Angular Distributions from Multiparticle Production Models

Using $\exp (-A{p_T}^2)\frac{d^{3}p}{E}$ as the momentum distribution of secondaries produced in ultrahigh-energy collisions—a result predicted by the multiperipheral model, by Feynman's parton model, and by Cheng and Wu's consideration of hadrons as extended objects with many internal degrees of freedom—we obtain the characteristic features of the angular distribution. We discuss the dependence on incident energy, mass of secondaries, and the value of $A$. We find that the c.m. angular distribution on the variable ${\eta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=-\ln tan\frac{1}{2}{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$. has a two-bump structure, whereas the lab angular distribution in $\eta =-\ln tan{\theta }_l$ is flat. This difference leads us to a discussion of the transformation between c.m. and lab angular distributions. We find that the usual relativistic approximation of the exact transformation leads to incorrect results. Finally, we point out that these momentum and angular distributions approach limiting distributions.