Factorization Algorithm for Parton Showers beyond the Leading   Logarithmic Order of QCD
  A factorization algorithm for a patron shower model based on the evolution of momentum distributions proposed in a previous work is studied. The scaling violation of initial state parton distributions is generated using parton showers to an accuracy of the next-to-leading logarithmic (NLL) order of quantum chromodynamics (QCD) using the information from only splitting functions and initial parton distributions at some fixed low energy. In the algorithm proposed in this paper, the total momentum of the initial state partons is conserved in any factorization scheme for mass singularities. As an example, the scaling violation of the parton distributions and the transverse momentum distributions due to initial state parton radiation are calculated with the jet calculs scheme. 
Hidekazu Tanaka (Rikkyo University), Tetsuya Sugiura (Waseda High   School), Yuya Wakabayashi (Rikkyo University)