The automation of next-to-leading order electroweak calculations

Abstract: We present the key features relevant to the automated computation of all the leading- and next-to-leading order contributions to short-distance cross sections in a mixed-coupling expansion, with special emphasis on the first subleading NLO term in the QCD+EW scenario, commonly referred to as NLO EW corrections. We discuss, in particular, the FKS subtraction in the context of a mixed-coupling expansion; the extension of the FKS subtraction to processes that include final-state tagged particles, defined by means of fragmentation functions; and some properties of the complex mass scheme. We combine the present paper with the release of a new version of MadGraph5_aMC@NLO, capable of dealing with mixed-coupling expansions. We use the code to obtain illustrative inclusive and differential results for the 13-TeV LHC.

• The paper presents an automated framework that integrates NLO electroweak corrections into MadGraph5_aMC@NLO for enhanced LHC simulation accuracy.
• It adapts the FKS subtraction method and employs a complex-mass scheme to manage singularities and unstable particle propagators effectively.
• Benchmark tests on processes such as top-quark pair and diboson production reveal significant electroweak effects that aid in probing potential new physics.

Overview of Electroweak NLO Automation

The paper entitled "The automation of next-to-leading order electroweak calculations" presents a detailed framework for automating electroweak (EW) corrections at the next-to-leading order (NLO) for particle physics processes. It pushes the boundaries of computational precision that are critical in interpreting data from the Large Hadron Collider (LHC) and other advanced experiments. This work integrates the electroweak NLO computations into the MadGraph5_aMC@NLO software, a tool fundamentally crucial for simulating high-energy physics events.

Core Contributions

1. Mixed-Coupling Expansion:
   • The research introduces a robust method for handling contributions from multiple coupling expansions, specifically QCD and EW interactions. It outlines procedures for systematically including leading order (LO) and subleading NLO terms pertinent to QCD+EW scenarios.
2. FKS Subtraction Method:
   • A significant portion of the paper is dedicated to adapting the FKS (Frixione, Kunszt, Signer) subtraction method to manage singularities intrinsic to mixed-coupling expansions within quantum field calculations. This is crucial for ensuring divergences from real and virtual corrections cancel and yield physically meaningful results.
3. Use of Complex-Mass Scheme:
   • The study employs the Complex Mass Scheme (CMS) to deal with unstable particles. This approach allows gauge-invariance preservation while leaving room for the resummation of self-energy corrections, ensuring that the propagators of particles like the W and Z bosons are handled consistently.
4. Technical Robustness:
   • Through integration into MadGraph5_aMC@NLO, the framework validates its versatility and accuracy by computing benchmark processes and comparing them with existing predictions. The added complexity of tagged particles and fragmentation functions in final states is also tackled, albeit not publicly released in the current software version.

Numerical Results and Implications

• The implementation is comprehensively tested against a series of high-energy physics processes typical at the LHC, such as top quark pair production, associated production of top quarks with bosons, and diboson production events.
• The study finds significant electroweak corrections, which exceed expected values in certain high-momentum-transfer regions, indicating the necessity of these computations for accurate theoretical predictions at the LHC energies.
• Such high-precision calculations have direct implications for searches for new physics beyond the Standard Model, as any discrepancies observed experimentally from these predictions might hint at new phenomena.

Future Directions

While this effort marks a substantial step forward, the authors also hint at various enhancements postulated for future work. Public code releases will further extend capabilities, such as better matching with parton showers and the automated handling of fragmentation functions, making them available for tagged photons and leptons. These improvements are necessary to push precision even higher, minimizing systematic uncertainties in theoretical predictions.

Conclusion

The automation of NLO electroweak calculations within MadGraph5_aMC@NLO represents a pivotal advancement for high-energy particle physics simulation. The strategies put forth in this work are comprehensive, addressing essential theoretical challenges and setting the stage for future explorations and discoveries using collider data. As theoretical predictions inch towards greater accuracy, they become pivotal in probing the yet uncharted territories of fundamental physics.