Analysis of the Singlet and Triplet Contributions to the Total-Cross-Section Differences $\Delta {\sigma }_T$ and $\Delta {\sigma }_L$ in $p-p$ Scattering between 1 and 3 GeV/c

The data from measurements of the total-cross-section differences $\Delta {\sigma }_T$ and $\Delta {\sigma }_L$ for $p-p$ scattering and the spin-averaged total cross sections are analyzed to determine the singlet (${{\sigma }_s}^T$) and (${{\sigma }_t}^T$) cross sections. The structures observed in $\Delta {\sigma }_T$ and $\Delta {\sigma }_L$ near 1.3 GeV/c are found to result primarily from increases in ${{\sigma }_s}^T$ and ${{\sigma }_t}^T$. These increases are shown to be consistent with the Mandelstam model of pion production. No resonantlike behavior is required to describe the structures in $\Delta {\sigma }_T$ and $\Delta {\sigma }_L$.