Triangle singularity mechanism for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mi>d</mml:mi></mml:mrow></mml:math> fusion reaction

Abstract

We develop a model for the $pp\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}d$ reaction based on the $pp\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1232)N$ transition followed by $\mathrm{\ensuremath{\Delta}}(1232)\ensuremath{\rightarrow}\ensuremath{\pi}{N}^{\ensuremath{'}}$ decay and posterior fusion of $N{N}^{\ensuremath{'}}$ 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 $L=2$ and $S=0$, which transfers $J=2$ to the final ${\ensuremath{\pi}}^{+}d$ system. This feature is shown to be well suited to provide $L=2$, $S=1$, and ${J}^{\mathrm{tot}}=3$ for $np$ in the $np(I=0)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}pp$ reaction followed by the $pp\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}d$ reaction, which has been proposed recently, as a means of describing the so far assumed dibaryon ${d}^{*}(2380)$ peak.

Topics & Concepts