Kinks Multiply Mesons

TL;DR

This paper calculates the probability of meson multiplication in a (1+1)-dimensional scalar quantum field theory, revealing how inelastic scattering behaves at high energies and contrasting quantum results with classical predictions.

Contribution

It provides the first leading-order quantum calculation of meson multiplication probabilities and differential distributions in a kink-meson scattering process.

Findings

Total probability approaches a constant in the ultrarelativistic limit

Quantum meson pressure on the kink is positive, unlike classical negative radiation pressure

Analytical results are obtained within the $^4$ model

Abstract

In a (1+1)-dimensional scalar quantum field theory, we calculate the leading-order probability of meson multiplication, which is the inelastic scattering process: kink + meson $\rightarrow$ kink + 2 mesons. We also calculate the differential probability with respect to the final meson momenta and the probability that one or two of the final mesons recoils back towards the source. In the ultrarelativistic limit of the initial meson, the total probability tends to a constant, which we calculate analytically in the $\phi^4$ model. At this order the meson sector conserves energy on its own, while the incoming meson applies a positive pressure to the kink. This is in contrast with the situation in classical field theory, where Romanczukiewicz and collaborators have shown that, in the presence of a reflectionless kink, only meson fusion is allowed, resulting in a negative radiation pressure on the kink.