%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This is a template ATLAS Paper that contains suggestions and hints on % how to get your paper in a form that minimizes the amount of work % needed to get it approved by the collaboration - assuming that the % physics is OK! % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file is for use with latex2e which was released as the official % version of latex at CERN in January 1995. % Note that it uses \includegraphics which is the latex2e replacement % for \epsfig. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \documentclass[12pt,a4paper,dvips]{article} \documentclass[11pt,a4paper]{article} \usepackage{a4p} % The default fonts are Computer Modern fonts. % You can get Postscript fonts by uncommenting the line below. % This means the font in the text and figures can be identical. % You have to use dvips -Ppsmath ... if you want to use the psmath package. %\usepackage{times,psmath} \usepackage{cite,mcite} \usepackage{graphicx} \usepackage{atlasphysics} \usepackage{atlas_title,ifthen} \usepackage{mathptmx} \usepackage{helvet} % \usepackage{eurosym} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \def\atlasnote#1{\def\mydocversion{{\large ATL-#1}}} \def\preprint#1{\def\mydocversion{{\large #1}}} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Instructions: % % Give the journal name, if appropriate % \journalname{Phys. Lett. B} % % Uncomment the relevant line % \atlasdraft for drafts % \preprint for preprints % % Draft version: uncomment the line below and give the version number \atlasdraft{0.01} % % Uncomment for an ATLAS note %\atlasnote{PHYS-PUB-2007-0XX} % % Uncomment for a preprint % \preprint{CERN-PH/2007-0XX} % % Give date: \today for drafts, a fixed date for final papers \def\thedate{\today} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Use \icaption instead of \caption in tables and figures to get a % caption that is indented. % Note that the label should be included inside \icaption for it to % work properly. % \newlength{\capindent} \setlength{\capindent}{0.5cm} \newlength{\capwidth} \setlength{\capwidth}{\textwidth} \addtolength{\capwidth}{-2\capindent} \newlength{\figwidth} \setlength{\figwidth}{\textwidth} \addtolength{\figwidth}{-2.0cm} \newcommand{\icaption}[2][!*!,!]{\hspace*{\capindent}% \begin{minipage}{\capwidth} \ifthenelse{\equal{#1}{!*!,!}}% {\caption{#2}}% {\caption[#1]{#2}} \vspace*{3mm} \end{minipage}} % % Shorthand for \phantom to use in tables \newcommand{\pho}{\phantom{0}} \newcommand{\bslash}{\ensuremath{\backslash}} \newcommand{\BibTeX}{{\sc Bib\TeX}} % Upsilon(1S) \newcommand{\UoneS}{\ensuremath{\Upsilon(\mathrm{1S})}} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This is where the document really begins %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \newcommand{\IDSCAN}{IDScan} \begin{document} % \begin{titlepage} % \vspace*{-6mm} \includegraphics[width=3cm]{atlas_logo1.pdf} \hfill \begin{minipage}[b]{7cm} \begin{center} \mbox{\Huge \bf CSC Note BT05} \\ \end{center} \begin{center} \mydocversion \end{center} \begin{center} \thedate \end{center} \end{minipage} \hfill \includegraphics[width=3cm]{cern_bw.pdf} % \vspace*{-1cm} \title{HLT $b$-tagging performance and strategies} \author{The ATLAS Collaboration$^{1)}$} %\begin{center} %$^{1}$ Dipartimento di Fisica, Universit\`a di Genova and INFN, Genova, Italy\\ %$^{2}$ Stanford Linear Accelerator Center, Menlo Park, CA, U.S.A %\end{center} \begin{abstract} The selection of $b$-jets at the trigger level aims at improving the flexibility of the High Level Trigger (HLT) scheme and possibly extending its physics performance, in particular for topologies containing more than one \mbox{$b$-jet}. It will be shown that the acceptance for $b$-jets can be increased and background reduced by lowering jet transverse energy thresholds and applying $b$-tagging selections based on impact parameters of tracks in jets. %increasing the acceptance for signal events %while reducing the background. This note reviews the $b$-jet selection in the HLT and discusses its integration into the ATLAS trigger menu. \end{abstract} % \vfill $^{1)}$ This note has been prepared by A. Coccaro, G. Critelli, F. Parodi, C. Schiavi and A. Schwartzman. \newpage %\boldmath \tableofcontents %\unboldmath \end{titlepage} \newpage % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Introduction %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \section{Introduction} Final states containing more than one $b$-jet have been proposed as signatures with substantial discovery potential in a variety of physics channels. The ability to separate $b$-jets from light-quark and gluon jets is thus an important ingredient of the online selection strategy in ATLAS.\\ One of the most interesting physics cases addressed by such a $b$-jet trigger selection involves events with final states containing four $b$-jets. This event class is relevant for Higgs bosons search in the low mass range, $m_H < 130\;\mathrm{GeV}$. The most promising channels are the $H \to b\bar{b}$ decay, where the Standard Model Higgs boson is produced by way of the associated production channel $t\bar{t}H$ and, in supersymmetric theories, the channels $b\bar{b}H$, $b\bar{b}A$ with $H/A \to b\bar{b}$ or $H \to hh \to b{\bar b}b{\bar b}$. The selection of $b$-jets at the trigger level is mainly meant to improve the flexibility of the HLT scheme, extending its physics performance for the above described topologies. This is achieved by increasing the acceptance for signal events, while, at the same time, reducing the background. The $b$-jet selection relies on tracking information %The first trigger level in which information from the Inner Detector tracking system \cite{DetPap} which is only available starting with the Second Level Trigger (L2). Therefore, the acceptance for signal can only be increased by simultaneously lowering L1 jet thresholds and applying a more discriminating $b$-jet selection in the High Level Trigger (L2 and EF). High rejection power from the $b$-jet trigger is required to compensate for less rejection due to lower L1 thresholds and thereby to cope with L2 and EF output rate budget. \section{Monte Carlo samples} The $b$-tagging performance on single jets, presented in this note, is evaluated on $b$-jets from $H \to b\bar{b}$ decays, where the Higgs boson has a mass of 120 GeV and is produced in association with a $W$ decaying leptonically. The standard background for single-jet studies are the corresponding $u$-jets, obtained by artificially replacing the $b$-quarks from the Higgs decay with $u$-quarks. While these events imprecisely model the real background from light-flavour jets they %that the $b$-jet trigger has to face, this choice is motivated by the %need to have a clean source of $u$-jets. Furthermore, the $H \to u\bar{u}$ decay can be seen as a worst case scenario since the kinematical properties of signal and background are very similar. Even in this very simple situation, the association between Regions of Interest (RoI), identified by the first level trigger, and jets is not uniquely defined: %As a matter of fact, a generic $x$-quark in the final state of an interaction or a decay can radiate gluons and, therefore, change its direction. An RoI from $H\rightarrow b\bar{b}$ or $H\rightarrow u\bar{u}$ is labeled as $x$-jet ($x=b,\,u$) if an $x$-quark from the original hard process points, after final state radiation, along the RoI direction within an angular distance of $\Delta R = \sqrt{\Delta\eta^2+\Delta\phi^2} < 0.1$. In order to evaluate the rate of the $b$-jet trigger menu, the rejection power must be evaluated on a more representative background sample. As for all the other trigger selections in ATLAS, di-jet samples are chosen for this purpose since they correctly include all contributions to the $b$-tagging background, including $c$-quarks and taus. All data samples studied in this note have been generated without pile-up, leaving the influence of pile-up for further studies. The activity due to underlying event is taken into account since it is built-in in the event generation (Pythia). %The simulation and digitazione of the samples have been performed with release 12.0.31.3, the reconstruction %has been done with release 13.0.30.2 \section{HLT $b$-jet selection} \subsection{L1 configuration} The HLT reconstruction starts from the RoIs selected by the L1 trigger \cite{DetPap}. In particular, the $b$-jet trigger starts from a L1 jet-RoI $\Delta\eta \times \Delta\phi = 0.8 \times 0.8$ and performs track and vertex reconstruction in a smaller RoI $\Delta\eta \times \Delta\phi = 0.4 \times 0.4$ in order to reduce data access and consequently processing time. %Figure \ref{fig:LVL1ETB} shows the $b$-quark $p_T$ acceptance of the different L1 $E_T$ thresholds. %\begin{figure}[htb] % \begin{center} % \includegraphics[width=0.8\textwidth]{./figures/LVL1ETB.pdf} % \caption[Transverse momentum distribution]{$p_T$ acceptance of $b$-quarks % matching different L1 jet-RoI $E_T$ thresholds.} % \label{fig:LVL1ETB} % \end{center} %\end{figure} \subsection{$b$-jet trigger feature extraction algorithms} The first step in the $b$-jet trigger chain is, both at L2 and EF, the reconstruction of the relevant quantities needed to perform the selection. The $b$-jet RoIs can be separated from light jet RoIs using the impact parameters of the charged tracks, the properties of reconstructed secondary vertices, or soft leptons; all these quantities are related to the $b$-quark lifetime and to its decay properties. The present $b$-jet trigger implementation relies only on the impact parameters of charged tracks. Primary vertex reconstruction is performed only in the $z$ direction while its coordinates in the transverse plane are assumed to be compatible with the origin. Track reconstruction algorithms are described, together with their performance, in \cite{CSCHLTTracking}. The two Inner Detector tracking algorithms available at L2 show equivalent performance when operating on jet samples \cite{CSCHLTTracking}. Thus to avoid unnecessary comparisons, the results obtained with the SiTrack algorithm are presented. For track reconstruction at the EF, the algorithm corresponding to that used for offline reconstruction has been adopted (NewTracking). \subsubsection{Primary vertex reconstruction} %The track impact parameter in the $RZ$ plane, i.e. $z_0$ of the reconstructed tracks, can be adopted to %build another discriminant variable for the $b$-tagging selection.\\ %In analogy with the $d_0$ impact parameter, the $z_0$ distribution shows a peak around the primary vertex %position ($z_{vtx}$) for tracks coming from $u$-jets, while larger values of $z_0 - z_{vtx}$ are expected for %$b$-jets. Anyway, unlike what happens for the transverse impact parameter, Along the $z$ direction no \textit{a priori} knowledge of primary vertex $z_{vtx}$ is available; this has hence to be reconstructed, starting from the tracks available in the RoI. This information is needed for the correct evaluation of the longitudinal parameter of each track with respect to the primary interaction position. The adopted algorithm, a simple histogramming method based on a sliding window, yields an efficiency of 98(99)\% and a resolution on $z_{vtx}$ of about $120(100)\mu$m at L2(EF) as illustrated in Figure~\ref{fig:primvtx}. \begin{figure}[htb] \begin{center} \includegraphics[width=0.6\textwidth]{./figures/PrimVtx.pdf} \caption{The distribution of the difference between the true and the reconstructed $z$ primary vertex coordinates at L2 (full line) and EF (dashed line). The widths as determined by a fit to the distributions are $120~\mu$ and $100~\mu$ respectively.} \label{fig:primvtx} \end{center} \end{figure} \subsection{Tagging variables} The HLT $b$-jet tagging methods are based on the transverse and longitudinal impact parameters of the reconstructed tracks. %In the following the methods on the transverse and longitudinal parameters of the tracks %reconstructed are discussed. Since the methods are the same for L2 and EF they will be described using L2 variables only. \subsubsection{Transverse impact parameter} The most natural choice is to build the $b$-tagging discriminant variable from the transverse impact parameter $d_0$ of the reconstructed tracks. Since the hadrons containing $b$-quarks have a finite lifetime ($\tau\sim~1.6~ps$), tracks from their decays are characterized by large $d_0$ values, while tracks from $u$-jets come dominantly from the primary vertex ($d_{vtx} = 0$). In particular, the significance of the transverse impact parameter $S=d_0/\sigma(d_0)$ is used, where $\sigma(d_0)$ is the error on the impact parameter. The error on the transverse impact parameter at L2 is parametrized as a function of reconstructed $p_T$ as: \begin{eqnarray*} \sigma(d_0) = \sqrt{p_0^2 + \left({p_1 \over p_T}\right)^{p_2}} \end{eqnarray*} where $p_0$ is the asymptotic term, $p_1$ is the term due to multiple scattering and $p_2$ is the exponent of the multiple scattering contribution (close to two). Although L2 tracking algorithms have recently reached a good level of precision in the error evaluation, the above error parametrization at L2 can still be useful in the early running of the experiment. At the EF, the reconstructed error is used. %\begin{figure}[htb] % \begin{center} % \ifpdf % \includegraphics[width=0.8\textwidth]{./figures/D0ErrorParametrization.pdf} % \fi % \caption{Parametrization of the error on $d_0$ as a function of the reconstructed $p_T$.} % \label{fig:D0ErrorParametrization} % \end{center} %\end{figure} Figure \ref{fig:VarD0s_L2} %and \ref{fig:VarD0s_EF} shows the distributions of the impact parameter significance $d_0/\sigma(d_0)$ for $b$-jets and light jets at L2. The significance has been rescaled according to the function $f(x)=log(1+|x|)$ in order to have a reasonably uniform bin population along the $x$ axis. From these plots it can be guessed that the impact parameter significance is a promising choice for the discriminant variable, since the two distribution are very well separated. \begin{figure}[!t] % \ifpdf \begin{center} \begin{minipage}[t]{0.48\textwidth} % \ifpdf \includegraphics[width=1.\textwidth]{./figures/VarD0s_L2.pdf} % \fi \caption{Distribution of the rescaled function (described in the text) of the transverse impact parameter significance for tracks coming from $b$-jets (solid line) and light jets (dashed line) at L2.} \label{fig:VarD0s_L2} \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} % \ifpdf \includegraphics[width=1.\textwidth]{./figures/VarZ0_L2.pdf} % \fi \caption{Distribution of the rescaled function (described in the text) of the longitudinal impact parameter significance for tracks coming from $b$-jets (solid line) and light jets (dashed line) at L2.} \label{fig:VarZ0_L2} \end{minipage} %\begin{minipage}[t]{0.48\textwidth} % \ifpdf % \includegraphics[width=1.\textwidth]{./figures/VarD0s_EF.pdf} % \fi % \caption{Distribution of the rescaled function (described in the text) of the transverse impact parameter significance for tracks coming from % $b$-jets (shaded plot) and light jets (dashed line) at EF.} % \label{fig:VarD0s_EF} % \end{minipage} \end{center} \end{figure} \subsubsection{Longitudinal impact parameter} The longitudinal impact parameter ($z_0$), i.e. the track's z-intercept, can be adopted, as well as the transverse impact parameter, to discriminate between $b$-jets and light jets. After the primary vertex position has been reconstructed, the $\delta z_0 = z_0 - z_{vtx}$ variable can be used to form a discriminant which can then be used for $b$-jet selection. Figure \ref{fig:VarZ0_L2} %and \ref{fig:VarZ0_EF} shows the distributions of the longitudinal impact parameter significance ($\delta z_0/\sigma(z_0)$) of $b$-jets and light jets at L2. The significance has been rescaled as described above for the transverse impact parameter. As for Figure~\ref{fig:VarD0s_L2}, the signal and background distributions are different although much less so than for the transverse impact parameter significance. From this comparison, it is clear %. Anyway, from these plots we can %already argue that most of the discriminant power will be provided by the measured transverse impact parameter significance. %, which shows a sharper separation between signal and background. The worse resolution of the longitudinal impact parameter significance is due both to the coarser resolution of the silicon tracking detectors along the $z$-direction, bigger extrapolation distance from innermost silicon layer hit to primary vertex at high $\eta$ and to the resolution of the reconstructed primary vertex. %\begin{figure}[htb] % \ifpdf % \begin{center} % \begin{minipage}[t]{0.48\textwidth} % \ifpdf % \includegraphics[width=1.\textwidth]{./figures/VarZ0_L2.pdf} % \fi % \caption{Distribution of the rescaled function (described in the text) % of the longitudinal impact parameter significance for tracks coming from % $b$-jets (shaded plot) and light jets (dashed line) at L2.} % \label{fig:VarZ0_L2} % \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} % \ifpdf % \includegraphics[width=1.\textwidth]{./figures/VarZ0_EF.pdf} % \fi % \caption{Distribution of the rescaled function (described in the text) % of the longitudinal impact parameter significance for tracks coming from % $b$-jets (shaded plot) and light jets (dashed line) at EF.} % \label{fig:VarZ0_EF} % \end{minipage} % \end{center} %\end{figure} \subsection{HLT $b$-jet tagging methods} In this section, HLT $b$-tagging methods are described. The likelihood ratio method is quite general and can be applied to different variables while the $\chi^2$ method is essentially designed to test the compatibility of the tracks with respect to the primary vertex using the transverse impact parameter. The likelihood ratio, using information on the signal and background shape that have to be estimated on real data, is more powerful but also more difficult to tune while the $\chi^2$ method can be easily tuned but is less powerful. \subsubsection{The likelihood-ratio method} The likelihood-ratio method is a statistical tool used to separate two or more event classes, and is based on a set of characteristic variables.\\ The likelihood-ratio variable $W$ is evaluated, for a given event, as the ratio between the probability distributions for two alternative hypotheses. In its application to $b$-jet selection, the likelihood-ratio variable is defined as \begin{displaymath} W = S(s)/S(b), \end{displaymath} where $S(s)$ and $S(b)$ are the probability densities for the signal, the $b$-jets, and the background, represented in this case by the $u$-jets.\\ This variable is widely used to obtain the best possible separation between signal and background, in terms of a single variable, in fits aimed at extracting the fraction of signal events in a given sample. The same variable can be also directly used, as in the $b$-jet selection case, to select signal events, for example by applying a cut on the likelihood-ratio variable itself.\\ The probability density distributions used in the $b$-tagging application can be functions of some parameter of each track (e.g. the transverse impact parameter $d_0$) or of some collective property of the jet (e.g. its track multiplicity). In the first case, these distributions take the form \begin{eqnarray*} s(par_{1}, par_{2}, par_{3}, \dots, par_{n}),\\ b(par_{1}, par_{2}, par_{3}, \dots, par_{n}), \end{eqnarray*} where the $1, \dots, n$ indices identify each track belonging to the jet. The corresponding likelihood-ratio variable is thus defined as \begin{displaymath} W = \frac{ s(par_{1}, par_{2}, par_{3}, \dots, par_{n})} { b(par_{1}, par_{2}, par_{3}, \dots, par_{n}) } \end{displaymath} Exact evaluation of the $s$ and $b$ functions is very difficult, since it would require an almost infinite amount of simulated data; for example, in order to reasonably populate an $n$-dimensional cube, about 100 entries are needed for each dimension, corresponding to $n^{100}$ tracks; even worse, the number of tracks in a jet is not fixed. However, if we assume that the variables corresponding to different tracks are independent, the ratio between the overall probability densities reduces to the product of the ratios of the single probability densities: \begin{displaymath} W = \prod_{i=1}^{n} \frac{ s(par_{i}) }{ b(par_{i}) }, \end{displaymath} which is much easier to evaluate.\\ In the $b$-tagging case, track parameters have complex correlations which depend on the proper time for the $B$ hadron and on its decay kinematics. Nevertheless it can be proven that, neglecting these correlations, no mistake is made; simply, the discriminant power of the $W$ variable will be slightly reduced.\\ The $W$ variable, can take any value between $0$ (for the background) and $+\infty$ (for the signal). For practical reasons, it is useful to handle a variable defined on a finite interval; to achieve this, $W$ is usually replaced by another variable \begin{displaymath} X = \frac{W}{1+W}, \end{displaymath} which can only range between $0$ and $1$.\\ As an illustration of the method, Figures \ref{fig:Dis2Ds_L2} and \ref{fig:Dis2Ds_EF} show the distributions of the discriminant variable $X$ which is based on the combination of the transverse and longitudinal impact parameter for $b$-jets and light jets respectively at L2 and EF. It can be seen that signal events ($b$-jets) accumulate near to $X=1$, while the background (light jets) tends to have $X$ close to $0$. \begin{figure}[!htb] \begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/Dis2D_L2.pdf} \caption{Distribution of the discriminant variable $X$ based on the combination of the transverse and longitudinal impact parameter significances for $b$-jets and $u$-jets (shaded area) at L2.} \label{fig:Dis2Ds_L2} \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/Dis2D_EF.pdf} \caption{Distribution of the discriminant variable $X$ based on the combination of the transverse and longitudinal impact parameter significances for $b$-jets and $u$-jets (shaded area) at EF.} \label{fig:Dis2Ds_EF} \end{minipage} \end{figure} Contrary to the offline $b$-tagging methods based on likelihood ratio the sign of the impact parameters is currently not used at HLT since the RoI direction doesn't give a precise estimation of the $b$-jet direction. Future studies will use the impact parameter sign determination described in the next Section. \input chi2_method.tex \section{HLT $b$-jet selection performance on single jet-RoIs} Every tagging method will be characterized by the curve showing the light-jet rejection versus the efficiency to select $b$-jets ($\epsilon_b$). The light-jet rejection is defined as the inverse of the efficiency of selecting $u$-jets ($R_u = 1/\epsilon_u$) where we have assumed that u-jets are representative of light jets in general. \subsection{Likelihood ratio method using impact parameters} Figures \ref{fig:RejD0s_L2} and \ref{fig:RejD0s_EF} show, respectively, the $b$-tagging performance for L2 and EF when the transverse impact parameter significance is used in defining the discriminant variable $X$, while figures \ref{fig:RejZ0s_L2} and \ref{fig:RejZ0s_EF} show the $b$-tagging performance curves for L2 and EF, when the significance of the longitudinal impact parameter with respect to the primary vertex is used instead. Figures \ref{fig:Rej2Ds_L2} and \ref{fig:Rej2Ds_EF} show the $b$-tagging performance curves for L2 and EF when the likelihood ratio method is built on the combination of the transverse and longitudinal impact parameter significances. %Figures \ref{fig:DisD0s_L2} and \ref{fig:RejD0s_L2} respectively show the distributions %of discriminant variable $X$, based on the transverse %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve %at L2. Figures \ref{fig:DisD0s_EF} and \ref{fig:RejD0s_EF} show the corresponding distributions %at EF. %TODO: normalizzare i plot in numero di entries e togliere griglia nella var. dis. % \begin{figure}[!h] % \begin{minipage}[t]{0.48\textwidth} % \includegraphics[width=0.9\textwidth]{./figures/DisD0s_L2.pdf} % \caption{Distribution of the discriminant variable $X$ based on transverse impact parameter % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at L2.} % \label{fig:DisD0s_L2} % \end{minipage}\hfill %\end{figure} %\begin{figure}[htb] % \begin{minipage}[t]{0.48\textwidth} % \includegraphics[width=0.9\textwidth]{./figures/DisD0s_EF.pdf} % \caption{Distribution of the discriminant variable $X$ based on transverse impact parameter % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at EF.} % \label{fig:DisD0s_EF} % \end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/RejD0s_L2.pdf} \caption{Performance of the $b$-jet selection based on the $d_0$ significance discriminant variable at L2.} \label{fig:RejD0s_L2} \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/RejD0s_EF.pdf} \caption{Performance of the $b$-jet selection based on the $d_0$ significance discriminant variable at EF.} \label{fig:RejD0s_EF} \end{minipage} \end{figure} %Figures \ref{fig:DisZ0s_L2} and \ref{fig:RejZ0s_L2} respectively show the distributions %of discriminant variable $X$, based on the longitudinal %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve at L2. Figures %\ref{fig:DisD0s_EF} and \ref{fig:RejD0s_EF} show the corresponding distributions %at EF. \begin{figure}[!htb] % \begin{minipage}[t]{0.48\textwidth} % \includegraphics[width=0.9\textwidth]{./figures/DisZ0s_L2.pdf} % \caption{Distribution of the discriminant variable $X$ based on longitudinal impact parameter % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at L2.} % \label{fig:DisZ0s_L2} % \end{minipage}\hfill % \begin{minipage}[t]{0.48\textwidth} % \includegraphics[width=0.9\textwidth]{./figures/DisZ0s_EF.pdf} % \caption{Distribution of the discriminant variable $X$ based on longitudinal impact parameter % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at EF.} % \label{fig:DisZ0s_EF} % \end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/RejZ0s_L2.pdf} \caption{Performance of the $b$-jet selection based on the $\delta z_0$ significance discriminant variable at L2.} \label{fig:RejZ0s_L2} \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/RejZ0s_EF.pdf} \caption{Performance of the $b$-jet selection based on the $\delta z_0$ significance discriminant variable at EF.} \label{fig:RejZ0s_EF} \end{minipage} \end{figure} \begin{figure}[!htb] \begin{minipage}[t]{0.48\textwidth} \includegraphics[width=0.9\textwidth]{./figures/Rej2D_L2.pdf} \caption{Performance of the $b$-jet selection based on the combination of the transverse and longitudinal impact parameter significances at L2.} \label{fig:Rej2Ds_L2} \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth}{ \includegraphics[width=0.9\textwidth]{./figures/Rej2D_EF.pdf} \caption{Performance of the $b$-jet selection based on the combination of the transverse and longitudinal impact parameter significances.} \label{fig:Rej2Ds_EF} }\end{minipage} \end{figure} %The combination of the methods analyzed so far will be treated. %The best way to combine $n$ different discriminant variables is to build an $n$-dimensional %discriminant function, since it correctly takes into account the %correlation between the variables. %Figures \ref{fig:Dis2Ds_L2} and \ref{fig:Rej2Ds_L2} respectively show the distributions %of discriminant variable $X$, based on the combination of the transverse and longitudinal %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve at L2. %\begin{figure}[!htb] % \begin{minipage}[t]{0.48\textwidth} % \includegraphics[width=0.9\textwidth]{./figures/Rej2D_L2.pdf} % \caption{Performance of the $b$-jet selection based on the combination of the transverse and % longitudinal impact parameter significances at L2.} % \label{fig:Rej2Ds_L2} % \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth}{ % \includegraphics[width=0.9\textwidth]{./figures/Rej2D_EF.pdf} % \caption{Performance of the $b$-jet selection based on the combination of the transverse % and longitudinal impact parameter significances.} % \label{fig:Rej2Ds_EF} % }\end{minipage} %\end{figure} %\subsubsection{Comparison between different tracking algorithms at L2} %\label{IDSCAN} %The comparison of the performance of the L2 HLT $b$-tagging built with tracks reconstructed by %SiTrack or \IDSCAN algorithm is shown in figure~\ref{fig:IDSCAN}. The tagging method %based on the combination of the transverse and longitudinal impact %parameter has been used. %\begin{figure}[!htb] % \begin{center} % \includegraphics[width=0.6\textwidth]{./figures/LVL1ETB.pdf} % \caption{Performance of the $b$-tagging selection based on the combination of the transverse % and longitudinal impact parameter significances using SiTrack (open dots) or \IDSCAN % (full dots) algorithm.} % \label{fig:IDSCAN} % \end{center} %\end{figure} \subsection{$\chi^2$ method} The performance of the $\chi^2$ $b$-tagging algorithm, evaluated as a function of the $\chi^2$ cut is shown in Figure~\ref{fig:chi2_performance}. The limited efficiency of the method is due to the request of at least two reconstructed tracks to define the track-jet. Cleary, an effort should be made to include RoIs having only a single track. Nonetheless, we note that the strength of the method lies in its impact intrisic robustness and this advantage must also be considered when %Beside the obvious effort to include the RoIs having %only one track in this method it has to be noticed that the strength of this method %consists in its intrinsic robustness. This advantage has to be considered %when comparing its performance with that of the likelihood method. \begin{figure}[!htb] % \begin{minipage}[t]{0.48\textwidth}{ \begin{center} \includegraphics[width=0.5\textwidth]{./figures/chi2_perf.pdf} \caption{Performance of the $b$-tagging selection based on the jet $\chi^2$ probability variable.} \label{fig:chi2_performance} \end{center} % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ % \includegraphics[width=1.1\hsize]{./figures/btgoff.pdf} % \caption{Correlation between L2, EF and offline taggers} %\label{fig:comp} % }\end{minipage} \end{figure} \subsection{Comparison with the offline selection} \label{CompOff} To tune the online working points so as to ensure the attainment of the overall (i.e. including offline cuts) efficiency goal of 60\% for $b$-jet tagging and avoid biases, it is crucial to evaluate the correlation between the online and offline algorithms. The performance of the L2 and EF trigger algorithms based on impact parameters in the transverse plane has been compared to that obtained with the corresponding offline algorithm. This choice is motivated by the wish to perform a coherent comparison; more exhaustive comparison studies will be performed on specific physics selections. Figure \ref{fig:comp} demonstrates that the L2, EF and Offline selections are well correlated. In particular it is always possible to recover the full offline performance at a given $b$-jet efficiency if the L2 and EF working points are set at an appropriate higher efficiency. In particular for the trigger menu studies shown in the following a working point of about 80\% efficiency at L2 and about 70\% at EF have been chosen in order to ensure full acceptance for the standard offline working point (60\%). \begin{figure}[!htb] % \begin{minipage}[t]{0.48\textwidth}{ % \includegraphics[width=1.0\textwidth]{./figures/chi2_perf.pdf} % \caption{Performance of the $b$-tagging selection based on the jet $\chi^2$ probability variable.} % \label{fig:chi2_performance} % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ \begin{center} \includegraphics[width=0.8\hsize]{./figures/btgoff.pdf} \caption{The correlation between L2, EF and offline taggers} \label{fig:comp} \end{center} % }\end{minipage} \end{figure} \subsection{Execution time at L2 and EF} The execution time needed to reconstruct relevant quantities described in this note and to perform $b$-jet selection was evaluated both at L2 and EF. Results highlight that the timing performance fits design requirements and that the overall time spent is dominated by data preparation and track reconstruction algorithms. Further details are given in \cite{CSCHLTTracking}. \section{$b$-tagging trigger strategy} After having defined and characterized the $b$-jet selection algorithm on single $b$-jet RoIs the $b$-jet trigger menu has to be built. Figure~\ref{fig:finalDP} illustrates the online $b$-jet selection algorithm's performance as evaluated using high statistics samples. The performance of the L2 algorithm is indicated along with the performance of the EF algorithm on events which are selected by L2 (at the nominal working point of 80\% efficiency). %The performance on single $b$-jet are summarized on high statistics on Figure~\ref{fig:finalDP} %showing explicitly the EF performance starting from the L2 working point (at about 80\% %$b$-jet efficiency). \begin{figure}[!htb] % \begin{minipage}[t]{0.48\textwidth}{ \begin{center} \includegraphics[width=0.8\hsize]{./figures/HLTbtag_R_vs_eff.pdf} \caption{\label{fig:finalDP} $b$-jet performance based on the combination of the transverse and longitudinal impact parameter (EF selection starts from the chosen L2 working point).} \end{center} \end{figure} \begin{figure}[!htb] % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ \begin{center} \includegraphics[width=0.8\hsize]{./figures/HLTbtag_rate_vs_ET.pdf} \caption{Rate reduction achieved with HLT $b$-jet as a function of the L1 $E_t$ threshold.} \label{fig:RateRed} \end{center} % }\end{minipage} \end{figure} It is clear that the $b$-jet selection can play an important role especially for multi $b$-jets events because the selective filtering of $b$-jets can produce very high rejection and thereby allow a significant decrease of the L1 thresholds while keeping the jet-RoI output rate of L2 and EF almost constant. \subsection{$b$-jet trigger menu} The possible $b$-jet signatures initiated by multi jet L1 signatures with given $E_t$ thresholds can be represented in general as %\begin{itemize} {\bf {\tt \bf nb$E_t$\_mL1J$E_t$}}, where n indicates the number of $b$-tagged jets required out of m L1 jets with transverse energy greater than $E_t$. % \item 3b$E_t$\_3L1J$E_t$: 3 $b$-tagged jet over 3 L1 jets with transverse energy greater than $E_t$ % \item 3b$E_t$\_4L1J$E_t$: 3 $b$-tagged jet over 4 L1 jets with transverse energy greater than $E_t$ % \item 4b$E_t$\_4L1J$E_t$: 4 $b$-tagged jet over 4 L1 jets with transverse energy greater than $E_t$ %\end{itemize} The HLT $b$-tagging working point is the one describe in section~\ref{CompOff}. The rate reduction as a function of the available L1 thresholds is shown in Figure~\ref{fig:RateRed}. The EF output rates of different multi $b$-jet signatures at the luminosity of $10^{31}~cm^{-2}s^{-1}$ are given in Table~\ref{tab:btagrate_summ}. The rates and uncertanties of these rates have been computed on di-jets samples using the relations \begin{eqnarray} \begin{array}{l} p_i = {N^i_{EF}/N^i_{Total}}\\ R = {\cal L}\sum p_i\sigma_i \\ \sigma(R) = {\cal L}\sqrt{\sum {p_i(1-p_i)\over N^i_{Total}}\sigma^2_i} \end{array} \end{eqnarray} where $N^i_{EF}$ and $N^i_{Total}$ are respectively the number of events selected at the end of the trigger chain and the total number of events in the sample $J_i$, $\sigma_i$ is the cross section of the sample $J_i$ and $\cal L$ is the luminosity. The uncertainties in the tables indicate that at high transverse energy, the rate computation is not very precise. Nevertheless, with the requirement of keeping the EF output rate at a few Hz for each multi $b$-jet signature, trigger menus for different luminosities can be chosen as: \begin{itemize} \item luminosity $10^{31}~cm^{-2}s^{-1}$: ~{\bf 3b23\_3L1J23}, ~{\bf 3b18\_4L1J18} \item luminosity $10^{32}~cm^{-2}s^{-1}$: ~{\bf 2b42\_3L1J42}, ~{\bf 3b35\_3L1J35}, ~{\bf 3b23\_4L1J23}, ~{\bf 4b18\_4L1J18} \item luminosity $10^{33}~cm^{-2}s^{-1}$: ~{\bf 2b70\_3L1J70}, ~{\bf 3b42\_3L1J42}, ~{\bf 3b35\_4L1J35}, ~{\bf 4b23\_4L1J23} \end{itemize} It can be noticed that as the luminosity increases, requiring more $b$-tagged jets is a viable alternative to increasing $E_t$ thresholds. \begin{table}[!htb] \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline Transverse energy & \multicolumn{4}{|c|}{Signature rate [Hz]} \\ $E_t$ [GeV] & $2b{E_t}\_3L1JE_t$ & $3b{E_t}\_3L1JE_t$ & $3b{E_t}\_4L1JE_t$ & $4b{E_t}\_4L1JE_t$\\ \hline 18 & $47\pm11$ & $1.5\pm0.4$ & $1.0\pm0.3$ & $0.2\pm0.1$ \\ \hline 23 & $18\pm7$ & $0.5\pm0.2$ & $0.4\pm0.2$ & $0.004\pm0.002$ \\ \hline 35 & $1.0\pm0.2$ & $0.04\pm0.01$ & $0.02\pm0.01$ & $0.0007\pm0.00006$ \\ \hline 42 & $0.4\pm0.1$ & $0.02\pm0.01$ & $0.01\pm0.01$ & $0.0007\pm0.00006$ \\ \hline 70 & $0.01\pm0.02$ & $0.0008\pm0.0006$ & $0.0007\pm0.0006$ & $0.0007\pm0.00006$ \\ \hline \end{tabular} \end{center} \caption{\label{tab:btagrate_summ} EF output rates for the different multi $b$-jet signatures.} \end{table} The strategy behind the evolution of the $b$-jet trigger signatures is to select more aggressively as luminosity increases and HLT tracking becomes better understood. Before the $b$-jet trigger achieves full performance, a good online resolution of track impact parameters %and a reasonable population of the likelihood used in the %tagging process must be achieved. In turn, this requires improving knowledge of the inner detector alignment and of the overall detector performance. % (e.g. to select %the $t$-quark samples required for populating the signal likelihood). %only 2 $b$-jets) and 4b/4j (for events having 4 $b$-jets in the final state), %but i \subsection{Prospects for measuring efficiency and correlation with offline on real data} The HLT $b$-tagging is closely following and contributing to the strategies adopted by the offline $b$-tagging to measure $b$-jet efficiency on real data since the problem is essentially the same. For an explanation of the method and a discussion of its performance we refer to the $b$-tagging note on di-jets~\cite{dijets_note}. In addition to the ``physics'' triggers listed in previous the Section , the $b$-jet group has introduced several ``technical'' triggers in order to study rate and correlation of the online and offline algorithms: \begin{itemize} \item single $b$-jet signatures: $b18$, $b23$, $b35$, $b42$, $b70$: prescaled to limit their contribution to the EF output to few Hz; \item each multi jet item is duplicated with an identical signature which selects, independently of the HLT $b$-jet result, one over $n$ events (where $n$ is presently set at 1000 but will be tuned according to the rate allocated to $b$-jet triggers). \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Summary and conclusion %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \section{Summary and conclusions} The HLT $b$-jet selection at L2 and EF stages of the ATLAS High Level Trigger has been described and characterized. A HLT $b$-tagging trigger menu has been implemented which demonstrates the feasibility of increasing the acceptance of events with more then one $b$-jet by decreasing L1 jet $E_t$ thresholds while keeping a reasonable output rate by introducing a $b$-jet selection at HLT. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Acknowledgements %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %\section{Acknowledgments} \setcounter{section}{0} \begin{thebibliography}{99} \bibitem{DetPap} G. Aad \etal, ATLAS Collaboration {\em The Atlas Experiment at the CERN Large Hadron Collider}, submitted to Journal of Instrumentation. \bibitem{CSCHLTTracking} ATLAS Collaboration, {\em HLT track reconstruction performance}, CSC note EG10 \bibitem{bOff} ATLAS Collaboration, {\em $b$-tagging performance}, CSC note BT0 \bibitem{dijets_note} ATLAS Collaboration, {\em $b$-tagging caibration with di-jet events}, CSC note BT10 \bibitem{chi2_lep} ALEPH Collaboration, {\em A precise measurement of $\Gamma_{Z \rightarrow b \bar{b}} / \Gamma_{Z \rightarrow hadrons}$}, Phys. Lett. B313 (1993) 535. \bibitem{chi2_d0} D$0$ Collaboration, {\em A Search for $Wb\bar{b}$ ad $WH$ Production in $p \bar{p}$ Collisions at $\sqrt{s} = 1.96 TeV$}, Phys. Rev. Lett. 94, 091802 (2005) \bibitem{chi2_cdf} CDF Collaboration, {\em Measurement of the $t\bar{t}$ production cross section in $p \bar{p}$ collisions at $\sqrt{s}=1.96 TeV$ using lepton+jets events with jet probability $b$-tagging}, Phys. Rev. D74, 072006 (2006) \end{thebibliography} % %\input /atlas/paper/authorlist.tex \appendix % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Monte Carlo data samples %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %\include{MC_data_samples} \end{document}