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\appendix
\addcontentsline{toc}{chapter}{APPENDICES}

\chapter{Kinematic Distributions for Spin-Parity}

This section provides detailed information on the kinematic
distributions which are relevant for spin-parity measurements.

The seven measurables which distinguish different signal models,
$m_1$, $m_2$, $\cos\theta_1$, $\cos\theta_2$, $\cos\theta^*$,
$\Phi$, and $\Phi_1$, are in figure~\ref{fig:??}.  Each plots
compare the pseudoscalar model against
the SM Higgs hypothesis in one of the 7 dimensions.  This allows
one to appreciate the relevant differences between these
two signal models.  It should be noted that these plots do not
fully represent the information in the KD since, there is
also information in the correlations between variables which
might be lost in projections. Instead, the $D_{0-}$ projection
can be compared directly, shown in figure~\ref{fig:???} with
and without a cut of $D_{bkg}>0.5$.  The effect of selecting
signal like events can shown more completely in the $D_{bkg}$
vs $D_{J^P}$ distributions.  These distributions for background,
SM Higgs signal, and the corresponding alternative signal model
are shown in
figures~\ref{fig:HZZ4lspin0KD},~\ref{fig:HZZ4lspin1KD},
and~\ref{fig:HZZ4lspin2KD}.

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta1_jhuGenV2PseH126_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta2_jhuGenV2PseH126_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_phi_jhuGenV2PseH126_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta1_jhuGenV2PseH126_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta2_jhuGenV2PseH126_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_phi_jhuGenV2PseH126_Proj_superKDcut.eps}
\label{fig:HZZ4lhelicityanglesKD}
\caption{}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta1_jhuGenV2PseH126_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_phi1_jhuGenV2PseH126_Proj.eps}\\
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_costheta1_jhuGenV2PseH126_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_phi1_jhuGenV2PseH126_Proj_superKDcut.eps}
\label{fig:HZZ4lprodanglesKD}
\caption{}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_z1mass_jhuGenV2PseH126_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_z2mass_jhuGenV2PseH126_Proj.eps}\\
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_z1mass_jhuGenV2PseH126_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_z2mass_jhuGenV2PseH126_Proj_superKDcut.eps}
\label{fig:HZZ4lmassesKD}
\caption{}
\end{center}
\end{figure}


\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_0minus_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_0hplus_Proj.eps}\\
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_0minus_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_0hplus_Proj_superKDcut.eps}
\label{fig:HZZ4lspin-0KD}
\caption{}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_1minus_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_1plus_Proj.eps}\\
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_1minus_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_1plus_Proj_superKDcut.eps}
\label{fig:HZZ4lspin-1KD}
\caption{}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_2mplus_gg_Proj.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_2mplus_qqbar_Proj.eps}\\
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_2mplus_gg_Proj_superKDcut.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/KD_2mplus_qqbar_Proj_superKDcut.eps}
\label{fig:HZZ4lspin-2KD}
\caption{}
\end{center}
\end{figure}


\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0m_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0m_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0m_ALTSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0hp_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0hp_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/0hp_ALTSignal_Moriond_signal126_lowmass.eps}
\label{fig:HZZ4lspin0KDvSKD}
\caption{Distribution of the $D_{bkg}$ and $D_{J^p}$ for continuum
ZZ background (left), SM Higgs signal (middle) and the
alternative $J^P$ signal model.  The top row show the KD and
alternative signal model relevant for $0_m^+$ vs $0^-$, the
bottom row for $0_m^+$ vs $0_h^+$ hypothesis separation.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1m_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1m_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1m_ALTSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1p_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1p_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/1p_ALTSignal_Moriond_signal126_lowmass.eps}
\label{fig:HZZ4lspin1KDvSKD}
\caption{Distribution of the $D_{bkg}$ and $D_{J^p}$ for continuum
ZZ background (left), SM Higgs signal (middle) and the
alternative $J^P$ signal model.  The top row show the KD and
alternative signal model relevant for $0_m^+$ vs $1^-$, the
bottom row for $0_m^+$ vs $1^+$ hypothesis separation.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/gg2mp_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/gg2mp_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/gg2mp_ALTSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/qq2mp_qqZZBackgr_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/qq2mp_SMSignal_Moriond_signal126_lowmass.eps}
\includegraphics[width=.32\linewidth]{HZZ4lPlots/qq2mp_ALTSignal_Moriond_signal126_lowmass.eps}
\label{fig:HZZ4lspin2KDvSKD}
\caption{Distribution of the $D_{bkg}$ and $D_{J^p}$ for continuum
ZZ background (left), SM Higgs signal (middle) and the
alternative $J^P$ signal model.  The top row show the KD and
alternative signal model relevant for $0_m^+$ vs $2_m^+(gg)$, the
bottom row for $0_m^+$ vs $2_m^+(q\bar{q})$ hypothesis separation.}
\end{center}
\end{figure}