

\subsection{\bf Particle Cluster Production---I}

\begin{slide}
{\Smallsize
\begin{itemize}
\item Particularly interesting is sensitivity to assumption of which
$y_i$ are chosen to be Poisson.

\item Note the Poisson distribution with mean (number of
objects) $=\lambda$, and where each object counts four units
(telephone calls, etc.), is much broader than ordinary Poisson of mean
$4\lambda$, where each object gives a single unit.  

\item This is of importance in particle physics where

\item We believe that $q\Underline{$q$}$ ``clusters'' are produced
independently in a high energy collision.  

\item These clusters are (assumed to be) Poissonly distributed and
decay into $4\rightarrow 6$ final particles.

\item One can show that if particles were produced in a Poisson
fashion singly, then

\item $f_2 = \sigma^2 - $ mean for final particles is zero.

\item However, in cluster model where one can assume $y_i$ are
distributed Gaussianly with the $4\rightarrow 6$ mean.  $f_2$ is
always $>0$.

\item Experimentally, one finds $f_2 >0$ except when perturbed by
kinematic constraints.

\item i.e., cluster model and experiment is broader than naive
Poisson.
\end{itemize}
}
\end{slide}

