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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 andposterior fusion of $N N'$ to give the deuteron. We show that the trianglediagram depicting this process develops a triangle singularity leading to alarge cross section of this reaction compared to ordinary fusion reactions. Theresults of the calculation also show that the process is largely dominated bythe $pp$ 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 describingthe so far assumed dibaryon $d^*(2380)$ peak.

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