Multi-Scalar Production At Large Center-Of-Mass Energy

In quantum field theory, the probability of producing scalar particles grows factorially as a function of the number of the particles produced. This poses a problem theoretically, in maintaining unitarity, and is counter-intuitive phenomenologically. The factorial growth is a byproduct of the perturbation theory, but has been found in some of the semi-classical and non-perturbative calculations as well. Recently, it has been proposed that the factorial growth might be observable in the future 100 TeV hadron collider. After reviewing some of the past calculations, we analyze the cancelation of IR divergences to find Altarelli-Parisi function and the Sudakov form factor. We then use these to write an equation for the generating function of scalar jet rates. We further argue that we can turn the jet rates into particle cross section by swapping the opening angle with particle mass. We will present our results for $\phi^3$ theory in four and six spacetime dimensions, and $\phi^4$ in four spacetime dimensions. We find that, while the final particles are relativistic, the cross sections do not grow factorially.