High-energy forward scattering and the Pomeron: Simple pole versus unitarized models

Using the largest data set available, we determine the best values that the data at $t=0\mathrm{}$ (total cross sections and real parts of the hadronic amplitudes) give for the intercepts and couplings of the soft Pomeron and of the $\rho /\omega$ and $a/f$ trajectories. We show that these data cannot discriminate between a simple-pole fit and asymptotic ${\log }^{2}s$ and $\log s$ fits, and hence are not sufficient to reveal the ultimate nature of the Pomeron. However, we evaluate the existing evidence (factorization, universality, quark counting) favoring the simple-pole hypothesis. We also examine the range of validity in energy of the fits, and show that one cannot rely on such fits in the region $\sqrt{s}<9\mathrm{}\hspace{0.5em}\mathrm{GeV}.$ We also establish bounds on the odderon and the hard Pomeron.