Finite-energy sum rule in the inclusive reaction and its application to the triple-Regge amplitude

To investigate the six-point function, the finite-energy sum rule is derived and is applied to π- + p →π- +anything and p + p →p +anything processes. It is shown that the most dominant contributions come not from the triple-Pomeron coupling but from the meson-meson-Pomeron coupling for the "background" term and the Pomeron-Pomeron-meson coupling for the resonance term. The proposition is made that the Harari-Freund conjecture also holds for the off-mass-shell amplitude, such as Reggeon+ p →Reggeon+ p scattering amplitude.