Information Content of Particle Tracks

Abstract

The information content of a track is analyzed with respect to the prime track-variable $g$ and to the particle velocity on which $g$ depends. Quantities are operationally defined that are applicable to emulsion, bubble-chamber or cloud-chamber tracks inclined with arbitrary dip angles. The theory is developed of the projected linear structure of such particle tracks. Previously derived connections between the true value of $g$ and measurable track features are reviewed. A new and independent estimate of $g$ based on the mean blob length is introduced. The two independent quantities, mean gap length and mean blob length, each yield measurements of $g$. These are combined into an estimate of maximum likelihood. It is argued that in a practical sense this exhausts the information content of the track. The statistical error of this result is evaluated. It is found that correct utilization of the information in the measured blob lengths greatly reduces the error. Suggestions are made regarding technique for the reduction of error in $g$ and in particle masses estimated from grain-density measurements.