cm}$ BTAG(0.4) \\      L3 & L3JET(3,15,3.6) JT(2,25,3.6) ${|z_{\mbox{PV}}|< 35\;cm}$ BTAG(0.4) \\
                 \hline                  \hline
     Name & JT2$\_$3JT15L$\_$IP$\_$VX  \\      Name & JT2$\_$3JT15L$\_$IP$\_$VX  \\
     \hline\hline      \hline\hline
Line 90  only at L3 and corresponds to a cut of 0 Line 91  only at L3 and corresponds to a cut of 0
   
 \subsection{\label{sub:trig_paramL1}\boldmath Level 1}  \subsection{\label{sub:trig_paramL1}\boldmath Level 1}
   
 \noindent Level 1 consists of jet terms only: 1 jet with $E_{T} >$ 30 GeV and $|\eta| < 2.4$, a second jet   \noindent Level 1 consists of jet terms only: One jet with $E_{T} >$ 30 GeV and $|\eta| < 2.4$, a second jet 
 with $E_{T} >$ 15 GeV and $|\eta| < 2.4$  with $E_{T} >$ 15 GeV and $|\eta| < 2.4$
 and a third jet with $E_{T} >$ 8 GeV and $|\eta| < 3.2$. The total L1 probability is given by  and a third jet with $E_{T} >$ 8 GeV and $|\eta| < 3.2$. The total L1 probability is given by
   
 \begin{equation}  \begin{equation}
 \begin{split}  \begin{split}
 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})]\\  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})]\\
       &* [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})] \\        &* [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})] \\
       &* [P(\geq 1 \mbox{jet}) + P(= 0 \mbox{jets})*P(\geq 1 \mbox{noise jet})]        &* [P(\geq 1 \hspace{0.2cm}  \mbox{jet}) + P(= 0 \hspace{0.2cm}  \mbox{jets})*P(\geq 1 \hspace{0.2cm}  \mbox{noise jet})]
 \end{split}  \end{split}
 \end{equation}  \end{equation}
   
Line 113  of offline $H_{T}$. All L1 turn-on curve Line 114  of offline $H_{T}$. All L1 turn-on curve
   
 \subsection{\label{sub:trig_paramL2}\boldmath Level 2}  \subsection{\label{sub:trig_paramL2}\boldmath Level 2}
   
 \noindent Level 2 part of this trigger consists of an OR of three terms (here classified as  \noindent The Level 2 part of this trigger consists of an OR of three terms (here classified as
 {\it top}, {\it hbb} and {\it mjt}), each with a variation for v15 and v16:  {\it top}, {\it hbb} and {\it mjt}), each with a variation for v15 and v16:
   
 \begin{description}  \begin{description}
Line 121  of offline $H_{T}$. All L1 turn-on curve Line 122  of offline $H_{T}$. All L1 turn-on curve
 \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 $\chi^{2} < 5.5$.  \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 $\chi^{2} < 5.5$.
 \item[v15 hbb:] 3 jets with $p_{T} >$6 GeV, $H_{T} >$75~GeV and sphericity $>$ 0.1  \item[v15 hbb:] 3 jets with $p_{T} >$6 GeV, $H_{T} >$75~GeV and sphericity $>$ 0.1
 \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 $\chi^{2} < 5.5$.  \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 $\chi^{2} < 5.5$.
 \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.  \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.
 \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.  \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.
 \end{description}  \end{description}
   
 For this level the net trigger probability is  For this level the net trigger probability is
Line 142  P(L2) &= P(hbb \cup mht \cup top)\\ Line 143  P(L2) &= P(hbb \cup mht \cup top)\\
 \noindent {\bf Level 2 jet terms}: from Table \ref{tabtrigcond} we see that for v15 trigger   \noindent {\bf Level 2 jet terms}: from Table \ref{tabtrigcond} we see that for v15 trigger 
 version, L2 jets terms are actually   version, L2 jets terms are actually 
 subsets of L1. As here conditional probability is used, it means that the probability of L2 jet terms   subsets of L1. As here conditional probability is used, it means that the probability of L2 jet terms 
 firing if L1 terms fired is unity. However in v16 the Pt requirement of jets in the first trigger term  firing if L1 terms fired is unity. However in v16 the $p_{T}$ requirement of jets in the first trigger term
 was loosened from 8 to 6 GeV and $\eta$ requirement on 8 GeV jets in the third trigger term   was loosened from 8 to 6 GeV and $\eta$ requirement on 8 GeV jets in the third trigger term 
 was tightened from $|\eta| < 3.2$ to $|\eta| < 2.4$. As in the L1 case, all L2 jets matching offline  was tightened from $|\eta| < 3.2$ to $|\eta| < 2.4$. As in the L1 case, all L2 jets matching offline
 ones had their turn-on curves parametrized as functions of offline jet $p_{T}$'s, except  ones had their turn-on curves parametrized as functions of offline jet $p_{T}$'s, except
 for noise jets, whose number in each event which paratrized as funcions of offline $H_{t}$.   for noise jets, whose number in each event which parametrized as funcions of offline $H_{t}$. 
 Turn-on curves for these cases are found in Appendix \ref{app:jetturnon_L2}.  Turn-on curves for these cases are found in Appendix \ref{app:jetturnon_L2}.
   
 \noindent {\bf Level 2 $H_{T}$ term}: this term consists of a cut of $H_{T}$ $> 75$~GeV for v15   \noindent {\bf Level 2 $H_{T}$ term}: this term consists of a cut of $H_{T}$ $> 75$~GeV for v15 
 and $H_{T}$ $>~100$~GeV for v16). Correspondent turn-on curves are shown in Appendix \ref{app:htturnon_L2}.  and $H_{T}$ $>~100$~GeV for v16. Corresponding turn-on curves are shown in Appendix \ref{app:htturnon_L2}.
   
 \noindent {\bf Level 2 $\not\!\!E_{T}$ term}: the correspondent $\not\!\!E_{T}$ cuts are $> 10~$GeV and $>~20$~GeV  \noindent {\bf Level 2 $\not\!\!E_{T}$ term}: the correspondent $\not\!\!E_{T}$ cuts are $> 10~$GeV and $>~20$~GeV
 for v15 and v16 respectively. Their turn-on are shown in Appendix \ref{app:mhtturnon_L2}.  for v15 and v16 respectively. Their turn-on are shown in Appendix \ref{app:mhtturnon_L2}.
Line 163  Corresponding turn-on curves are shown i Line 164  Corresponding turn-on curves are shown i
 L1, L2 (L2top OR L2hbb) and L3 (except L3 b-tag)   L1, L2 (L2top OR L2hbb) and L3 (except L3 b-tag) 
 trigger requirements and the offline three to five jet selection. The efficiency was measured versus   trigger requirements and the offline three to five jet selection. The efficiency was measured versus 
 the invariant mass of the two   the invariant mass of the two 
 leading jets, separately for 0, 1, 2 and 3 offline tight NN b-tagged events, in the three different luminosity regions.   leading jets, separately for 0, 1, 2 and 3 offline tight NN b-tagged events, in the three different luminosity bins. 
 Appendix \ref{app:sttip_L2} shows the STTIP(1,5.5,3) efficiency versus the   Appendix \ref{app:sttip_L2} shows the STTIP(1,5.5,3) efficiency versus the 
 leading invariant di-jet mass in the low, medium and high luminosity range for different number of offline b-tags.     leading invariant di-jet mass in the low, medium and high luminosity range for different numbers of offline b-tags.   
   
 \subsection{\label{sub:trig_paramL3}\boldmath Level 3}  \subsection{\label{sub:trig_paramL3}\boldmath Level 3}
   
Line 174  determined for events passing both L1 an Line 175  determined for events passing both L1 an
   
 \begin{equation}  \begin{equation}
 \begin{split}  \begin{split}
 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})]\\  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})]\\
       &* [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})]         &* [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})] 
 \end{split}  \end{split}
 \end{equation}  \end{equation}
   
Line 185  JT(2,25,$\mathrm{|\eta|<3.6}$). Here was Line 186  JT(2,25,$\mathrm{|\eta|<3.6}$). Here was
 jets as in L1 and L2 jet terms. Corresponding turn-on curves are shown in Appendix \ref{app:jetturnon_L1}.  jets as in L1 and L2 jet terms. Corresponding turn-on curves are shown in Appendix \ref{app:jetturnon_L1}.
   
   
 Efficiencies for the b-tag part of L3 were measured in two different ways depending whether the trigger list was v15   Efficiencies for the b-tag part of L3 were measured in two different ways depending on whether the trigger list was v15 
 or v16. In the v15 case events were recorded with the JT2$\_$4JT20 and JT2$\_$3JT12L$\_$MM3$\_$V triggers,   or v16. In v15 case events were recorded with the JT2$\_$4JT20 and JT2$\_$3JT12L$\_$MM3$\_$V triggers, 
 since their L1 and L2 conditions were exactly the same. Events were further required to pass the   since their L1 and L2 conditions were exactly the same. Events were further required to pass the 
 rest of L3 conditions of JT2$\_$3JT15L$\_$IP$\_$VX and the offline event selection. In the v16 case   rest of L3 conditions of JT2$\_$3JT15L$\_$IP$\_$VX and the offline event selection. In v16 case 
 efficiencies were measured in a similar fashion, but using  efficiencies were measured in a similar fashion, but using
 trigger JT4$\_$3JT15L$\_$VX (which has no L2STT or L3BTAG requirements). Events were then required   trigger JT4$\_$3JT15L$\_$VX (which has no L2STT or L3BTAG requirements). Events were then required 
 to have fired one of the three L2 branches of JT2$\_$3JT15L$\_$IP$\_$VX and to pass the offline   to have fired one of the three L2 branches of JT2$\_$3JT15L$\_$IP$\_$VX and to pass the offline 

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