We present Fuchsia -an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients

We calculate transverse momentum dependent quark splitting kernels P gq and P qq within k T -factorization, completing earlier results which concentrated on gluon splitting functions P gg and P qg . The complete set of splitting kernels is an essential requirement for the formulation of a complete set of evolution equations for transverse momentum dependent parton distribution functions and the development of corresponding parton shower algorithms.

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The project of constructing a complete NLO-level Parton Shower Monte Carlo for the QCD processes developed in IFJ PAN in Kraków is reviewed. Four issues are discussed: (1) the extension of the standard inclusive collinear factorization into a new, fully exclusive scheme; (2) reconstruction of the LO Parton Shower in the new scheme; (3) inclusion of the exclusive NLO corrections into the hard process and (4) inclusion of the exclusive NLO corrections into the evolution (ladder) part.

A method for calculating phase-space master integrals for the decay process 1 → n massless partons in QCD using integration-by-parts and differential equations techniques is discussed. The method is based on the appropriate choice of the basis for master integrals which leads to significant simplification of differential equations. We describe an algorithm how to construct the desirable basis, so that the resulting system of differential equations can be recursively solved in terms of (G)HPLs as a series in the dimensional regulator ǫ to any order. We demonstrate its power by calculating master integrals for the NLO time-like splitting functions and discuss future applications of the proposed method at the NNLO precision.