Extending CKKW-merging to One-Loop Matrix Elements

Abstract: We extend earlier schemes for merging tree-level matrix elements with parton showers to include also merging with one-loop matrix elements. In this paper we make a first study on how to include one-loop corrections, not only for events with a given jet multiplicity, but simultaneously for several different jet multiplicities. Results are presented for the simplest non-trivial case of hadronic events at LEP as a proof-of-concept.

• The paper presents an extension of the CKKW merging scheme to one-loop matrix elements, enhancing multi-jet QCD simulations.
• The algorithm merges the first two orders of αs with parton showers while effectively handling divergent soft and collinear regions.
• Validation against LEP data and jet observables confirms improved consistency between simulation results and experimental measurements.

Extending CKKW-merging to One-Loop Matrix Elements: An Insightful Overview

The paper at hand presents an extension of the CKKW merging scheme, which is pivotal for combining matrix elements and parton showers within Monte Carlo event generators, to include one-loop matrix elements. This development is motivated by the necessity to better describe multi-jet states in Quantum Chromodynamics (QCD) processes—an essential aspect given their prominence as background configurations at high-energy colliders like the LHC.

The Context and Challenges

Monte Carlo event generators are indispensable tools in simulations of particle collisions, relying on a combination of parton showers and hadronization models to mimic the suite of processes observed in reality. Parton showers, while adept at describing soft and collinear emissions by resumming leading logarithms, fall short in regions away from these limits where the tree-level and one-loop matrix elements offer a more precise description. However, directly integrating matrix elements into the shower presents challenges due to their divergent nature in the soft and collinear regions and the complex virtual correction structures at one-loop order.

Algorithmic Development

The authors propose a general algorithm that achieves a consistent merging of one-loop matrix elements with parton shower simulations. Here, the first two terms in the expansion of the coupling constant $\alpha_s$ (from one-loop matrix elements) are merged with the parton shower description, while higher-order terms are handled by the shower. This innovative approach ensures a consistent inclusion of different jet multiplicities and compensates the traditional parton shower description's inadequacies in these configurations.

A distinctive feature of the algorithm is its extension to multiple jet multiplicities. The algorithm generates two distinct datasets: one from event samples calculated using the one-loop matrix elements capped with a parton shower and another using tree-level matrix elements corrected for parton shower emissions. These datasets are combined post-calculation, ensuring each matrix element is appropriately weighted and corrected for contributions not simulated at the tree-level.

Implementation and Results

The algorithm is implemented using \ariadne and tested on hadronic events at LEP, employing modified routines from \pythia to generate matrix elements. Results focus primarily on validation via parton-level and jet distributions, where comparisons against both the default \ariadne shower and experimental data underscore the extension's consistency and efficacy.

When tested with different configurations and cutoffs, the approach demonstrated its ability to adapt particle physics parameters optimally, implementing \ariadne with its modified $\alpha_s$. Though certain overshoots in jet distributions were noted, the introduced modifications to the coupling constant scaling (according to PDG values) helped align the theoretical predictions with empirical data more closely, proving the method's effectiveness in handling several-parton states.

Furthermore, the algorithm's capabilities were further corroborated when applied against shape observables like thrust and oblateness measured at LEP. While no drastic improvements over the preexisting \ariadne descriptions were expected, the method still showed consistency with the data, validating the approach as a robust framework that paves the way for sophisticated parton-level event modeling at next-to-leading order (NLO) accuracy.

Implications and Future Outlook

The implications of this work are both practical and theoretical. From a practical standpoint, the extended merging scheme showcases potential for more precise simulations of high-energy collider events, crucial for extracting subtle signals from complex backgrounds at the LHC. Theoretically, it enhances the predictive potential of Monte Carlo models, providing an avenue for refining other aspects such as heavy ion collisions and precision measurements.

Future work could build on this foundation by incorporating processes involving incoming hadrons, a non-trivial but essential extension for fully capitalizing on the LHC's potential. With developments in automated one-loop matrix element calculations, there is a promising horizon for comprehensive integration into event generators, reinforcing the pursuit of precision physics.

In summary, this paper is a significant step toward a richer integration of higher-order corrections in parton showers, reinforcing the robustness of simulations necessary for contemporary and future particle physics research.