The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

Abstract: We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5_aMC@NLO, capable of handling all these computations -- parton-level fixed order, shower-matched, merged -- in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV $e^+e^-$ collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

• The paper introduces a fully automated framework for computing tree-level and NLO differential cross sections with minimal human intervention.
• It employs advanced techniques such as FKS subtraction and loop-induced process integration to enhance simulation precision.
• The framework demonstrates robust performance in LHC-relevant processes, paving the way for extensions to NNLO and beyond the Standard Model physics.

Overview of Automated Computation of Differential Cross Sections

The paper at hand presents a comprehensive framework for the automated computation of tree-level and next-to-leading order (NLO) differential cross sections, as well as their integration with parton shower simulations. This framework is embodied in a computer program designed to perform various tasks such as fixed-order computations, parton shower matching, and multi-parton merging. This program stands out due to its flexibility, high parallelization, and minimal need for human intervention. Here, we will discuss the theoretical underpinnings, numerical results, and future implications of this work.

Theoretical Framework

The foundation of this research lies in the automation of perturbative quantum chromodynamics (QCD) calculations, aiming to streamline the transition from theoretical formulations to practical simulations. At the heart of the framework are tree-level matrix elements generated using Feynman diagrams and helicity amplitudes, enhanced by color decomposition techniques. The program also employs the FKS subtraction method for managing infrared singularities in NLO calculations. A significant advancement is the integration of loop-induced processes, such as Higgs production in effective field theory approaches, which are treated with enhanced automation for ultraviolet (UV) renormalization and rational term computation ($R_2$) necessary for complete one-loop corrections.

Numerical Results

The study showcases various applications of the automated system to processes relevant to the Large Hadron Collider (LHC) and potential future electron-positron colliders. Specifically, the program was used to calculate NLO cross sections for a diverse set of processes, including:

• Vector boson production with up to three jets
• Higgs and Higgs pair production in association with jets or vector bosons
• Multi-boson productions such as triple and quadruple vector boson processes

The numerical results demonstrate significant precision improvements over leading order calculations, highlighting the importance of including NLO corrections. The system's ability to handle complex and computationally intensive processes efficiently is underscored by the reported integration errors and the calculated scale and PDF uncertainties. These results affirm the robustness of the program in dealing with high-multiplicity final states where traditional techniques often fall short.

Implications and Future Directions

This automated approach presents substantial advancements for both theoretical and experimental particle physics. The ability to calculate complex cross sections with minimal manual intervention makes it a valuable tool for high-energy physics laboratories around the world, particularly at the LHC. The framework's automation overcomes hurdles of traditional methods, offering a scalable solution as collider energies and luminosities increase.

Looking forward, the program's development suggests several directions for future improvements:

• Extending to full next-to-next-to-leading order (NNLO) computations
• Including more sophisticated parton-shower algorithms
• Enhancing support for beyond the standard model (BSM) physics processes

By continuing to refine these areas, the research will further enhance the predictive power required for both ongoing and upcoming experimental efforts. The work not only establishes a foundation for more precise studies of known physics but also sets the stage for potential new physics discoveries.