Calculation of nucleon-nucleon two-pion exchange utilizing theoretical and experimentalππ,πN, ande Ninformation

The $J=0,1,2\mathrm{}$ $N\overline{N}\to \pi \pi$ amplitudes are evaluated in the physical region of the two pions, $t\ge 4{\mu }^2$, and used in a dispersion-theoretic calculation of nucleon-nucleon two-pion exchange. Experimental input to the evaluations of the $N\overline{N}\to \pi \pi$ amplitudes is via $\pi \pi$ phase shifts, $\pi N$ scattering lengths, and $\pi N$ phase shifts. The effect of varying the $I=J=0\mathrm{} \pi \pi$ phase shift within its present uncertainty is investigated. Experimentally determined nucleon electromagnetic form factors are used in the evaluation of the $J=1\mathrm{}$ $N\overline{N}\to \pi \pi$ amplitude. After adding $\pi$ and $\omega$ exchange to the two-pion-exchange amplitude, the theoretical phase shifts are compared with phase-shift-analysis results. The calculated ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ potential is also shown and compared with the phenomenological one of Hamada and Johnston.