Parton Cascades, Small x, Multiple Interactions, and Saturation

In e+e−-annihilation the total hadronic cross section is given by the probability to produce an initial qq̄ pair, which is determined by QED. The effects of the strong interaction is here only a correction with relative magnitude αs/π. The emission of a gluon cascade is, however, essential for the properties of the final state, although it does not change the total cross section. Here angular ordering is crucial for the result, and the dipole formulation particularly convenient. DIS and hadronic collisions are more complicated. In a high energy ep or pp collision the initial partons in a target proton develop virtual parton cascades. A projectile can interact with any of the partons in the cascade, which implies that the total cross section grows with increasing collision energy. The development of the cascade in this “initial state radiation” determines the inclusive total and elastic cross sections, but for exclusive final states also “final state radiation” has to be added. In the initial state radiation the virtualities are spacelike. The final state radiation is more similar to the cascades in e+e−-ann.; it does not change the inclusive cross sections, and the virtualities are timelike. Thus in DIS and hadronic collisions we have two different problems, the total cross section and the final