Implementing NLO DGLAP evolution in Parton Showers
Stefan Höche, Frank Krauss, Stefan Prestel
TL;DR
The paper addresses incorporating next-to-leading order DGLAP evolution into parton showers for both initial- and final-state radiation. It formulates a subtraction scheme that removes the LO cusp contribution and uses a weighting method to handle negative NLO terms, enabling purely collinear NLO kernels to be added without double counting. Implemented in DIRE within Pythia and Sherpa, the approach yields reduced renormalization-scale uncertainties and improved agreement with data, especially for hadron-collider observables like Z-boson pT and Higgs production. As a baseline for full NLO accuracy, the work also identifies remaining challenges (leading-color effects and soft multi-emissions) and provides a framework for future refinements.
Abstract
We present a parton shower which implements the DGLAP evolution of parton densities and fragmentation functions at next-to-leading order precision up to effects stemming from local four-momentum conservation. The Monte-Carlo simulation is based on including next-to-leading order collinear splitting functions in an existing parton shower and combining their soft enhanced contributions with the corresponding terms at leading order. Soft double counting is avoided by matching to the soft eikonal. Example results from two independent realizations of the algorithm, implemented in the two event generation frameworks Pythia and Sherpa, illustrate the improved precision of the new formalism.