A multi-channel Poissonian model for multi-parton scatterings

1 The simplest Poissonian model A standard way to introduce multiple parton interactions in Montecarlo codes is to assume a Poissonian distribution of multiple parton collisions, with average number depending on the value of the impact parameter. The motivations were discussed long ago in several articles [1] [2] [3]: One introduces the three dimensional parton densityD(x, b), namely the average number of partons with a given momentum fraction x and with transverse coordinate b (the dependence on flavor and on the resolution of the process is understood) and one makes the simplifying assumption D(x, b) = G(x)f(b), with G(x) the usual parton distribution function and f(b) normalized to one. The inclusive cross section for large pt parton production σS may hence be expressed as