Merging Multi-leg NLO Matrix Elements with Parton Showers

Abstract: We discuss extensions the CKKW-L and UMEPS tree-level matrix element and parton shower merging approaches to next-to-leading order accuracy. The generalisation of CKKW-L is based on the NL3 scheme previously developed for e+e- -annihilation, which is extended to also handle hadronic collisions by a careful treatment of parton densities. NL3 is further augmented to allow for more readily accessible NLO input. To allow for a more careful handling of merging scale dependencies we introduce an extension of the UMEPS method. This approach, dubbed UNLOPS, does not inherit problematic features of CKKW-L, and thus allows for a theoretically more appealing definition of NLO merging. We have implemented both schemes in Pythia8, and present results for the merging of W- and Higgs-production events, where the zero- and one-jet contribution are corrected to next-to-leading order simultaneously, and higher jet multiplicities are described by tree-level matrix elements. The implementation of the procedure is completely general and can be used for higher jet multiplicities and other processes, subject to the availability of programs able to correctly generate the corresponding partonic states to leading and next-to-leading order accuracy.

• The paper introduces two novel methodologies, NL3 and UNLOPS, that merge multi-leg NLO matrix elements with parton showers.
• It extends conventional CKKW-L and UMEPS techniques by reweighting multi-jet events to preserve NLO accuracy.
• Implemented in Pythia and validated with W and Higgs production, the methods reduce scale uncertainties and improve simulation fidelity.

Merging Multi-leg NLO Matrix Elements with Parton Showers

This paper explores extending CKKW-L and UMEPS merging techniques to next-to-leading order (NLO) accuracy in Quantum Chromodynamics (QCD) simulations. The authors introduce two innovative methodologies, the NL$^3$ and UNLOPS procedures, for incorporating multiple NLO calculations with parton showers in the \textsc{Pythia} event generator.

CKKW-L and UMEPS Techniques

The paper begins by outlining the limitations of conventional multi-jet merging techniques based on CKKW-L and UMEPS algorithms. Traditional methods, while widely used, are constrained to tree-level accuracy, falling short of the precision required for many LHC analyses. CKKW-L and UMEPS are limited by their inability to maintain consistent inclusive cross-sections upon inclusion of high multiplicity jets. The authors propose a natural next step toward enhanced background simulations: developing methods that integrate NLO precision with parton showers.

NL$^3$: Extension of CKKW-L

The authors extend the CKKW-L tree-level merging method to NLO accuracy via the NL$^3$ approach. The algorithm introduces corrective weights to samples, ensuring the preservation of NLO accuracy while accommodating parton shower resummation. The methodology operates by separately considering multi-jet configurations with exclusive $n$-jet observables, reweighting events to incorporate NLO corrections, and preserving the evolution history used in tree-level merging to maintain accuracy beyond NLO.

UNLOPS: Beyond UMEPS

The UNLOPS approach generalizes UMEPS to NLO multi-jet configurations. Unlike NL$^3$, UNLOPS emphasizes maintaining inclusive cross-sections across computations by introducing systematic subtractions. The method involves subtracting integrated multi-jet events to maintain consistency, employing unitarity corrections to reduce dependence on the merging scale. This process allows UNLOPS to account for logarithmic contributions that might otherwise destabilize calculations.

Implementation and Results

The paper details the implementation of both methodologies in the \textsc{Pythia} platform. The NL$^3$ and UNLOPS methods are validated through $\W$- and Higgs-boson production cases. The approaches show improvements in the description of experimental data, with UNLOPS yielding a more accurate result for configurations heavily influenced by higher multiplicity events, such as Higgs production in gluon fusion.

Impact and Speculation

By incorporating NLO corrections into parton shower simulations, these methods minimize theoretical uncertainties due to scale variations and enhance the reliability of LHC predictions. The paper sets a foundation for further accuracy improvements, with potential extensions into next-to-next-to-leading order (NNLO) regimes hinted at. The methodologies open pathways for more precise multiparton interactions and ultimately, a deeper understanding of QCD dynamics at high energies.

In summary, this paper significantly advances the merging model landscape by innovatively reconciling NLO matrix element calculations with parton showers, ensuring a profound leap in theoretical accuracy and practical reliability for LHC-observable predictions. Future developments could include more automated workflows for NNLO calculations and further refinement of event generators to enhance our understanding of high-energy particle physics.