Difference of the total cross sections and the ratio of the differential cross sections of high energy $\pi^\pm p$ forward scattering

The general properties of the scattering amplitude and the experimental data on the total and the differential cross sections of $\pi^\pm p$ forward scattering yield
\begin{gather*} \int^\infty_{30\mathrm{\,GeV}}\ln\biggl(\frac{d\sigma_+(E,0)}{dt}\bigg/\frac{d\sigma_-(E,0)}{dt}\biggr)\frac{dE}E=-0.112\pm0.025, \\ \int^\infty_{60\mathrm{\,GeV}}\frac{\sigma_+(E)-\sigma_-(E)}E\,dE=-0.103\pm0.016. \end{gather*}