A posteriori inclusion of PDFs in NLO QCD final-state calculations

TL;DR

The paper tackles the high cost of evaluating NLO QCD final-state observables across multiple PDF sets by introducing an a posteriori PDF inclusion method. It constructs a PDF-independent representation using grids: PDFs on a $y$–$\tau$ grid and final-state weights on a corresponding grid, enabling rapid recomputation with any PDF and scale choice via high-order interpolation. The authors extend the approach to hadron-hadron collisions, including multiple initial-state channels and a posteriori variations of renormalisation and factorisation scales, all implemented and tested with NLOJET++ and CTEQ6. This framework facilitates consistent inclusion of final-state data from HERA, Tevatron, and LHC in global PDF analyses, potentially improving sensitivity to deviations from Standard Model predictions. The work provides a practical, scalable path to integrate diverse final-state measurements into PDF fits while controlling memory and accuracy trade-offs.

Abstract

Any NLO calculation of a QCD final-state observable involves Monte Carlo integration over a large number of events. For DIS and hadron colliders this must usually be repeated for each new PDF set, making it impractical to consider many `error' PDF sets, or carry out PDF fits. Here we discuss ``a posteriori'' inclusion of PDFs, whereby the Monte Carlo run calculates a grid (in x and Q) of cross section weights that can subsequently be combined with an arbitrary PDF. The procedure is numerically equivalent to using an interpolated form of the PDF. The main novelty relative to prior work is the use of higher-order interpolation, which substantially improves the tradeoff between accuracy and memory use. An accuracy of about 0.01% has been reached for the single inclusive cross-section in the central rapidity region |y|<0.5 for jet transverse momenta from 100 to 5000 GeV. This method should facilitate the consistent inclusion of final-state data from HERA, Tevatron and LHC in PDF fits, thus helping to increase the sensitivity of LHC to deviations from standard Model predictions.