Solving QCD evolution equations in rapidity space with Markovian Monte Carlo

This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with ∼ 0.1% precision, against the non-MC program APCheb especially devised for this purpose. Submitted to Acta Physica Polonica IFJPAN-IV-07-09 CERN-PH-TH/2007-142 August 2007 This work is partly supported by the EU grant MTKD-CT-2004-510126 in partnership with the CERN Physics Department and by the Polish Ministry of Scientific Research and Information Technology grant No 620/E-77/6.PR UE/DIE 188/2005-2008.