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

Abstract

We develop a model for the $pp\to {\pi }^{+}d$ reaction based on the $pp\to \Delta (1232)N$ transition followed by $\Delta (1232)\to \pi N^{\prime }$ decay and posterior fusion of $N{N}^{\prime }$ 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 $d^{\ast }(2380)$ peak.

23 pages, 12 figures, 2 tables