We provide a simple Regge parametrization of forward hadronic scattering from the multi-TeV range down to approximately 1 GeV above the threshold of each reaction. We show how, at these relatively low energies, mass effects are relevant and should be properly taken into account, and that the data favor a logarithmic growth of the Pomeron contribution that is based on an improved unitarity bound at intermediate energies as well as a separate factorization of the singularities. Data on both the imaginary and real parts of amplitudes are remarkably well described with this parametrization. Here we also show that the description does not depend on the strategy adopted to include or not systematic uncertainties in different data sets.

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