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

TL;DR

This paper investigates the factorial growth of scalar particle production probabilities in quantum field theory, analyzing cancellations of divergences and applying the findings to various scalar theories, concluding that cross sections do not grow factorially.

Contribution

The study introduces a method to analyze scalar jet rates and cross sections, demonstrating the absence of factorial growth in these quantities across different theories.

Findings

Cross sections do not grow factorially despite relativistic final particles.

IR divergence cancellations lead to stable scalar jet rate calculations.

Results apply to $$ and $$ scalar theories in various dimensions.

Abstract

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.