Constraints on a possible dibaryon from combined analysis of the $pn \to d π^+ π^-$ and $pn \to pn π^+ π^-$ cross sections

We use recent data that show a narrow peak around $\sqrt{s}=2.37\ \text{GeV}$ in the $pn \to d \pi^+ \pi^-$ cross section, with about double strength at the peak than in the analogous $pn \to d \pi^0 \pi^0$ reaction, and, assuming that it is due to the excitation of a dibaryon resonance, we evaluate the cross section for the $pn \to pn \pi^+ \pi^-$ reaction, with the final $pn$ unbound but with the same quantum numbers as the deuteron. We use accurate techniques to determine the final state interaction in the case of the $pn$ forming a deuteron or a positive energy state, which allow us to get the $pn \to pn \pi^+ \pi^-$ cross section with $pn$ in I=0 and S=1, that turns out to be quite close or saturates the experimental $pn \to pn \pi^+ \pi^-$ total cross section around $\sqrt{s} = 2.37\ \text{GeV}$, depending on the angular momentum assumed. We then parametrize a background with different methods, and the sum of the resonant and background contributions is fitted to present data. The resulting cross section exceeds the experimental results in the region of the resonant peak, showing a problem in the dibaryon hypothesis. Yet, in view of the dispersion of present experimental data, and the scarce information around $\sqrt{s} = 2.37\ \text{GeV}$, a call is made for precise measurements of the $pn \to pn\pi^+\pi^-$ reaction around this energy, to further clarify this issue.