Determination of the Slopes of Diffraction Peaks for Hadronic Processes

A dispersion formula for the Pomeranchukon form factor is derived in the bootstrap model. In this model the Pomeranchukon is a fixed branch point at $j=1\mathrm{}$. Furthermore, the discontinuity of the branch cut vanishes at the tip of the cut. Thus, in the neighborhood of $j=1\mathrm{}$, the Pomeranchukon is weak. This property makes possible the linearization of the $t$-channel unitarity equation, which relates the Pomeranchukon form factor with the non-Pomeranchukon background. Assuming only $f\left(1260\right)\mathrm{}$ and $f^{\prime }\mathrm{}\left(1514\right)\mathrm{}$ contributions to the $I=0\mathrm{}$, even-signature, non-Pomeranchukon background, we calculate the slopes of the diffraction peaks for high-energy processes involving $N$, $\pi$, $K$, $\rho$, $\omega$, and $\phi$. No parameters are used. The results agree well with experimental data.