Meson production from kink-meson scattering

In a ($1+1$)-dimensional scalar quantum field theory, we calculate the leading-order probability of meson multiplication, which is the inelastic scattering process: $\mathrm{kink}+\text{meson}$ $\to$ 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 ${\varphi }^4$ 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.

Figure 1

The probability density, $P_{\mathrm{diff}}(k_2)$, that one of the final mesons has momentum $k_2$, plotted for various values of $k_0$. The factor of $\lambda$ has been divided out.

Figure 2

The total meson multiplication probability $P_{\mathrm{tot}}$ as a function of $k_0$, rescaled by $1/\lambda$. The dashed line is the asymptotic value derived in Eq. (4.27).

Figure 3

The probability $P_n$ that $n$ of the momenta of the outgoing mesons are negative. These are all rescaled by $1/\lambda$ and also by other factors, given in the legend, to make them visible in the plot. The dashed line is again the asymptotic value in Eq. (4.27).