Dynamically Based Coupling Scheme for the Pomeranchukon

Abstract

We present a coupling scheme for the Pomeranchukon which relates its couplings to those of the $f$ and $f^{\prime }$ trajectories. In this scheme the Pomeranchukon couplings factorize and transform as a combination of SU(3) singlet and octet in a prescribed ratio. This enables us to explain the observed deviation of the ratios of SU(3)-related total cross sections from their symmetry values and, qualitatively, the difference between $\pi p$ and $\mathrm{Kp}$ diffraction slopes. A certain "universality principle" concerning the relative importance of Pomeranchukon exchange to $f$-trajectory exchange emerges in this scheme. This is tested with and supported by the available data on $\pi p$, $\mathrm{pp}$, $\gamma p$, and $\mathrm{Kp}$ total cross sections. The scheme accommodates quite naturally the observation of $s$-channel helicity conservation at high energies in $\pi N$ scattering and $\rho$ photoproduction. On the other hand, it does not predict $s$-channel helicity conservation in $\pi N\to A_{1}N$. Indeed, we discuss the possibility that the observation of $t$-channel helicity conservation in this process may be understood on kinematical grounds. We stress that our coupling scheme is compatible with a large class of dynamical models which differ in their descriptions of the detailed nature of the Pomeranchukon. Thus, our successful confrontation with the available data must be credited to the indispensably essential assumptions that are shared by these different dynamical models.