Modifications of the analytical properties of the two-point correlation function in Drell-Yan scattering, caused by rescattering-induced decorrelation of the initial hadron state

In a recent work, factorization breaking interactions and T-odd distributions have been analyzed from the point of view of statistical mechanics. One of the central points was the process leading from the coherent initial hadron state to an incoherent set of short-range parton states, in presence of factorization breaking interactions. This time evolution was named ``partonization'', or also ``de-correlation'', to distinguish it from an ordinary hadron-quark-spectator splitting vertex. Here an example is shown for a correlation amplitude describing an extreme case for such a process, where the initial state phases are lost, but the probability distributions are perfectly conserved. This requires introducing degrees of freedom that are not normally considered in a factorized scheme, and that must disappear at some stage of the calculations for the factorization scheme to survive. The explicit time-evolution character of the decorrelation process disappears when these degrees of freedom are integrated, but the integrated correlator presents modified analytical properties as a consequence. for the factorization scheme to survive. The explicit time-evolution character of the de-correlation process disappears when these degrees of freedom are integrated, but the integrated correlator presents nontrivial analytic properties as a consequence. At certain conditions, factorization is preserved, at the price of introducing T-odd contributions.