Triangle singularity mechanism for the $pp \to \pi^+ d$ fusion reaction

We develop a model for the $pp \to \pi^+ d$ reaction based on the $pp \to \Delta(1232) N$ transition followed by $\Delta(1232) \to \pi N'$ decay and posterior fusion of $N N'$ to give the deuteron. We show that the triangle diagram depicting this process develops a triangle singularity leading to a large cross section of this reaction compared to ordinary fusion reactions. The results of the calculation also show that the process is largely dominated by the $pp$ system in $L=2, S=0$, which transfers $J=2$ to the final $\pi^+ d$ system. This feature is shown to be well suited to provide $L=2,S=1$, $J^\mathrm{tot}=3$ for $np$ in the $np(I=0) \to \pi^- pp$ followed by $pp \to \pi^+ d$ reaction, which has been proposed recently, as a means of describing the so far assumed dibaryon $d^*(2380)$ peak.