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| 97 : | \begin{document} | ||
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| 100 : | \begin{titlepage} | ||
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| 103 : | \includegraphics[width=3cm]{atlas_logo1.pdf} \hfill | ||
| 104 : | \begin{minipage}[b]{7cm} | ||
| 105 : | \begin{center} | ||
| 106 : | \mbox{\Huge \bf CSC Note BT05} \\ | ||
| 107 : | \end{center} | ||
| 108 : | \begin{center} | ||
| 109 : | \mydocversion | ||
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| 115 : | \hfill \includegraphics[width=3cm]{cern_bw.pdf} | ||
| 116 : | |||
| 117 : | % \vspace*{-1cm} | ||
| 118 : | \title{HLT $b$-tagging performance and strategies} | ||
| 119 : | |||
| 120 : | \author{The ATLAS Collaboration$^{1)}$} | ||
| 121 : | |||
| 122 : | %\begin{center} | ||
| 123 : | %$^{1}$ Dipartimento di Fisica, Universit\`a di Genova and INFN, Genova, Italy\\ | ||
| 124 : | %$^{2}$ Stanford Linear Accelerator Center, Menlo Park, CA, U.S.A | ||
| 125 : | %\end{center} | ||
| 126 : | |||
| 127 : | \begin{abstract} | ||
| 128 : | |||
| 129 : | The selection of $b$-jets at the trigger level aims at improving the flexibility of | ||
| 130 : | the High Level Trigger (HLT) scheme and possibly extending its physics performance, in particular for | ||
| 131 : | topologies containing more than one \mbox{$b$-jet}. | ||
| 132 : | It will be shown that the acceptance for $b$-jets can be increased and background reduced by lowering | ||
| 133 : | jet transverse energy thresholds and applying $b$-tagging selections based on impact parameters of tracks in jets. | ||
| 134 : | %increasing the acceptance for signal events | ||
| 135 : | %while reducing the background. | ||
| 136 : | |||
| 137 : | This note reviews the $b$-jet selection in the HLT and discusses its integration | ||
| 138 : | into the ATLAS trigger menu. | ||
| 139 : | |||
| 140 : | \end{abstract} | ||
| 141 : | % | ||
| 142 : | |||
| 143 : | \vfill | ||
| 144 : | |||
| 145 : | $^{1)}$ This note has been prepared by | ||
| 146 : | A. Coccaro, | ||
| 147 : | G. Critelli, | ||
| 148 : | F. Parodi, | ||
| 149 : | C. Schiavi and | ||
| 150 : | A. Schwartzman. | ||
| 151 : | |||
| 152 : | |||
| 153 : | \newpage | ||
| 154 : | %\boldmath | ||
| 155 : | \tableofcontents | ||
| 156 : | %\unboldmath | ||
| 157 : | |||
| 158 : | |||
| 159 : | \end{titlepage} | ||
| 160 : | |||
| 161 : | \newpage | ||
| 162 : | % | ||
| 163 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 164 : | % Introduction | ||
| 165 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 166 : | % | ||
| 167 : | \section{Introduction} | ||
| 168 : | Final states containing more than one $b$-jet have been proposed as signatures with substantial | ||
| 169 : | discovery potential in a variety of physics channels. The ability to separate $b$-jets from light-quark and | ||
| 170 : | gluon jets is thus an important ingredient of the online selection strategy in ATLAS.\\ | ||
| 171 : | One of the most interesting physics cases addressed by such a $b$-jet trigger selection | ||
| 172 : | involves events with final states containing four $b$-jets. | ||
| 173 : | This event class is relevant for Higgs bosons search in | ||
| 174 : | the low mass range, $m_H < 130\;\mathrm{GeV}$. The most promising channels are the $H \to b\bar{b}$ decay, | ||
| 175 : | where the Standard Model Higgs boson is produced by way of the associated production channel $t\bar{t}H$ and, in | ||
| 176 : | supersymmetric theories, the channels $b\bar{b}H$, $b\bar{b}A$ with $H/A \to b\bar{b}$ or | ||
| 177 : | $H \to hh \to b{\bar b}b{\bar b}$. | ||
| 178 : | |||
| 179 : | The selection of $b$-jets at the trigger level is mainly meant to improve the flexibility of | ||
| 180 : | the HLT scheme, extending its physics performance for the above described topologies. This is achieved | ||
| 181 : | by increasing the acceptance for signal events, while, at the same time, reducing the background. | ||
| 182 : | |||
| 183 : | The $b$-jet selection relies on tracking information | ||
| 184 : | %The first trigger level in which information from the Inner Detector tracking system \cite{DetPap} | ||
| 185 : | which is only available | ||
| 186 : | starting with the Second Level Trigger (L2). Therefore, the acceptance for signal can only be increased by simultaneously | ||
| 187 : | lowering L1 jet thresholds and applying a more discriminating $b$-jet selection in the High Level Trigger (L2 and EF). | ||
| 188 : | High rejection power from the $b$-jet trigger is required | ||
| 189 : | to compensate for less rejection due to lower L1 thresholds and thereby to cope with L2 and EF output rate | ||
| 190 : | budget. | ||
| 191 : | |||
| 192 : | \section{Monte Carlo samples} | ||
| 193 : | |||
| 194 : | The $b$-tagging performance on single jets, presented in this note, is evaluated on $b$-jets from | ||
| 195 : | $H \to b\bar{b}$ decays, where the Higgs boson has a mass of 120 GeV and is produced in association with | ||
| 196 : | a $W$ decaying leptonically. | ||
| 197 : | The standard background for single-jet studies are the corresponding $u$-jets, obtained by artificially | ||
| 198 : | replacing the $b$-quarks from the Higgs decay with $u$-quarks. | ||
| 199 : | While these events imprecisely model | ||
| 200 : | the real | ||
| 201 : | background from light-flavour jets they | ||
| 202 : | %that the $b$-jet trigger has to face, this choice is motivated by the | ||
| 203 : | %need to have a clean source of $u$-jets. Furthermore, the $H \to u\bar{u}$ decay | ||
| 204 : | can be seen as a worst case scenario since the kinematical properties of signal | ||
| 205 : | and background are very similar. | ||
| 206 : | |||
| 207 : | Even in this very simple situation, the association between Regions of Interest (RoI), identified by the | ||
| 208 : | first level trigger, and jets is not uniquely defined: | ||
| 209 : | %As a matter of fact, | ||
| 210 : | a generic $x$-quark in the final state of an interaction or a decay can radiate gluons | ||
| 211 : | and, therefore, change its direction. An RoI from $H\rightarrow b\bar{b}$ or $H\rightarrow u\bar{u}$ | ||
| 212 : | is labeled as $x$-jet ($x=b,\,u$) if an $x$-quark from the original hard process points, after final | ||
| 213 : | state radiation, along the RoI direction within an angular distance of | ||
| 214 : | $\Delta R = \sqrt{\Delta\eta^2+\Delta\phi^2} < 0.1$. | ||
| 215 : | |||
| 216 : | In order to evaluate the rate of the $b$-jet trigger menu, the rejection power must be evaluated on | ||
| 217 : | a more representative background sample. As for all the other trigger selections in ATLAS, di-jet samples | ||
| 218 : | are chosen for this purpose since they correctly include all contributions to the $b$-tagging background, | ||
| 219 : | including $c$-quarks and taus. | ||
| 220 : | |||
| 221 : | All data samples studied in this note have been generated | ||
| 222 : | without pile-up, leaving the influence of pile-up | ||
| 223 : | for further studies. The activity due to underlying event is taken into account since it is built-in | ||
| 224 : | in the event generation (Pythia). | ||
| 225 : | %The simulation and digitazione of the samples have been performed with release 12.0.31.3, the reconstruction | ||
| 226 : | %has been done with release 13.0.30.2 | ||
| 227 : | \section{HLT $b$-jet selection} | ||
| 228 : | |||
| 229 : | \subsection{L1 configuration} | ||
| 230 : | |||
| 231 : | The HLT reconstruction starts from the RoIs selected by the L1 trigger \cite{DetPap}. | ||
| 232 : | In particular, the $b$-jet trigger starts from a L1 jet-RoI $\Delta\eta \times \Delta\phi = 0.8 \times 0.8$ | ||
| 233 : | and performs track and vertex reconstruction in a smaller RoI $\Delta\eta \times \Delta\phi = 0.4 \times 0.4$ | ||
| 234 : | in order to reduce data access and consequently processing time. | ||
| 235 : | |||
| 236 : | %Figure \ref{fig:LVL1ETB} shows the $b$-quark $p_T$ acceptance of the different L1 $E_T$ thresholds. | ||
| 237 : | %\begin{figure}[htb] | ||
| 238 : | % \begin{center} | ||
| 239 : | % \includegraphics[width=0.8\textwidth]{./figures/LVL1ETB.pdf} | ||
| 240 : | % \caption[Transverse momentum distribution]{$p_T$ acceptance of $b$-quarks | ||
| 241 : | % matching different L1 jet-RoI $E_T$ thresholds.} | ||
| 242 : | % \label{fig:LVL1ETB} | ||
| 243 : | % \end{center} | ||
| 244 : | %\end{figure} | ||
| 245 : | |||
| 246 : | \subsection{$b$-jet trigger feature extraction algorithms} | ||
| 247 : | |||
| 248 : | The first step in the $b$-jet trigger chain is, both at L2 and EF, the reconstruction of the relevant | ||
| 249 : | quantities needed to perform the selection. | ||
| 250 : | The $b$-jet RoIs can be separated from light jet RoIs using the impact parameters of the charged tracks, | ||
| 251 : | the properties of reconstructed secondary vertices, or soft leptons; all these quantities are | ||
| 252 : | related to the $b$-quark lifetime and to its decay properties. | ||
| 253 : | |||
| 254 : | |||
| 255 : | The present $b$-jet trigger implementation relies only on the impact parameters of charged tracks. | ||
| 256 : | Primary vertex reconstruction is performed only in the $z$ direction while its coordinates in the transverse | ||
| 257 : | plane are assumed to be compatible with the origin. | ||
| 258 : | |||
| 259 : | Track reconstruction algorithms are described, together with their performance, in \cite{CSCHLTTracking}. | ||
| 260 : | The two Inner Detector tracking algorithms available at L2 show equivalent performance when operating on | ||
| 261 : | jet samples \cite{CSCHLTTracking}. Thus to avoid unnecessary comparisons, the results | ||
| 262 : | obtained with the SiTrack algorithm are presented. | ||
| 263 : | For track reconstruction at the EF, the algorithm corresponding to that used for offline reconstruction | ||
| 264 : | has been adopted (NewTracking). | ||
| 265 : | |||
| 266 : | \subsubsection{Primary vertex reconstruction} | ||
| 267 : | |||
| 268 : | %The track impact parameter in the $RZ$ plane, i.e. $z_0$ of the reconstructed tracks, can be adopted to | ||
| 269 : | %build another discriminant variable for the $b$-tagging selection.\\ | ||
| 270 : | %In analogy with the $d_0$ impact parameter, the $z_0$ distribution shows a peak around the primary vertex | ||
| 271 : | %position ($z_{vtx}$) for tracks coming from $u$-jets, while larger values of $z_0 - z_{vtx}$ are expected for | ||
| 272 : | %$b$-jets. Anyway, unlike what happens for the transverse impact parameter, | ||
| 273 : | |||
| 274 : | Along the $z$ direction no \textit{a priori} knowledge of primary vertex $z_{vtx}$ is available; | ||
| 275 : | this has hence to be reconstructed, starting from the tracks available in the RoI. This information is | ||
| 276 : | needed for the correct evaluation of the longitudinal parameter of each track with respect to the primary interaction position. | ||
| 277 : | |||
| 278 : | The adopted algorithm, a simple histogramming method based on a sliding window, yields | ||
| 279 : | an efficiency of 98(99)\% and a | ||
| 280 : | resolution on $z_{vtx}$ of about $120(100)\mu$m at L2(EF) as illustrated in Figure~\ref{fig:primvtx}. | ||
| 281 : | |||
| 282 : | \begin{figure}[htb] | ||
| 283 : | \begin{center} | ||
| 284 : | \includegraphics[width=0.6\textwidth]{./figures/PrimVtx.pdf} | ||
| 285 : | \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 | ||
| 286 : | are $120~\mu$ and $100~\mu$ respectively.} | ||
| 287 : | \label{fig:primvtx} | ||
| 288 : | \end{center} | ||
| 289 : | \end{figure} | ||
| 290 : | |||
| 291 : | |||
| 292 : | \subsection{Tagging variables} | ||
| 293 : | The HLT $b$-jet tagging methods are based on the transverse and longitudinal | ||
| 294 : | impact parameters of the reconstructed tracks. | ||
| 295 : | %In the following the methods on the transverse and longitudinal parameters of the tracks | ||
| 296 : | %reconstructed are discussed. | ||
| 297 : | Since the methods are the same for L2 and EF they will be described using L2 variables only. | ||
| 298 : | |||
| 299 : | |||
| 300 : | \subsubsection{Transverse impact parameter} | ||
| 301 : | The most natural choice is to build the $b$-tagging discriminant variable from the transverse impact | ||
| 302 : | parameter $d_0$ of the reconstructed tracks. | ||
| 303 : | Since the hadrons containing $b$-quarks have a finite lifetime ($\tau\sim~1.6~ps$), | ||
| 304 : | tracks from their decays are characterized by large $d_0$ values, while tracks from | ||
| 305 : | $u$-jets come dominantly from the primary vertex ($d_{vtx} = 0$). | ||
| 306 : | |||
| 307 : | In particular, the significance of the transverse impact parameter $S=d_0/\sigma(d_0)$ is used, | ||
| 308 : | where $\sigma(d_0)$ is the error on the impact parameter. | ||
| 309 : | The error on the transverse impact parameter at L2 is parametrized as a function | ||
| 310 : | of reconstructed $p_T$ as: | ||
| 311 : | \begin{eqnarray*} | ||
| 312 : | \sigma(d_0) = \sqrt{p_0^2 + \left({p_1 \over p_T}\right)^{p_2}} | ||
| 313 : | \end{eqnarray*} | ||
| 314 : | where $p_0$ is the asymptotic term, $p_1$ is the term due to multiple scattering and $p_2$ is the exponent | ||
| 315 : | of the multiple scattering contribution (close to two). | ||
| 316 : | Although L2 | ||
| 317 : | tracking algorithms have recently reached a good level of precision in the error evaluation, | ||
| 318 : | 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. | ||
| 319 : | |||
| 320 : | %\begin{figure}[htb] | ||
| 321 : | % \begin{center} | ||
| 322 : | % \ifpdf | ||
| 323 : | % \includegraphics[width=0.8\textwidth]{./figures/D0ErrorParametrization.pdf} | ||
| 324 : | % \fi | ||
| 325 : | % \caption{Parametrization of the error on $d_0$ as a function of the reconstructed $p_T$.} | ||
| 326 : | % \label{fig:D0ErrorParametrization} | ||
| 327 : | % \end{center} | ||
| 328 : | %\end{figure} | ||
| 329 : | |||
| 330 : | Figure \ref{fig:VarD0s_L2} | ||
| 331 : | %and \ref{fig:VarD0s_EF} | ||
| 332 : | shows the distributions | ||
| 333 : | of the impact parameter significance $d_0/\sigma(d_0)$ for $b$-jets and light jets at L2. | ||
| 334 : | The significance has been rescaled according to the function | ||
| 335 : | $f(x)=log(1+|x|)$ in order to have a reasonably uniform bin population along the $x$ axis. | ||
| 336 : | From these plots it can be guessed that the impact parameter significance is a promising | ||
| 337 : | choice for the discriminant variable, since the two distribution are very well separated. | ||
| 338 : | \begin{figure}[!t] | ||
| 339 : | % \ifpdf | ||
| 340 : | \begin{center} | ||
| 341 : | \begin{minipage}[t]{0.48\textwidth} | ||
| 342 : | % \ifpdf | ||
| 343 : | \includegraphics[width=1.\textwidth]{./figures/VarD0s_L2.pdf} | ||
| 344 : | % \fi | ||
| 345 : | \caption{Distribution of the rescaled function (described in the text) of the transverse impact parameter significance for tracks coming from | ||
| 346 : | $b$-jets (solid line) and light jets (dashed line) at L2.} | ||
| 347 : | \label{fig:VarD0s_L2} | ||
| 348 : | \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} | ||
| 349 : | % \ifpdf | ||
| 350 : | \includegraphics[width=1.\textwidth]{./figures/VarZ0_L2.pdf} | ||
| 351 : | % \fi | ||
| 352 : | \caption{Distribution of the rescaled function (described in the text) | ||
| 353 : | of the longitudinal impact parameter significance for tracks coming from | ||
| 354 : | $b$-jets (solid line) and light jets (dashed line) at L2.} | ||
| 355 : | \label{fig:VarZ0_L2} | ||
| 356 : | \end{minipage} | ||
| 357 : | %\begin{minipage}[t]{0.48\textwidth} | ||
| 358 : | % \ifpdf | ||
| 359 : | % \includegraphics[width=1.\textwidth]{./figures/VarD0s_EF.pdf} | ||
| 360 : | % \fi | ||
| 361 : | % \caption{Distribution of the rescaled function (described in the text) of the transverse impact parameter significance for tracks coming from | ||
| 362 : | % $b$-jets (shaded plot) and light jets (dashed line) at EF.} | ||
| 363 : | % \label{fig:VarD0s_EF} | ||
| 364 : | % \end{minipage} | ||
| 365 : | \end{center} | ||
| 366 : | \end{figure} | ||
| 367 : | |||
| 368 : | \subsubsection{Longitudinal impact parameter} | ||
| 369 : | |||
| 370 : | The longitudinal impact parameter ($z_0$), i.e. the track's z-intercept, can be adopted, | ||
| 371 : | as well as the transverse impact parameter, to discriminate between $b$-jets and light jets. | ||
| 372 : | After the primary vertex position has been reconstructed, the $\delta z_0 = z_0 - z_{vtx}$ variable can be | ||
| 373 : | used to form a discriminant which can then be used for $b$-jet selection. | ||
| 374 : | Figure \ref{fig:VarZ0_L2} | ||
| 375 : | %and \ref{fig:VarZ0_EF} | ||
| 376 : | shows the distributions | ||
| 377 : | of the longitudinal impact parameter significance | ||
| 378 : | ($\delta z_0/\sigma(z_0)$) of $b$-jets and light jets at L2. | ||
| 379 : | The significance has been rescaled as described above for the transverse impact parameter. | ||
| 380 : | |||
| 381 : | |||
| 382 : | As for Figure~\ref{fig:VarD0s_L2}, | ||
| 383 : | the signal and background distributions are different | ||
| 384 : | although much less so than for the transverse impact parameter significance. | ||
| 385 : | From this comparison, it is clear | ||
| 386 : | %. Anyway, from these plots we can | ||
| 387 : | %already argue | ||
| 388 : | that most of the discriminant power will be provided by the measured | ||
| 389 : | transverse impact parameter significance. | ||
| 390 : | %, which shows a sharper separation between signal and background. | ||
| 391 : | The worse resolution of the longitudinal impact parameter significance | ||
| 392 : | is due both to the coarser resolution of the silicon tracking detectors along the $z$-direction, | ||
| 393 : | bigger extrapolation distance from innermost silicon layer hit to primary vertex at high $\eta$ | ||
| 394 : | and to the resolution of the reconstructed primary vertex. | ||
| 395 : | |||
| 396 : | %\begin{figure}[htb] | ||
| 397 : | % \ifpdf | ||
| 398 : | % \begin{center} | ||
| 399 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 400 : | % \ifpdf | ||
| 401 : | % \includegraphics[width=1.\textwidth]{./figures/VarZ0_L2.pdf} | ||
| 402 : | % \fi | ||
| 403 : | % \caption{Distribution of the rescaled function (described in the text) | ||
| 404 : | % of the longitudinal impact parameter significance for tracks coming from | ||
| 405 : | % $b$-jets (shaded plot) and light jets (dashed line) at L2.} | ||
| 406 : | % \label{fig:VarZ0_L2} | ||
| 407 : | % \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} | ||
| 408 : | % \ifpdf | ||
| 409 : | % \includegraphics[width=1.\textwidth]{./figures/VarZ0_EF.pdf} | ||
| 410 : | % \fi | ||
| 411 : | % \caption{Distribution of the rescaled function (described in the text) | ||
| 412 : | % of the longitudinal impact parameter significance for tracks coming from | ||
| 413 : | % $b$-jets (shaded plot) and light jets (dashed line) at EF.} | ||
| 414 : | % \label{fig:VarZ0_EF} | ||
| 415 : | % \end{minipage} | ||
| 416 : | % \end{center} | ||
| 417 : | %\end{figure} | ||
| 418 : | |||
| 419 : | |||
| 420 : | |||
| 421 : | \subsection{HLT $b$-jet tagging methods} | ||
| 422 : | |||
| 423 : | In this section, HLT $b$-tagging methods are described. | ||
| 424 : | The likelihood ratio method is quite general and can be applied to different variables | ||
| 425 : | while the $\chi^2$ method is essentially designed to test the compatibility of the tracks | ||
| 426 : | with respect to the primary vertex using the transverse impact parameter. | ||
| 427 : | |||
| 428 : | The likelihood ratio, using information on the signal and background shape that have to be | ||
| 429 : | estimated on real data, is more powerful but also more difficult to tune while the $\chi^2$ | ||
| 430 : | method can be easily tuned but is less powerful. | ||
| 431 : | |||
| 432 : | \subsubsection{The likelihood-ratio method} | ||
| 433 : | The likelihood-ratio method is a statistical tool used to separate two or more event classes, and is based on a set of | ||
| 434 : | characteristic variables.\\ | ||
| 435 : | The likelihood-ratio variable $W$ is evaluated, for a given event, as the ratio between the probability distributions for | ||
| 436 : | two alternative hypotheses. In its application to $b$-jet selection, the likelihood-ratio variable is defined as | ||
| 437 : | \begin{displaymath} | ||
| 438 : | W = S(s)/S(b), | ||
| 439 : | \end{displaymath} | ||
| 440 : | where $S(s)$ and $S(b)$ are the probability densities for the signal, the $b$-jets, and the background, represented in | ||
| 441 : | this case by the $u$-jets.\\ | ||
| 442 : | This variable is widely used to obtain the best possible separation between signal and background, in terms of a single | ||
| 443 : | variable, in fits aimed at extracting the fraction of signal events in a given sample. The same variable can be also | ||
| 444 : | directly used, as in the $b$-jet selection case, to select signal events, for example by applying a cut on the | ||
| 445 : | likelihood-ratio variable itself.\\ | ||
| 446 : | The probability density distributions used in the $b$-tagging application can be functions of some parameter of each track | ||
| 447 : | (e.g. the transverse impact parameter $d_0$) or of some collective property of the jet (e.g. its track multiplicity). In | ||
| 448 : | the first case, these distributions take the form | ||
| 449 : | \begin{eqnarray*} | ||
| 450 : | s(par_{1}, par_{2}, par_{3}, \dots, par_{n}),\\ | ||
| 451 : | b(par_{1}, par_{2}, par_{3}, \dots, par_{n}), | ||
| 452 : | \end{eqnarray*} | ||
| 453 : | where the $1, \dots, n$ indices identify each track belonging to the jet. The corresponding likelihood-ratio variable is | ||
| 454 : | thus defined as | ||
| 455 : | \begin{displaymath} | ||
| 456 : | W = \frac{ s(par_{1}, par_{2}, par_{3}, \dots, par_{n})} | ||
| 457 : | { b(par_{1}, par_{2}, par_{3}, \dots, par_{n}) } | ||
| 458 : | \end{displaymath} | ||
| 459 : | Exact evaluation of the $s$ and $b$ functions is very difficult, since it would require an almost infinite amount of | ||
| 460 : | simulated data; for example, in order to reasonably populate an $n$-dimensional cube, about 100 entries are needed | ||
| 461 : | for each dimension, corresponding to $n^{100}$ tracks; even worse, the number of tracks in a jet is not fixed. | ||
| 462 : | However, if we assume that the variables corresponding to different tracks are independent, the ratio between the overall | ||
| 463 : | probability densities reduces to the product of the ratios of the single probability densities: | ||
| 464 : | \begin{displaymath} | ||
| 465 : | W = \prod_{i=1}^{n} \frac{ s(par_{i}) }{ b(par_{i}) }, | ||
| 466 : | \end{displaymath} | ||
| 467 : | which is much easier to evaluate.\\ | ||
| 468 : | In the $b$-tagging case, track parameters have complex correlations which depend | ||
| 469 : | on the proper time for the $B$ hadron and on its decay kinematics. Nevertheless it can be proven that, neglecting these | ||
| 470 : | correlations, no mistake is made; simply, the discriminant power of the $W$ variable will be slightly reduced.\\ | ||
| 471 : | The $W$ variable, can take any value between $0$ (for the background) and $+\infty$ (for the signal). For practical | ||
| 472 : | reasons, it is useful to handle a variable defined on a finite interval; to achieve this, $W$ is usually replaced by | ||
| 473 : | another variable | ||
| 474 : | \begin{displaymath} | ||
| 475 : | X = \frac{W}{1+W}, | ||
| 476 : | \end{displaymath} | ||
| 477 : | which can only range between $0$ and $1$.\\ | ||
| 478 : | |||
| 479 : | As an illustration of the method, | ||
| 480 : | Figures \ref{fig:Dis2Ds_L2} and \ref{fig:Dis2Ds_EF} show the distributions | ||
| 481 : | of the discriminant variable $X$ which is based on the combination of the transverse and longitudinal | ||
| 482 : | impact parameter for $b$-jets and light jets respectively at L2 and EF. | ||
| 483 : | It can be seen that signal events ($b$-jets) accumulate near to $X=1$, | ||
| 484 : | while the background (light jets) tends to have $X$ close to $0$. | ||
| 485 : | |||
| 486 : | \begin{figure}[!htb] | ||
| 487 : | \begin{minipage}[t]{0.48\textwidth} | ||
| 488 : | \includegraphics[width=0.9\textwidth]{./figures/Dis2D_L2.pdf} | ||
| 489 : | \caption{Distribution of the discriminant variable $X$ based on the combination of the transverse | ||
| 490 : | and longitudinal impact parameter significances for $b$-jets and $u$-jets | ||
| 491 : | (shaded area) at L2.} | ||
| 492 : | \label{fig:Dis2Ds_L2} | ||
| 493 : | \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} | ||
| 494 : | \includegraphics[width=0.9\textwidth]{./figures/Dis2D_EF.pdf} | ||
| 495 : | \caption{Distribution of the discriminant variable $X$ based on the combination of the transverse | ||
| 496 : | and longitudinal impact parameter significances for $b$-jets and $u$-jets | ||
| 497 : | (shaded area) at EF.} | ||
| 498 : | \label{fig:Dis2Ds_EF} | ||
| 499 : | \end{minipage} | ||
| 500 : | \end{figure} | ||
| 501 : | |||
| 502 : | |||
| 503 : | |||
| 504 : | |||
| 505 : | |||
| 506 : | Contrary to the offline $b$-tagging methods based on likelihood ratio the sign of the impact parameters | ||
| 507 : | is currently not used at HLT since the RoI direction doesn't give a precise estimation of the $b$-jet direction. | ||
| 508 : | Future studies will use the impact parameter sign determination described in the next Section. | ||
| 509 : | |||
| 510 : | \input chi2_method.tex | ||
| 511 : | |||
| 512 : | \section{HLT $b$-jet selection performance on single jet-RoIs} | ||
| 513 : | |||
| 514 : | Every tagging method will be characterized by the curve showing the light-jet | ||
| 515 : | rejection | ||
| 516 : | versus the efficiency to select $b$-jets ($\epsilon_b$). | ||
| 517 : | The light-jet rejection is defined as the inverse of the efficiency | ||
| 518 : | of selecting $u$-jets ($R_u = 1/\epsilon_u$) where we have assumed that u-jets are | ||
| 519 : | representative of light jets in general. | ||
| 520 : | |||
| 521 : | |||
| 522 : | |||
| 523 : | \subsection{Likelihood ratio method using impact parameters} | ||
| 524 : | |||
| 525 : | Figures \ref{fig:RejD0s_L2} and \ref{fig:RejD0s_EF} | ||
| 526 : | show, respectively, the $b$-tagging performance for L2 and EF | ||
| 527 : | when the transverse | ||
| 528 : | impact parameter significance is used in defining the discriminant variable $X$, while | ||
| 529 : | figures \ref{fig:RejZ0s_L2} and \ref{fig:RejZ0s_EF} | ||
| 530 : | show the $b$-tagging performance curves for L2 and EF, | ||
| 531 : | when the significance of the longitudinal impact parameter with respect | ||
| 532 : | to the primary vertex is used instead. | ||
| 533 : | |||
| 534 : | |||
| 535 : | Figures \ref{fig:Rej2Ds_L2} and \ref{fig:Rej2Ds_EF} | ||
| 536 : | show the $b$-tagging performance curves for L2 and EF | ||
| 537 : | when the likelihood ratio method is built on the combination of the transverse and longitudinal impact parameter significances. | ||
| 538 : | |||
| 539 : | |||
| 540 : | %Figures \ref{fig:DisD0s_L2} and \ref{fig:RejD0s_L2} respectively show the distributions | ||
| 541 : | %of discriminant variable $X$, based on the transverse | ||
| 542 : | %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve | ||
| 543 : | %at L2. Figures \ref{fig:DisD0s_EF} and \ref{fig:RejD0s_EF} show the corresponding distributions | ||
| 544 : | %at EF. | ||
| 545 : | |||
| 546 : | %TODO: normalizzare i plot in numero di entries e togliere griglia nella var. dis. | ||
| 547 : | % | ||
| 548 : | \begin{figure}[!h] | ||
| 549 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 550 : | % \includegraphics[width=0.9\textwidth]{./figures/DisD0s_L2.pdf} | ||
| 551 : | % \caption{Distribution of the discriminant variable $X$ based on transverse impact parameter | ||
| 552 : | % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at L2.} | ||
| 553 : | % \label{fig:DisD0s_L2} | ||
| 554 : | % \end{minipage}\hfill | ||
| 555 : | %\end{figure} | ||
| 556 : | %\begin{figure}[htb] | ||
| 557 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 558 : | % \includegraphics[width=0.9\textwidth]{./figures/DisD0s_EF.pdf} | ||
| 559 : | % \caption{Distribution of the discriminant variable $X$ based on transverse impact parameter | ||
| 560 : | % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at EF.} | ||
| 561 : | % \label{fig:DisD0s_EF} | ||
| 562 : | % \end{minipage}\hfill | ||
| 563 : | \begin{minipage}[t]{0.48\textwidth} | ||
| 564 : | \includegraphics[width=0.9\textwidth]{./figures/RejD0s_L2.pdf} | ||
| 565 : | \caption{Performance of the $b$-jet selection based on the $d_0$ significance | ||
| 566 : | discriminant variable at L2.} | ||
| 567 : | \label{fig:RejD0s_L2} | ||
| 568 : | \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} | ||
| 569 : | \includegraphics[width=0.9\textwidth]{./figures/RejD0s_EF.pdf} | ||
| 570 : | \caption{Performance of the $b$-jet selection based on the $d_0$ significance | ||
| 571 : | discriminant variable at EF.} | ||
| 572 : | \label{fig:RejD0s_EF} | ||
| 573 : | \end{minipage} | ||
| 574 : | \end{figure} | ||
| 575 : | |||
| 576 : | %Figures \ref{fig:DisZ0s_L2} and \ref{fig:RejZ0s_L2} respectively show the distributions | ||
| 577 : | %of discriminant variable $X$, based on the longitudinal | ||
| 578 : | %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve at L2. Figures | ||
| 579 : | %\ref{fig:DisD0s_EF} and \ref{fig:RejD0s_EF} show the corresponding distributions | ||
| 580 : | %at EF. | ||
| 581 : | |||
| 582 : | \begin{figure}[!htb] | ||
| 583 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 584 : | % \includegraphics[width=0.9\textwidth]{./figures/DisZ0s_L2.pdf} | ||
| 585 : | % \caption{Distribution of the discriminant variable $X$ based on longitudinal impact parameter | ||
| 586 : | % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at L2.} | ||
| 587 : | % \label{fig:DisZ0s_L2} | ||
| 588 : | % \end{minipage}\hfill | ||
| 589 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 590 : | % \includegraphics[width=0.9\textwidth]{./figures/DisZ0s_EF.pdf} | ||
| 591 : | % \caption{Distribution of the discriminant variable $X$ based on longitudinal impact parameter | ||
| 592 : | % significance for $b$-jets (shaded plot) and $u$-jets (dashed line) at EF.} | ||
| 593 : | % \label{fig:DisZ0s_EF} | ||
| 594 : | % \end{minipage}\hfill | ||
| 595 : | \begin{minipage}[t]{0.48\textwidth} | ||
| 596 : | \includegraphics[width=0.9\textwidth]{./figures/RejZ0s_L2.pdf} | ||
| 597 : | \caption{Performance of the $b$-jet selection based on the $\delta z_0$ significance | ||
| 598 : | discriminant variable at L2.} | ||
| 599 : | \label{fig:RejZ0s_L2} | ||
| 600 : | \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth} | ||
| 601 : | \includegraphics[width=0.9\textwidth]{./figures/RejZ0s_EF.pdf} | ||
| 602 : | \caption{Performance of the $b$-jet selection based on the $\delta z_0$ significance | ||
| 603 : | discriminant variable at EF.} | ||
| 604 : | \label{fig:RejZ0s_EF} | ||
| 605 : | \end{minipage} | ||
| 606 : | \end{figure} | ||
| 607 : | |||
| 608 : | \begin{figure}[!htb] | ||
| 609 : | \begin{minipage}[t]{0.48\textwidth} | ||
| 610 : | \includegraphics[width=0.9\textwidth]{./figures/Rej2D_L2.pdf} | ||
| 611 : | \caption{Performance of the $b$-jet selection based on the combination of the transverse and | ||
| 612 : | longitudinal impact parameter significances at L2.} | ||
| 613 : | \label{fig:Rej2Ds_L2} | ||
| 614 : | \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth}{ | ||
| 615 : | \includegraphics[width=0.9\textwidth]{./figures/Rej2D_EF.pdf} | ||
| 616 : | \caption{Performance of the $b$-jet selection based on the combination of the transverse | ||
| 617 : | and longitudinal impact parameter significances.} | ||
| 618 : | \label{fig:Rej2Ds_EF} | ||
| 619 : | }\end{minipage} | ||
| 620 : | \end{figure} | ||
| 621 : | |||
| 622 : | |||
| 623 : | %The combination of the methods analyzed so far will be treated. | ||
| 624 : | %The best way to combine $n$ different discriminant variables is to build an $n$-dimensional | ||
| 625 : | %discriminant function, since it correctly takes into account the | ||
| 626 : | %correlation between the variables. | ||
| 627 : | %Figures \ref{fig:Dis2Ds_L2} and \ref{fig:Rej2Ds_L2} respectively show the distributions | ||
| 628 : | %of discriminant variable $X$, based on the combination of the transverse and longitudinal | ||
| 629 : | %impact parameter, for $b$-jets and light jets and the corresponding $b$-tagging curve at L2. | ||
| 630 : | |||
| 631 : | %\begin{figure}[!htb] | ||
| 632 : | % \begin{minipage}[t]{0.48\textwidth} | ||
| 633 : | % \includegraphics[width=0.9\textwidth]{./figures/Rej2D_L2.pdf} | ||
| 634 : | % \caption{Performance of the $b$-jet selection based on the combination of the transverse and | ||
| 635 : | % longitudinal impact parameter significances at L2.} | ||
| 636 : | % \label{fig:Rej2Ds_L2} | ||
| 637 : | % \end{minipage}\hfill\begin{minipage}[t]{0.48\textwidth}{ | ||
| 638 : | % \includegraphics[width=0.9\textwidth]{./figures/Rej2D_EF.pdf} | ||
| 639 : | % \caption{Performance of the $b$-jet selection based on the combination of the transverse | ||
| 640 : | % and longitudinal impact parameter significances.} | ||
| 641 : | % \label{fig:Rej2Ds_EF} | ||
| 642 : | % }\end{minipage} | ||
| 643 : | %\end{figure} | ||
| 644 : | |||
| 645 : | |||
| 646 : | %\subsubsection{Comparison between different tracking algorithms at L2} | ||
| 647 : | %\label{IDSCAN} | ||
| 648 : | |||
| 649 : | %The comparison of the performance of the L2 HLT $b$-tagging built with tracks reconstructed by | ||
| 650 : | %SiTrack or \IDSCAN algorithm is shown in figure~\ref{fig:IDSCAN}. The tagging method | ||
| 651 : | %based on the combination of the transverse and longitudinal impact | ||
| 652 : | %parameter has been used. | ||
| 653 : | |||
| 654 : | %\begin{figure}[!htb] | ||
| 655 : | % \begin{center} | ||
| 656 : | % \includegraphics[width=0.6\textwidth]{./figures/LVL1ETB.pdf} | ||
| 657 : | % \caption{Performance of the $b$-tagging selection based on the combination of the transverse | ||
| 658 : | % and longitudinal impact parameter significances using SiTrack (open dots) or \IDSCAN | ||
| 659 : | % (full dots) algorithm.} | ||
| 660 : | % \label{fig:IDSCAN} | ||
| 661 : | % \end{center} | ||
| 662 : | %\end{figure} | ||
| 663 : | |||
| 664 : | |||
| 665 : | |||
| 666 : | \subsection{$\chi^2$ method} | ||
| 667 : | |||
| 668 : | The performance of the $\chi^2$ $b$-tagging algorithm, evaluated as a function of the $\chi^2$ cut | ||
| 669 : | is shown in Figure~\ref{fig:chi2_performance}. | ||
| 670 : | The limited efficiency of the method is due to the request of at least two reconstructed | ||
| 671 : | tracks to define the track-jet. | ||
| 672 : | Cleary, an effort should be made to include RoIs having only a single track. | ||
| 673 : | Nonetheless, we note that the strength of the method lies in its impact | ||
| 674 : | intrisic robustness and this advantage must also be considered when | ||
| 675 : | %Beside the obvious effort to include the RoIs having | ||
| 676 : | %only one track in this method it has to be noticed that the strength of this method | ||
| 677 : | %consists in its intrinsic robustness. This advantage has to be considered | ||
| 678 : | %when | ||
| 679 : | comparing its performance with that of the likelihood method. | ||
| 680 : | |||
| 681 : | \begin{figure}[!htb] | ||
| 682 : | % \begin{minipage}[t]{0.48\textwidth}{ | ||
| 683 : | \begin{center} | ||
| 684 : | \includegraphics[width=0.5\textwidth]{./figures/chi2_perf.pdf} | ||
| 685 : | \caption{Performance of the $b$-tagging selection based on the jet $\chi^2$ probability variable.} | ||
| 686 : | \label{fig:chi2_performance} | ||
| 687 : | \end{center} | ||
| 688 : | % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ | ||
| 689 : | % \includegraphics[width=1.1\hsize]{./figures/btgoff.pdf} | ||
| 690 : | % \caption{Correlation between L2, EF and offline taggers} | ||
| 691 : | %\label{fig:comp} | ||
| 692 : | % }\end{minipage} | ||
| 693 : | \end{figure} | ||
| 694 : | |||
| 695 : | |||
| 696 : | |||
| 697 : | |||
| 698 : | |||
| 699 : | |||
| 700 : | |||
| 701 : | |||
| 702 : | \subsection{Comparison with the offline selection} | ||
| 703 : | \label{CompOff} | ||
| 704 : | |||
| 705 : | 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 | ||
| 706 : | between the online and offline algorithms. | ||
| 707 : | |||
| 708 : | |||
| 709 : | The performance of the L2 and EF trigger algorithms based on impact parameters in the transverse plane | ||
| 710 : | has been compared to that obtained with the corresponding offline algorithm. This | ||
| 711 : | choice is motivated by the wish to perform a coherent comparison; more exhaustive | ||
| 712 : | comparison studies will be performed on specific physics selections. | ||
| 713 : | |||
| 714 : | Figure \ref{fig:comp} demonstrates that the L2, EF and Offline selections are well correlated. | ||
| 715 : | In particular it is always possible to recover the full offline performance at a given | ||
| 716 : | $b$-jet efficiency if the L2 and EF working points are set at an appropriate higher efficiency. | ||
| 717 : | In particular for the trigger menu studies shown in the following a working point of about 80\% | ||
| 718 : | efficiency at L2 and about 70\% at EF have been chosen in order to ensure | ||
| 719 : | full acceptance for the standard offline working point (60\%). | ||
| 720 : | |||
| 721 : | |||
| 722 : | |||
| 723 : | \begin{figure}[!htb] | ||
| 724 : | % \begin{minipage}[t]{0.48\textwidth}{ | ||
| 725 : | % \includegraphics[width=1.0\textwidth]{./figures/chi2_perf.pdf} | ||
| 726 : | % \caption{Performance of the $b$-tagging selection based on the jet $\chi^2$ probability variable.} | ||
| 727 : | % \label{fig:chi2_performance} | ||
| 728 : | % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ | ||
| 729 : | \begin{center} | ||
| 730 : | \includegraphics[width=0.8\hsize]{./figures/btgoff.pdf} | ||
| 731 : | \caption{The correlation between L2, EF and offline taggers} | ||
| 732 : | \label{fig:comp} | ||
| 733 : | \end{center} | ||
| 734 : | % }\end{minipage} | ||
| 735 : | \end{figure} | ||
| 736 : | |||
| 737 : | \subsection{Execution time at L2 and EF} | ||
| 738 : | |||
| 739 : | The execution time needed to reconstruct relevant quantities described in this note | ||
| 740 : | and to perform $b$-jet selection was evaluated both at L2 and EF. Results highlight that the timing performance fits design | ||
| 741 : | requirements and that the overall time spent is dominated by data preparation and track reconstruction | ||
| 742 : | algorithms. | ||
| 743 : | Further details are given in \cite{CSCHLTTracking}. | ||
| 744 : | |||
| 745 : | \section{$b$-tagging trigger strategy} | ||
| 746 : | |||
| 747 : | After having defined and characterized the $b$-jet selection algorithm on single $b$-jet RoIs | ||
| 748 : | the $b$-jet trigger menu has to be built. | ||
| 749 : | 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 | ||
| 750 : | the performance of the EF algorithm on events which are selected by L2 (at the nominal working point of 80\% efficiency). | ||
| 751 : | %The performance on single $b$-jet are summarized on high statistics on Figure~\ref{fig:finalDP} | ||
| 752 : | %showing explicitly the EF performance starting from the L2 working point (at about 80\% | ||
| 753 : | %$b$-jet efficiency). | ||
| 754 : | \begin{figure}[!htb] | ||
| 755 : | % \begin{minipage}[t]{0.48\textwidth}{ | ||
| 756 : | \begin{center} | ||
| 757 : | \includegraphics[width=0.8\hsize]{./figures/HLTbtag_R_vs_eff.pdf} | ||
| 758 : | \caption{\label{fig:finalDP} $b$-jet performance based on the combination of the transverse and longitudinal | ||
| 759 : | impact parameter (EF selection starts from the chosen L2 working point).} | ||
| 760 : | \end{center} | ||
| 761 : | \end{figure} | ||
| 762 : | \begin{figure}[!htb] | ||
| 763 : | % }\end{minipage}\hfill \begin{minipage}[t]{0.48\textwidth}{ | ||
| 764 : | \begin{center} | ||
| 765 : | \includegraphics[width=0.8\hsize]{./figures/HLTbtag_rate_vs_ET.pdf} | ||
| 766 : | \caption{Rate reduction achieved with HLT $b$-jet as a function of the L1 $E_t$ threshold.} | ||
| 767 : | \label{fig:RateRed} | ||
| 768 : | \end{center} | ||
| 769 : | % }\end{minipage} | ||
| 770 : | \end{figure} | ||
| 771 : | It is clear that the $b$-jet selection can play an important role especially for | ||
| 772 : | multi $b$-jets events because the selective filtering of $b$-jets can produce | ||
| 773 : | very high rejection and thereby allow a significant decrease of the L1 thresholds | ||
| 774 : | while keeping the jet-RoI output rate of L2 and EF almost constant. | ||
| 775 : | |||
| 776 : | \subsection{$b$-jet trigger menu} | ||
| 777 : | |||
| 778 : | The possible $b$-jet signatures initiated by multi jet L1 signatures with given $E_t$ thresholds | ||
| 779 : | can be represented in general as | ||
| 780 : | %\begin{itemize} | ||
| 781 : | {\bf {\tt \bf nb$E_t$\_mL1J$E_t$}}, | ||
| 782 : | where n indicates the number of $b$-tagged jets required out of m L1 jets with transverse energy greater than $E_t$. | ||
| 783 : | % \item 3b$E_t$\_3L1J$E_t$: 3 $b$-tagged jet over 3 L1 jets with transverse energy greater than $E_t$ | ||
| 784 : | % \item 3b$E_t$\_4L1J$E_t$: 3 $b$-tagged jet over 4 L1 jets with transverse energy greater than $E_t$ | ||
| 785 : | % \item 4b$E_t$\_4L1J$E_t$: 4 $b$-tagged jet over 4 L1 jets with transverse energy greater than $E_t$ | ||
| 786 : | %\end{itemize} | ||
| 787 : | The HLT $b$-tagging working point is the one describe in section~\ref{CompOff}. | ||
| 788 : | The rate reduction as a function of the available L1 thresholds is | ||
| 789 : | shown in Figure~\ref{fig:RateRed}. | ||
| 790 : | The EF output rates of different multi $b$-jet signatures at the luminosity of $10^{31}~cm^{-2}s^{-1}$ | ||
| 791 : | are given in Table~\ref{tab:btagrate_summ}. | ||
| 792 : | The rates and uncertanties of these rates have been computed on di-jets samples using the relations | ||
| 793 : | \begin{eqnarray} | ||
| 794 : | \begin{array}{l} | ||
| 795 : | p_i = {N^i_{EF}/N^i_{Total}}\\ | ||
| 796 : | R = {\cal L}\sum p_i\sigma_i \\ | ||
| 797 : | \sigma(R) = {\cal L}\sqrt{\sum {p_i(1-p_i)\over N^i_{Total}}\sigma^2_i} | ||
| 798 : | \end{array} | ||
| 799 : | \end{eqnarray} | ||
| 800 : | where $N^i_{EF}$ and $N^i_{Total}$ are respectively the number of events selected at the end of the trigger chain and | ||
| 801 : | the total number of events in the sample $J_i$, $\sigma_i$ is the cross section of the sample $J_i$ and $\cal L$ | ||
| 802 : | is the luminosity. | ||
| 803 : | |||
| 804 : | The uncertainties in the tables indicate that at high transverse energy, the rate computation is not | ||
| 805 : | very precise. Nevertheless, with the requirement of keeping the EF output rate at a few Hz for each | ||
| 806 : | multi $b$-jet signature, trigger menus for different luminosities can be chosen as: | ||
| 807 : | \begin{itemize} | ||
| 808 : | \item luminosity $10^{31}~cm^{-2}s^{-1}$: | ||
| 809 : | ~{\bf 3b23\_3L1J23}, | ||
| 810 : | ~{\bf 3b18\_4L1J18} | ||
| 811 : | \item luminosity $10^{32}~cm^{-2}s^{-1}$: | ||
| 812 : | ~{\bf 2b42\_3L1J42}, ~{\bf 3b35\_3L1J35}, | ||
| 813 : | ~{\bf 3b23\_4L1J23}, | ||
| 814 : | ~{\bf 4b18\_4L1J18} | ||
| 815 : | \item luminosity $10^{33}~cm^{-2}s^{-1}$: | ||
| 816 : | ~{\bf 2b70\_3L1J70}, | ||
| 817 : | ~{\bf 3b42\_3L1J42}, | ||
| 818 : | ~{\bf 3b35\_4L1J35}, | ||
| 819 : | ~{\bf 4b23\_4L1J23} | ||
| 820 : | \end{itemize} | ||
| 821 : | It can be noticed that as the luminosity increases, requiring more $b$-tagged jets is a viable alternative to | ||
| 822 : | increasing $E_t$ thresholds. | ||
| 823 : | |||
| 824 : | \begin{table}[!htb] | ||
| 825 : | \begin{center} | ||
| 826 : | \begin{tabular}{|c|c|c|c|c|} | ||
| 827 : | \hline | ||
| 828 : | Transverse energy & \multicolumn{4}{|c|}{Signature rate [Hz]} \\ | ||
| 829 : | $E_t$ [GeV] & $2b{E_t}\_3L1JE_t$ & $3b{E_t}\_3L1JE_t$ & $3b{E_t}\_4L1JE_t$ & $4b{E_t}\_4L1JE_t$\\ \hline | ||
| 830 : | 18 & $47\pm11$ & $1.5\pm0.4$ & $1.0\pm0.3$ & $0.2\pm0.1$ \\ \hline | ||
| 831 : | 23 & $18\pm7$ & $0.5\pm0.2$ & $0.4\pm0.2$ & $0.004\pm0.002$ \\ \hline | ||
| 832 : | 35 & $1.0\pm0.2$ & $0.04\pm0.01$ & $0.02\pm0.01$ & $0.0007\pm0.00006$ \\ \hline | ||
| 833 : | 42 & $0.4\pm0.1$ & $0.02\pm0.01$ & $0.01\pm0.01$ & $0.0007\pm0.00006$ \\ \hline | ||
| 834 : | 70 & $0.01\pm0.02$ & $0.0008\pm0.0006$ & $0.0007\pm0.0006$ & $0.0007\pm0.00006$ \\ \hline | ||
| 835 : | \end{tabular} | ||
| 836 : | \end{center} | ||
| 837 : | \caption{\label{tab:btagrate_summ} EF output rates for the different multi $b$-jet signatures.} | ||
| 838 : | \end{table} | ||
| 839 : | |||
| 840 : | |||
| 841 : | The strategy behind the evolution of the $b$-jet trigger signatures | ||
| 842 : | is to select more aggressively as luminosity increases and HLT tracking becomes better understood. | ||
| 843 : | Before the $b$-jet trigger achieves full performance, a good online resolution of | ||
| 844 : | track impact parameters | ||
| 845 : | %and a reasonable population of the likelihood used in the | ||
| 846 : | %tagging process | ||
| 847 : | must be achieved. | ||
| 848 : | In turn, this requires improving knowledge of | ||
| 849 : | the inner detector alignment and of the overall detector performance. | ||
| 850 : | % (e.g. to select | ||
| 851 : | %the $t$-quark samples required for populating the signal likelihood). | ||
| 852 : | |||
| 853 : | %only 2 $b$-jets) and 4b/4j (for events having 4 $b$-jets in the final state), | ||
| 854 : | %but i | ||
| 855 : | |||
| 856 : | \subsection{Prospects for measuring efficiency and correlation with offline on real data} | ||
| 857 : | |||
| 858 : | The HLT $b$-tagging is closely following and contributing to the strategies adopted | ||
| 859 : | by the offline $b$-tagging to measure $b$-jet efficiency on real data since | ||
| 860 : | the problem is essentially the same. For an explanation of the method and a discussion | ||
| 861 : | of its performance we refer to the $b$-tagging note on di-jets~\cite{dijets_note}. | ||
| 862 : | |||
| 863 : | In addition to the ``physics'' triggers listed in previous the Section | ||
| 864 : | , the $b$-jet group has introduced several ``technical'' triggers in order to study rate | ||
| 865 : | and correlation of the online and offline algorithms: | ||
| 866 : | \begin{itemize} | ||
| 867 : | \item single $b$-jet signatures: $b18$, $b23$, $b35$, $b42$, $b70$: | ||
| 868 : | prescaled to limit their contribution to the EF output to few Hz; | ||
| 869 : | \item each multi jet item is duplicated with an identical signature which selects, independently | ||
| 870 : | of the HLT $b$-jet result, one over $n$ events (where $n$ is presently set | ||
| 871 : | at 1000 but will be tuned according to the rate allocated to $b$-jet triggers). | ||
| 872 : | \end{itemize} | ||
| 873 : | |||
| 874 : | |||
| 875 : | |||
| 876 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 877 : | % Summary and conclusion | ||
| 878 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 879 : | % | ||
| 880 : | |||
| 881 : | \section{Summary and conclusions} | ||
| 882 : | |||
| 883 : | The HLT $b$-jet selection at L2 and EF stages of the ATLAS High Level Trigger | ||
| 884 : | has been described and characterized. | ||
| 885 : | A HLT $b$-tagging trigger menu has been implemented which demonstrates | ||
| 886 : | the feasibility of increasing the acceptance of events with more then one $b$-jet | ||
| 887 : | by decreasing L1 jet $E_t$ thresholds while keeping a reasonable output rate | ||
| 888 : | by introducing a $b$-jet selection at HLT. | ||
| 889 : | |||
| 890 : | % | ||
| 891 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 892 : | % Acknowledgements | ||
| 893 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 894 : | % | ||
| 895 : | |||
| 896 : | %\section{Acknowledgments} | ||
| 897 : | |||
| 898 : | \setcounter{section}{0} | ||
| 899 : | \begin{thebibliography}{99} | ||
| 900 : | |||
| 901 : | \bibitem{DetPap} G. Aad \etal, ATLAS Collaboration {\em The Atlas Experiment at the CERN Large Hadron Collider}, | ||
| 902 : | submitted to Journal of Instrumentation. | ||
| 903 : | \bibitem{CSCHLTTracking} ATLAS Collaboration, {\em HLT track reconstruction performance}, CSC note EG10 | ||
| 904 : | \bibitem{bOff} ATLAS Collaboration, {\em $b$-tagging performance}, CSC note BT0 | ||
| 905 : | \bibitem{dijets_note} ATLAS Collaboration, {\em $b$-tagging caibration with di-jet events}, CSC note BT10 | ||
| 906 : | \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. | ||
| 907 : | \bibitem{chi2_d0} D$0$ Collaboration, {\em A Search for $Wb\bar{b}$ ad $WH$ Production in $p \bar{p}$ Collisions at | ||
| 908 : | $\sqrt{s} = 1.96 TeV$}, Phys. Rev. Lett. 94, 091802 (2005) | ||
| 909 : | \bibitem{chi2_cdf} CDF Collaboration, {\em Measurement of the $t\bar{t}$ production cross section in $p \bar{p}$ | ||
| 910 : | collisions at $\sqrt{s}=1.96 TeV$ using lepton+jets events with jet probability $b$-tagging}, | ||
| 911 : | Phys. Rev. D74, 072006 (2006) | ||
| 912 : | \end{thebibliography} | ||
| 913 : | |||
| 914 : | |||
| 915 : | % | ||
| 916 : | %\input /atlas/paper/authorlist.tex | ||
| 917 : | |||
| 918 : | \appendix | ||
| 919 : | % | ||
| 920 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 921 : | % Monte Carlo data samples | ||
| 922 : | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| 923 : | % | ||
| 924 : | |||
| 925 : | %\include{MC_data_samples} | ||
| 926 : | |||
| 927 : | |||
| 928 : | \end{document} |
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