Possible Existence of a Spin-2 Regge Recurrence of theS01 p−pPole (The Unbound Diproton)

Abstract

A model is developed wherein the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}p-p$ partial-wave amplitude is coupled through $\frac{N}{D}$ equations to a second, inelastic channel containing a proton and a second particle in a relative $S$ wave. The mass of the second particle is "smeared out" according to an appropriate Breit-Wigner form around the (3,3) resonance at $1260-i120$ MeV. The phenomenological potential is adjusted to fit the elastic ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ phase shift to 400 MeV and the existing imprecise data at 660 MeV. The model, when adjusted to fit experiment, predicts a pole on the second Riemann sheet at $400-i300$ MeV. This pole may be interpreted as a bound state in the inelastic channel and has quantum numbers ($I=1\mathrm{}$, $B=2\mathrm{}$, $J=2\mathrm{}$) consistent with the spin-2 Regge recurrence of the pole in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ amplitude, the "unbound" diproton. An alternative coupled-channel model is developed which fits the elastic data but which does not predict the pole. The high-energy predictions for elastic scattering which are derived from the second model are found to differ drastically from those of the first model and from the predictions of various theories for high-energy inelastic processes.