Monte Carlo Event Generators Using Collinear Factorization

In the Monte Carlo simulations based on the DGLAP evolution, collinear factorization of the parton density distributions and the hard matrix elements is assumed. In the DGLAP approximation the evolution from the partons density distributions leads to a strong ordering of radiated partons in transverse momentum $k_t$. The matrix elements are evaluated at leading order and effects from higher orders are mimicked using parton showers (PS) which are radiated from the initial and final state partons using a soft collinear approximation. The acronym LO+PS is generally used to indicate programs that implement the combination of leading order matrix elements with parton showers.

• The PYTHIA Monte Carlo generator [108] implements a number of different approaches to calculate $ee$, $ep$ and $pp$ cross sections and distributions. For the simulation of heavy quark production in $ep$ scattering, most commonly, PYTHIA is used in the massive mode in which $c$ and $b$ quarks are generated dynamically using the boson-gluon fusion process. Alternatively, PYTHIA can be used in an inclusive mode in which direct and resolved events are generated using massless matrix elements for all quark flavours. Many analysis have confirmed that PYTHIA describes the shapes of event distributions in photoproduction impressively well. In contrast, the $Q^2$ distribution in electroproduction is, for most parameter choices, poorly described.

• The RAPGAP Monte Carlo generator [124] produces events using the massive approach. In contrast to older event generators, such as DJANGO [126] or AROMA [103], it provides a correct treatment of the diffractive contribution of inclusive scattering which makes up about 10% of the cross section. RAPGAP is interfaced with the program HERACLES [127] which simulates QED initial and final state radiation.

• AROMA [103] is a program to simulate the production of heavy quarks in the direct photon-gluon fusion process in $ep$ scattering. AROMA does not include the generation of cross section contributions from resolved photon processes, and is thus of limited use for the photoproduction, and possibly the low-$Q^2$ regime, at HERA.

• HERWIG [125] is a general purpose physics event generator which includes the simulation of hard lepton-lepton, lepton-hadron and hadron-hadron scattering and soft hadron-hadron collisions in one package. HERWIG implements the cluster hadronization approach to describe the fragmentation of quarks into hadrons via non-perturbative gluon splitting. The colored objects in the final state are combined to color-singlet clusters which are subsequently fragmented into hadrons.