Evidence for $\xi-$ and t-dependent damping of the Pomeron Flux in the proton

We show that a triple-Regge parametrization of inclusive single diffraction agrees with the data in the following two domains: (a) xi > 0.03 at all t, (b) |t| > 1 GeV^2 at all xi. Since the triple-Regge parametrization fails when applied to the full xi-t range of the total single-diffractive cross section, we conclude that damping occurs only at low-xi and low-|t|. We give a (``toy'') parametrization of the damping factor, D(xi), valid at low-|t|, which describes the diffractive differential cross-section (dsig/dt) data at the ISR and roughly accounts for the observed s-dependence of diffractive total cross-section up to Tevatron energies. However, an effective damping factor calculated for the CDF fitted function for dsig/dxidt at sqrt(s} = 1800 GeV and |t| = 0.05 GeV^2, suggests that, at fixed-xi, damping increases as s increases. We conjecture that, in the regions where the triple-Regge formalism describes the data and there is no evidence of damping, factorization is valid and the Pomeron-flux-factor may be universal. With the assumption that the observed damping is due to multi-Pomeron exchange, our results imply that the recent UA8 demonstration that the effective Pomeron trajectory flattens for |t| > 1 GeV$^2 is evidence for the onset of the perturbative 2-gluon pomeron. Our damping results may also shed some light on the self-consistency of recent measurements of hard-diffractive jet production cross sections in the UA8, CDF and ZEUS experiments