Lattice approach to high–energy hadron–hadron scattering

The prediction from first principles of total cross sections at high energy is one of the oldest open problems of hadronic physics. Present– day experimental data are well described by a universal pomeron–like power–law behaviour (see, for example, Ref. [1] and references therein), σ (hh) tot (s) ∼ s→∞ (s/s0) ǫP , where the so–called soft pomeron intercept is ǫP ≃ 0.08, but this is forbidden as a true asymptotic behaviour by the well– known Froissart–Lukaszuk–Martin theorem [2]. As we believe QCD to be the fundamental theory of strong interactions, it should predict the correct asymptotic behaviour; nevertheless, a satisfactory explanation is still lacking. The problem of total cross sections is part of the more general problem of high–energy scattering at low transferred momentum, the so–called soft high–energy scattering. As soft high–energy processes possess two different energy scales, the total center–of–mass energy squared s and the transferred momentum squared t, smaller than the typical energy scale of strong interactions (|t| . 1 GeV ≪ s), we cannot fully rely on perturbation theory. A genuine non perturbative approach in the framework of QCD has been proposed by Nachtmann in [3], and further developed in [4,5,6,7,8]: using a functional integral approach, high–energy hadron–hadron elastic scattering amplitudes are shown to be governed by the correlation function of certain Wilson loops defined in Minkowski space. Moreover, as it has been shown in [9,10], such a correlation func-