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1	<	The dominant (excluding rare decays to kaons, which are not considered here.)
2	<	hadronic decays of taus consist of a varying number of charged and neutral
3	<	pions.  The neutral pions undergo prompt decay to photon pairs. These decays
4	<	proceed through intermediate resonances, given in
5	<	table~\ref{table:decay_modes}.  Each of these decay modes uniquely maps to a
6	<	tau final state multiplicity, and each resonance has a different invariant
7	<	mass.  This implies that the problem of hadronic tau identification can be
8	<	reframed from a global search for collimated hadrons under the tau mass into an
9	<	ensemble of searches for single production of the various decay resonances
10	<	given in table~\ref{table:decay_modes}.  In this paper, we present a novel
11	<	algorithm, the ``Tau Neural Classifier'' (TaNC) which uses this approach to
12	<	improve on traditional tau-ID strategies.
1	>	The tau identification strategy described previously can be extended by
2	>	looking at the different hadronic decay modes of the tau individually.
3	>	The dominant hadronic decays of taus consist of a one or three charged
4	>	$\pi^{\pm}$ mesons and up to two $\pi^0$ mesons and are enumerated in
5	>	table~\ref{tab:decay_modes}.  The majority of these decays proceed through
6	>	intermediate resonances and each of these decay modes maps directly to a tau
7	>	final state multiplicity. Each intermediate resonance has a different invariant
8	>	mass (see figure~\ref{fig:trueInvMass}).  This implies that the problem of
9	>	hadronic tau identification can be re-framed from a global search for
10	>	collimated hadrons satisfying the tau mass constraint into a ensemble of
11	>	searches for single production of the different hadronic tau decay resonances.
12	>	The Tau Neural Classifier algorithm implements this approach using two
13	>	complimentary techniques: a method to reconstruct the decay mode and an
14	>	ensemble of neural network classifiers used to discriminant the individual
15	>	decay modes.
16
17		\begin{table}
15	–	\caption{Visible products of hadronic tau decays}
18		\centering
19		\begin{tabular}{ l c r r }
20	<	Visible Decay Products  & Resonance & Mass (M$e$V/$c^2$) & Fraction \\
20	>	Visible Decay Products  & Resonance & Mass (M$e$V/$c^2$) &
21	>	Fraction~\cite{pdg} \\
22		\hline
23	<	$\pi^{-}$                    & n/a    & 135  & fixme \\
24	<	$\pi^{-}\pi^0$               & $\rho$ & 770  & fixme \\
25	<	$\pi^{-}\pi^0\pi^0$          & $a1$   & 1200 & fixme \\
26	<	$\pi^{-}\pi^{-}\pi^{+}$      & $a1$   & 1200 & fixme \\
27	<	$\pi^{-}\pi^{-}\pi^{+}\pi^0$ & $a1$   & 1200 & fixme \\
23	>	$\pi^{-}$                    & -      & 135  & 10.9\% \\
24	>	$\pi^{-}\pi^0$               & $\rho$ & 770  & 25.5\% \\
25	>	$\pi^{-}\pi^0\pi^0$          & $a1$   & 1200 & 9.3\% \\
26	>	$\pi^{-}\pi^{-}\pi^{+}$      & $a1$   & 1200 & 9.03\% \\
27	>	$\pi^{-}\pi^{-}\pi^{+}\pi^0$ & $a1$   & 1200 & 4.5\% \\
28		\hline
29	<	Total & & & 65\% \\
29	>	Total & & & 59.2\% \\
30	>	\hline
31	>	Other hadronic modes & & & 5.59\% \\
32		\end{tabular}
33	<	\label{table:decay_modes}
33	>	\label{tab:decay_modes}
34	>	\caption{Resonances and branching ratios of the dominant hadronic decays of
35	>	the tau lepton.  The decay products listed correspond to a negatively
36	>	charged tau lepton; the table is identical under charge conjugation.}
37		\end{table}
38
39	+	\begin{figure}[thbp]
40	+	\begin{center}
41	+	\includegraphics[width=90mm]{figures/truthIMvsDM.pdf}
42	+	\end{center}
43	+	\caption{The invariant mass of the visible decay products in hadronic tau
44	+	decays.  The decay mode $\tau^{-} \rightarrow \pi^{-} \nu_\tau$ is omitted.
45	+	The different decay modes have different invariant masses corresponding to
46	+	the intermediate resonance in the decay.}
47	+	\label{fig:trueInvMass}
48	+	\end{figure}

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