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

TL;DR

This study investigates a potential dibaryon resonance near 2.37 GeV by analyzing $pn$ to $d \, \pi^+ \pi^-$ and $pn$ to $pn \, \pi^+ \pi^-$ reactions, finding current data inconsistent with the dibaryon hypothesis and calling for more precise measurements.

Contribution

The paper provides a combined analysis of cross sections to constrain the existence of a dibaryon resonance, highlighting discrepancies and the need for improved experimental data.

Findings

The $pn \to pn \pi^+ \pi^-$ cross section saturates the experimental data around 2.37 GeV.

The resonant contribution exceeds the experimental data, challenging the dibaryon hypothesis.

Current data are too scarce and dispersed to confirm the resonance.

Abstract

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.