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The dominant hadronic decays of taus consist of a one or three charged
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$\pi^{\pm}$ mesons and up to two $\pi^0$ mesons and are enumerated in
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table~\ref{table:decay_modes}. Most of these decays proceed through
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intermediate resonances and each of these decay modes maps directly to a tau
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final state multiplicity. Each intermediate resonance has a different invariant
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mass (see figure~\ref{fig:trueInvMass}. The implies that the problem of
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hadronic tau identification can be re-framed from a global search for collimated
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hadrons satisfying the tau mass constraint into a ensemble of searches for
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single production of the different hadronic tau decay resonances. The TaNC
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algorithm applies this approach using two complimentary techniques: a method to
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reconstruct the decay mode and an ensemble of neural network classifiers used to
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discriminant the individual decay modes.
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\begin{table}
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\centering
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\begin{tabular}{ l c r r }
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Visible Decay Products & Resonance & Mass (M$e$V/$c^2$) &
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Fraction~\ref{pdtTauBR} \\
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\hline
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$\pi^{-}$ & n/a & 135 & 10.9\% \\
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$\pi^{-}\pi^0$ & $\rho$ & 770 & 25.5\% \\
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$\pi^{-}\pi^0\pi^0$ & $a1$ & 1200 & 9.3\% \\
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$\pi^{-}\pi^{-}\pi^{+}$ & $a1$ & 1200 & 9.03\% \\
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$\pi^{-}\pi^{-}\pi^{+}\pi^0$ & $a1$ & 1200 & 4.5\% \\
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\hline
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Total & & & 59.2\% \\
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\hline
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Other hadronic modes & & & 5.59\% \\
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\end{tabular}
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\label{tab:decay_modes}
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\caption{Resonances and branching ratios of the dominant hadronic decays of
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the tau lepton.}
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\end{table}
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\begin{figure}[t]
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\begin{center}
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\includegraphics[width=60mm]{figures/truthIMvsDM.pdf}
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\end{center}
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\caption{The invariant mass of the visible decay products in hadronic tau
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decays. The decay mode $\tau^{-} \rightarrow \pi^{-} \nu_\tau$ is omitted.
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The different decay modes have different invariant masses corresponding to
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the intermediate resonance in the decay.}
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\label{fig:trueInvMass}
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\end{figure}
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