| 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}
|
| 18 |
\centering
|
| 19 |
\begin{tabular}{ l c r r }
|
| 20 |
Visible Decay Products & Resonance & Mass (M$e$V/$c^2$) &
|
| 21 |
Fraction~\cite{pdg} \\
|
| 22 |
\hline
|
| 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 & & & 59.2\% \\
|
| 30 |
\hline
|
| 31 |
Other hadronic modes & & & 5.59\% \\
|
| 32 |
\end{tabular}
|
| 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}[t]
|
| 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}
|
