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1.1     ! uid12904    1: \section{Object Identification \label{sec:objects}}
        !             2: 
        !             3: \noindent In this section we describe the main objects used in this study: \met, 
        !             4: jets and hadronic tau candidates.
        !             5: 
        !             6: 
        !             7: \subsection{\label{sub:tau--ID}\boldmath Taus}
        !             8: 
        !             9: %\subsubsection{Tau decay modes}
        !            10: 
        !            11: \noindent Taus are reconstructed in the D{\O} detector from energy in the calorimeter and one or more 
        !            12: tracks.The tau reconstruction algorithm uses a cone of 
        !            13: $\Delta R = \sqrt{{\delta \eta}^{2} + {\delta \phi}^{2}} < 0.5$ and an inner cone of $\Delta R < 0.3$
        !            14: is used to calculate tau isolation variables. 
        !            15: 
        !            16: For us, the most important discriminating variables for $\tau$-leptons are \cite{tau-id}:
        !            17: 
        !            18: \begin{itemize}
        !            19: \item Profile - $\frac{E_{T}^{1}+E_{T}^{2}}{\sum_{i}E_{T}^{i}}$, where
        !            20: $E_{T}^{i}$ is the $E_{T}$ of the $i^{\rm th}$ highest $E_{T}$ tower in
        !            21: the cluster.
        !            22: \item Isolation, defined as $\frac{E(0.5)-E(0.3)}{E(0.3)}$, where $E(R)$
        !            23: is the energy contained in a $y,\phi$ of radius $R$ around the calorimeter cluster centroid.
        !            24: \item Track isolation, defined as scalar sum of the $p_{T}'$ of non-$\tau$ tracks in a $\eta,\phi$
        !            25: cone of 0.5 around the calorimeter cluster centroid divided by similar sum for tracks associated with $\tau$.
        !            26: \end{itemize}
        !            27: 
        !            28: Such variables are chosen based on the possible tau decays:
        !            29: 
        !            30: 
        !            31: \begin{itemize}
        !            32: \item electron or muon ($\tau\rightarrow e\nu_{e}\nu_{\tau}$ or $\tau\rightarrow\mu\nu_{\mu}\nu_{\tau})$,
        !            33: BR = 35\% .
        !            34: \item single charged hadron and no neutral hadrons ($\tau\rightarrow\pi^{-}\nu_{\tau}$), BR =12\% .
        !            35: \item single charged hadron + $\geq1$ neutral 
        !            36: hadron (i.e.,  $\tau\rightarrow\rho^{-}\nu_{\tau}\rightarrow (\pi^0+\pi^{-})\nu_{\tau}$)
        !            37: , BR = 38\% .
        !            38: \item 3 charged hadrons + $\geq0$ neutral hadrons, BR = 15\% (so-called
        !            39: {}``3-prong'' decays). 
        !            40: \end{itemize}
        !            41: 
        !            42: 
        !            43: \noindent which leads us classificate reconstructed taus into three different types
        !            44: depending on the number of tracks and electromagnetic (EM) clusters \cite{PDG}:
        !            45: 
        !            46: \begin{enumerate}
        !            47: \item {\bf Type1}: calorimeter cluster, one matched charged track and no associated EM subcluster. 
        !            48: Mainly $\tau\rightarrow\pi^{-}\nu_{\tau}$.
        !            49: \item {\bf Type2}: calorimeter cluster, one matched charged track and one or more associated EM subclusters. 
        !            50: Mainly $\tau\rightarrow\rho^{-}\nu_{\tau}\rightarrow \pi^0\pi^{-}\nu_{\tau}$.
        !            51: \item {\bf Type3}: calorimeter cluster, two or more matched charged tracks and with or without EM subcluster. 
        !            52: Mainly $\tau\rightarrow\pi^{-}\pi^{-}\pi^{+}(\pi^{0})\nu_{\tau}$.
        !            53: \end{enumerate}
        !            54: 
        !            55: In order to provide an optimal tau identification,three Neural Networks (NNs) are trained to
        !            56: identify the three types of the taus (1,2 and 3).
        !            57: 
        !            58: The output of these NNs provides a set of three variables ({\tt{nnout}} = 1,2,3)
        !            59: to be used to select the tau in the event. The types roughly 
        !            60: correspond to the $\tau$ lepton decay modes. High values 
        !            61: of NN correspond to the physical taus, while low ones
        !            62: should indicate jets misidentified as taus (fakes). 
        !            63: 
        !            64: \subsection{\label{sub:jet--ID}\boldmath Jets}
        !            65: 
        !            66: \noindent Jets are identified using the RunII cone algorithm \cite{jet-id} with cone size of
        !            67: $\Delta R < 0.5$. The jet algorithm T42 \cite{t42} is ran before jet reconstruction
        !            68: to remove isolated small energy deposits due to noise. D\O\ standard jet quality cuts \cite{jet-qual}
        !            69: include L1 Trigger information, calorimeter electromagnetic fraction and coarse hadronic fraction.
        !            70: 
        !            71: Jets used in this analysis are required to have at least two primary vertex tracks associated to them
        !            72: (vertex confirmed jets). It implies that although a calorimeter cluster
        !            73: is still reconstructed as a jet, it will be discarded if it has less than 2 associated PV tracks.
        !            74: In order to correct the energies of reconstructed jets in data and MC back to
        !            75: parton-level energies, we apply certified jet energy scale correction (JES)\cite{jes}. Additionally,
        !            76: jets containing a muon with $\Delta R(\mu , jet) < 0.5$ from a $b$-quark decay are corrected to take into
        !            77: account the momentum carried away by the muon and the neutrino \cite{jesmu}.
        !            78: 
        !            79: 
        !            80: \subsection{\label{sub:met-id}\boldmath \met}
        !            81: 
        !            82: \noindent Presence of neutrinos in an event causes an imbalance of energy in the transverse plane (\met).
        !            83: This quantity is calculated from the transverse energies of all calorimeter cells that pass the 
        !            84: T42 algorithm, except those of the coarse hadronic layers due to high noise level. However, they are included
        !            85: in the case that they are clustered within a reconstructed jet. This raw \met is corrected for the energies
        !            86: of other objects like photons, electrons, taus and jets. As muons deposit only a small portion of their
        !            87: energy in the calorimeter, their momenta is subtracted from the \met vector.
        !            88: 
        !            89: 
        !            90: \subsection{The Neural Network b-tagging Algorithm \label{sec:nntag}}
        !            91: 
        !            92: Being QCD and $W$ + jets the main sources of backgrounds in this analysis, requiring
        !            93: the presence of at least one jet coming from a $b$-quark is a very powerful method of background 
        !            94: rejection. The $b$-tagging algorithm used in this measurement is a
        !            95: Neural Network (NN) tagging algorithm developed by the b-ID group \cite{bID-p20},
        !            96: which combines 7 characteristic variables of SVT, JLIP and CSIP tagging algorithms into the NN 
        !            97: discriminant. As in the previous analysis we have chosen the operating
        !            98: point TIGHT, which is equivalent to requiring the NN discriminant output to be greater than 0.775.
        !            99: Both the average efficiency and fake rate are comparable between this p20 version of the
        !           100: algorithm and the version used in p17 \cite{bID-p17}.
        !           101: 
        !           102: \paragraph{$b$-tagging efficiency}
        !           103: 
        !           104: In data we apply the b-tagging algorithm directly to jets selected in our sample. In MC such ``direct tag''
        !           105: is not done. Instead we have to apply a certain efficiency to MC samples. This inclusive b-decay efficiency ($\epsilon_{b}$)
        !           106: is measured in data and it is the product of the probability to tag a b-jet in an MC sample ($\epsilon_{b}^{MC}$)
        !           107: containing inclusive decays of the b quark times a scale factor. This data/MC scale factor is given by the ratio
        !           108: of data semileptonic efficiency ($\epsilon^{DATA}_{b\rightarrow \mu}$) and a MC semileptonic efficiency ($\epsilon^{MC}_{b\rightarrow \mu}$).
        !           109: This scale factor, that measures the effect on the tagging rate
        !           110: caused by the differences in tracking between data and MC, is then used to properly scale
        !           111: the MC-derived efficiency. It is assumed that such factor could be applied to any MC tagging efficiency \cite{bID-p20}.
        !           112: 
        !           113: \paragraph{$c$-tagging efficiency}
        !           114: 
        !           115: It is assumed that the same procedure adopted in the b-jet case is also valid for c-jets,
        !           116: namely, a c-jet scale factor ($\epsilon^{DATA}_{b\rightarrow \mu}$)/($\epsilon^{MC}_{b\rightarrow \mu}$)
        !           117: multiplies the probability to tag a c-jet in an MC sample ($\epsilon_{b}^{MC}$) to get the
        !           118: c-tagging efficiency.
        !           119: 
        !           120: 
        !           121: \paragraph{Light jet tagging efficiency}
        !           122: 
        !           123: The $b$-tag fake rate from light quarks is computed by measuring the
        !           124: negative tag rate as defined in \cite{b_fake}. The method uses fits of
        !           125: b-, c- and light jets tagging rates to binned data combined with sample
        !           126: composition estimated from data. Binned NN output ($NN_{out}$) distributions
        !           127: for b, c and light jets is fitted to data distribution using b- and c-jet efficiencies
        !           128: provided by standard bID TRF's.
        !           129: 
        !           130: 
        !           131: 
        !           132: \paragraph{Taggability}
        !           133: 
        !           134: $b$-tag algorithm can't be applied to any jet, but only the ones that contain tracks. 
        !           135: Such jets are called ``taggable'' and are defined by matching within $\Delta R$ $<$ 0.5 to 
        !           136: a track jet, composed of at least two tracks. 
        !           137: Just like b-tagging, taggability is different in data and MC, due to imperfect 
        !           138: simulation of tracking system. To account for this, taggability rate functions are applied
        !           139: to MC events. Such functions are parametrized in terms of jet $p_{T}$, jet $\eta$ and
        !           140: primary vertex $z$. They were derived on the single top loose data samples, where the isolation
        !           141: quality of the lepton is loose.The validity of these functions is tested by comparing observed
        !           142: and predicted taggability to tight samples. The results show a good agreement as described in \cite{single top}. 
        !           143: 
        !           144: \clearpage