Particle Cluster Production---I

• Particularly interesting is sensitivity to assumption of which are chosen to be Poisson.

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

• This is of importance in particle physics where

• We believe that ``clusters'' are produced independently in a high energy collision.

• These clusters are (assumed to be) Poissonly distributed and decay into final particles.

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

• mean for final particles is zero.

• However, in cluster model where one can assume are distributed Gaussianly with the mean. is always >0.

• Experimentally, one finds except when perturbed by kinematic constraints.

• i.e., cluster model and experiment is broader than naive Poisson.