A parton shower consistent with parton densities at LO and NLO: PDF2ISR

We present a method for obtaining an initial-state parton shower model where the (backward) evolution fully consistent with the (forward) evolution of the collinear parton density used. As a proof-of-concept we use parton densities obtained with the Parton Branching (PB) approach, and modify the default initial-state shower in PYTHIA8 with this method to be consistent with them. PB is ideally suited for checking the validity of our method since, in addition to producing collinear parton densities, it also produces the corresponding transverse-dependent (TMD) ones, and these can then be directly compared to the transverse momentum distribution obtained from the parton shower. We show that TMD distributions which we in this way obtain from our modified PYTHIA8 shower using leading order (LO) parton densities and splitting functions are fully consistent with the corresponding leading order TMD densities. At next-to-leading order (NLO) it is not possible to achieve the same consistency using the built-in LO splitting functions in the shower, but we show that by introducing NLO splitting functions using a reweighting procedure, we can achieve consistency also at NLO. The method presented here, which we have named PDF2ISR, can be easily extended to any collinear parton densities, as long as the exact conditions for the evolution are known. With the PDF2ISR method we obtain an initial-state parton shower which in principle has no free parameters, and is fully consistent with collinear parton densities at LO and NLO.