  Total and differential cross sections for high energy and small momentum
transfer elastic hadron-hadron scattering are studied in QCD using a functional
integral approach. The hadronic amplitudes are governed by vacuum expectation
values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion
is derived. The cumulants are evaluated within the framework of the Minkowskian
version of the model of the stochastic vacuum. Using the second cumulant, we
calculate elastic differential cross sections for hadron-hadron scattering. The
agreement with experimental data is good.
