Monte Carlo Calculations Related to the Analysis of Ultrahigh-Energy Nucleon-Nucleon Interactions

The Monte Carlo method is applied to an investigation of angular-distribution parameters currently in use in studies of ultrahigh-energy nuclear interactions. Specifically, center-of-mass system properties of meson showers having a total multiplicity of 16 and corresponding to nucleon-nucleon collisions at 3×${10}^{12}$ eV are calculated using the Monte Carlo method and employing input information based largely on experimentally determined average properties of ultrahigh-energy nuclear interactions. The resulting meson showers conserve energy and momentum, the angular distributions on the average possess forward-backward symmetry in the center-of-mass system, and the produced particles of each shower possess only those correlations introduced by energy-momentum conservation. After making an exact transformation of the showers to the laboratory system, some conventional analysis procedures are carried out with the resulting Monte Carlo jets using parameters calculated from the angular distributions of the charged particles. The results give insight into the sensitivity of the parameters to approximations used in the interpretation of the parameters and indicate how well, on the average as well as for individual jets, a parameter $Y\left(\theta \right)$ is a measure of the physical quantity $y$ which the parameter is expected to represent. The parameters are studied using the means and standard deviations of their $log\left[\frac{Y\left(\theta \right)}{y}\right]$ distributions. The Castagnoli energy is found, rather independently of the details of the Monte Carlo calculations, to be an overestimate of the energy of a jet by an average factor of about 1.8 (antilogarithm of the mean), with a factor 2.3 (antilogarithm of the standard deviation) defining the approximate 68% confidence interval for statistical fluctuations about this average factor in the case of individual jets. Seven other parameters are examined and are found to be generally more sensitive to the details of the Monte Carlo calculations. The factor defining the approximate 68% confidence interval for statistical fluctuations of individual $\frac{Y\left(\theta \right)}{y}$ values about the average factor ranges from 1.5 to 3.1 for these other parameters. An application of the $\frac{(x-〈x〉)}{\sigma }$ analysis of the Krakow-Warsaw group indicates that, at least for the jet models considered, fluctuations will not result in spurious two-center effects being indicated by the analysis.