One-Boson-Exchange Model ofNNandNN¯Interaction

Abstract

The elastic nucleon-nucleon scattering, due to the exchange of $\ensuremath{\pi}$, $\ensuremath{\eta}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$, $\ensuremath{\phi}$, and an effective $I=0$ scalar $\ensuremath{\sigma}$ meson is calculated using unsubtracted partial-wave dispersion relations with a cutoff. The $\ensuremath{\rho},\ensuremath{\omega}$, and $\ensuremath{\phi}$ vector coupling constants are related by $S{U}_{3}$ to a single constant assuming pure $F$ coupling. The ratio of the vector to tensor coupling of the $\ensuremath{\rho}$ meson is determined by the $I=1$ charge and anomalous magnetic moment ratio and the tensor couplings of $\ensuremath{\omega}$ and $\ensuremath{\phi}$ are neglected. The $\ensuremath{\eta}$-nucleon axial-vector coupling constant is related to that of the pion by $S{U}_{3}$ with a $\frac{D}{F}$ ratio of $\frac{3}{2}$. The $I=0$ and $I=1$ phase shifts are calculated using a total of four adjustable parameters: the mass and coupling constant of the effective $\ensuremath{\sigma}$ meson, the octet-vector coupling constant, and the cutoff parameter. For each of the cutoff values corresponding to laboratory kinetic energies of 600, 700, and 800 MeV, the remaining three parameters are adjusted to fit the $I=1$, $^{1}S_{0}$, $^{3}P_{0}$, $^{3}P_{1}$, and $^{3}P_{2}$, and the $I=0$, $^{3}S_{1}$ phase shifts at 25, 50, 95, 142, 210, and 310 MeV. In each of the three cases, a goodness-of-fit parameter is obtained corresponding to a theory with approximately 10% inherent uncertainty. A deuteron pole appears in the solution for the $^{3}S_{1}$ amplitude corresponding to a binding energy of \ensuremath{\sim}10 MeV. All of the calculated higher partial-wave phase shifts are in good agreement with results of phase-shift analyses. Having obtained a fit to the nucleon-nucleon phase shifts, the nucleon-antinucleon scattering amplitudes are calculated after changing the signs of the odd $G$-parity exchange terms ($\ensuremath{\pi}$, $\ensuremath{\omega}$, and $\ensuremath{\phi}$) but keeping the same values for the four parameters. For each of the three cutoff energies, a bound-state pole is found in the $I=0,^{1}S_{0},^{3}S_{1}$, and $^{3}P_{0}$, and the $I=1$, $^{1}S_{0}$ and $^{3}S_{1}$ amplitudes. These bound states have the same quantum numbers as the $\ensuremath{\eta}$, $\ensuremath{\omega}$, $\ensuremath{\sigma}$, $\ensuremath{\pi}$, and $\ensuremath{\rho}$, respectively. Although the masses of the bound states are not near those of the physical mesons, it is argued that if the important meson channels (annihilation) were included, the bound-state poles would move toward the physical values. These results lend strong support to the conjecture that the observed mesons are composite particles.