Importance of theNΔinelastic threshold for understanding low-energyNNamplitudes

The authors relate three interesting aspects of low-energy $\mathrm{NN}$ reactions: (1) The large value of $\Delta {\sigma }_T={\sigma }_T\left(\uparrow \downarrow \right)-{\sigma }_T\left(\uparrow \uparrow \right)$ for $\mathrm{pp}$ scattering for $P_{\mathrm{LAB}}$ below 3 GeV/c; (2) the existence at low energies of large unnatural-parity $t$-channel amplitudes with nonpion quantum numbers; (3) the anomalous variation with energy of the slope and differential cross section at $t=0\mathrm{}$ in $\mathrm{np}\to \mathrm{pn}$ in the range $P_{\mathrm{LAB}}=0.5-2\mathrm{}$ GeV/c. Based on the somewhat crude phase-shift analyses which exist above the single-pion inelastic threshold, it is argued that all three of the above aspects of $\mathrm{NN}$ reactions are the reflections of the dominant inelastic channel $\mathrm{pp}\to N\Delta$. The well-known possibility that the large amplitudes so generated are related to resonant behavior (in the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ partial wave of $\mathrm{pp}\to \mathrm{pp}$) is discussed. That some low-energy amplitudes are strongly affected by $s$-channel threshold effects demonstrates one cannot, in general, equate features of high-energy amplitudes with those of low-energy amplitudes whenever inelastic thresholds are important.