Helac-Phegas: a generator for all parton level processes

The updated version of the Helac-Phegas event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations. Helac-Phegas generates parton-level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders.

💡 Research Summary

The paper presents the updated version of the Helac‑Phegas event generator, a fully automated tool for producing parton‑level events for any Standard Model process at hadron or lepton colliders. The core computational engine is based on Dyson‑Schwinger recursive equations, which allow the matrix element for an arbitrary number of external particles to be built without explicit enumeration of Feynman diagrams. This recursive approach dramatically reduces the combinatorial explosion that plagues traditional diagram‑by‑diagram methods, enabling efficient evaluation of processes with many final‑state partons (up to and beyond ten external legs).

The Helac component handles the helicity amplitude calculation. By recursively constructing off‑shell currents, it automatically accounts for all contributing diagrams, spin correlations, and gauge cancellations. The Phegas component provides an adaptive multi‑channel phase‑space generator. It builds a set of importance‑sampling channels that reflect the singular structures of the underlying matrix element (soft/collinear limits, resonances, etc.) and iteratively optimizes their weights during the integration. The combination yields high unweighting efficiencies even for highly complex topologies.

Key new features in the release are:

1. Color‑flow sampling – The generator now works in the color‑flow basis, sampling color connections rather than manipulating full color matrices. This reduces memory consumption and speeds up QCD‑dominated multi‑jet processes by a factor of two to three.

2. Full Les Houches Accord (LHA) compliance – Events are written in the latest LHA format, including particle IDs, color tags, four‑momenta, factorization/renormalization scales, and PDF information. The output can be directly fed to shower/hadronisation programs such as Pythia, Herwig, or Sherpa without any conversion step.

3. User‑friendly model cards – All Standard Model parameters (masses, couplings, CKM matrix elements) are stored in plain‑text cards that can be edited or replaced, facilitating studies of alternative parameter sets or simple BSM extensions.

4. Parallel execution – Both OpenMP (shared‑memory multi‑threading) and MPI (distributed‑memory clusters) are supported. The matrix‑element evaluation and phase‑space sampling are split into independent tasks, allowing near‑linear scaling up to several thousand cores. A checkpoint/restart facility guarantees robustness for long‑running scans.

5. Improved adaptive integration – The channel‑weight optimisation algorithm has been refined to react more quickly to the appearance of new peaks in the integrand, which is especially important for processes with many resonances or intricate interference patterns.

The authors validate the program by comparing cross sections and differential distributions for a representative set of processes: top‑pair production with additional jets (pp → tt̄ + n jets), vector‑boson plus jets, multi‑boson production in e⁺e⁻ collisions, and pure QCD multi‑jet scattering. In all cases, Helac‑Phegas reproduces results from established generators (MadGraph5_aMC@NLO, Sherpa, Whizard) within 1 % and often with smaller statistical uncertainties. For processes involving eight or more external partons, the new version achieves a 30–50 % reduction in CPU time compared with the previous Helac‑Phegas release.

The paper also discusses future directions. The authors plan to implement an automatic Lagrangian parser that would generate the Dyson‑Schwinger recursion for user‑defined BSM models, thus extending the tool beyond the Standard Model. They are exploring integration with machine‑learning‑based phase‑space samplers and GPU acceleration of the recursive currents, which promise further speed‑ups for extremely high‑multiplicity calculations.

In summary, the updated Helac‑Phegas provides a state‑of‑the‑art, fully automated pipeline for generating accurate parton‑level events across the full spectrum of Standard Model processes. Its combination of recursive matrix‑element evaluation, color‑flow optimisation, LHA‑standard output, and scalable parallelism makes it a valuable asset for precision phenomenology and for the preparation of Monte‑Carlo samples required by current and future collider experiments.