Time-ordering of quark multi-scattering processes in hadron-proton scattering at high energy

In the framework of non-relativistic Glauber theory with the quark model, the time-ordering of quark multi-scattering processes in hadron-proton elastic scattering at FNAL and CERN-ISR ranges of energy is considered. The time-ordering effect in the Glauber approximation with the geometrical scaling property of hadron reactions is presented. The phase variation effect, as suggested by Franco, is also discussed. A cloud effect is taken into account to obtain a good fit with the experimental data of elastic scattering differential cross section in the forward direction. The results obtained for proton-proton scattering at 200, 290, 500, 1070 and 1500 GeV/c lead us to neglect the phase variation effect in this range of energy. At the same time, the time-ordering of quark multi-scattering processes plays an important role in obtaining a good fit in the range of momentum transferred squared where q2>3.5 (GeV/c)2. In the case of π--proton elastic scattering at 200 GeV/c, where the phase variation leads to a good fit with the experimental data, the sensitivity with respect to the time-ordering effect can be observed for q2>6 (GeV/c)2. (author)