Resonant partial-wave amplitudes inπN→ππNaccording to the naive quark-pair-creation model

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Abstract

We make an extensive comparison of the naive quark-pair-creation model of strong-interaction vertices for $\ensuremath{\pi}N\ensuremath{\rightarrow}{N}^{*}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$,$\ensuremath{\rho}N$,$\ensuremath{\sigma}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ with recent experimental results. The model describes any vertex in terms of a quark-pair creation in the $^{3}P_{0}$ state and a rearrangement leading to final states. The hadron states are given by SU(6) harmonic-oscillator wave functions. We show that the model correctly describes, without any additional assumption, the centrifugal barrier effect and also the "anti-${\mathrm{SU}(6)}_{W}$" coupling signs, features that are present in most reactions (with the important exception of $F{P}_{15}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$ for the second feature) and are included phenomenologically in the works of Rosner et al. Both facts are related to the presence, in the limit of elementary meson emission, of recoil terms depending on internal quark momenta. Contrary to other works, the model predicts the relative coupling signs for all the two-body baryonic decays leading to $\ensuremath{\pi}\ensuremath{\pi}N$. Concerning $\ensuremath{\Delta}\ensuremath{\pi}$ and $\ensuremath{\rho}N$ channels, among 18 predictions, 15 agree with experiment, comparing our results to the last report of the Particle Data Group, and three disagree. One of these three is the very serious failure $F{P}_{15}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$, which is among the best determined experimental coupling signs. We compare our predictions with parallel works. Unlike the model of Feynman, Kislinger, and Ravndal, in the limit of elementary $\ensuremath{\rho}$ emission, our model presents a recoil term in the spin part of the interaction, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}[({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\rho}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{i})\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\epsilon}}}_{\ensuremath{\rho}}]$. Thus, for $F{P}_{35}\ensuremath{\rightarrow}N{\ensuremath{\rho}}_{3}$, our model predicts an "anti-${\mathrm{SU}(6)}_{W}$" sign, in agreement with experiment and contrary to the prediction of Moorhouse and Parsons. For the controversial $\ensuremath{\sigma}$ production, the model is contradicted by experiment; we show, however, that the model could be compatible with experiment if the $I=0$, ${J}^{P}={0}^{+}$ dipion observed is not really a resonance.

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