Source-linked AI summary
HELAC-Onia 2.0: an upgraded matrix-element and event generator for heavy quarkonium physics
Hua-Sheng Shao
TL;DR
Heavy-quarkonium production requires complex NRQCD calculations and reliable collider simulations, while available Monte Carlo tools are limited. HELAC-Onia 2.0 upgrades recursive helicity-amplitude computation with showering, spin-entangled decays, reweighting, plotting, and parallel workflows. The update broadens practical simulation capabilities, though PDF reweighting becomes approximate when combined with parton-shower evolution and mixed coupling orders complicate renormalization-scale evaluation.
Problem
Heavy-quarkonium studies need complex NRQCD calculations and reliable Monte Carlo simulations, but dedicated simulation tools remain limited.
Method
HELAC-Onia 2.0 uses off-shell recursion for helicity amplitudes and adds interfaces, decay, uncertainty-reweighting, plotting, and parallel-computation modules.
Results
The upgraded program supports practical heavy-quarkonium event generation with Pythia 8 and QEDPS, spin-entangled cascade decays, uncertainty estimation, and on-the-fly plots.
Takeaways & Limitations
HELAC-Onia 2.0 broadens the practical simulation and analysis capabilities available for heavy-quarkonium phenomenology.
Takeaways & Limitations
PDF reweighting is approximate with parton-shower Monte Carlo, and mixed coupling orders make renormalization-scale dependence difficult to evaluate correctly.
Abstract
from arXiv · showhide
We present an upgraded version (denoted as version 2.0) of the program HELAC-Onia for the automated computation of heavy-quarkonium helicity amplitudes within non-relativistic QCD framework. The new code has been designed to include many new and useful features for practical phenomenological simulations. It is designed for job submissions under cluster enviroment for parallel computations via Python scripts. We have interfaced HELAC-Onia to the parton shower Monte Carlo programs Pythia 8 and QEDPS to take into account the parton-shower effects. Moreover, the decay module guarantees that the program can perform the spin-entangled (cascade-)decay of heavy quarkonium after its generation. We have also implemented a reweighting method to automatically estimate the uncertainties from renormalization and/or factorization scales as well as parton-distribution functions to weighted or unweighted events. A futher update is the possiblity to generate one-dimensional or two-dimensional plots encoded in the analysis files on the fly. Some dedicated examples are given at the end of the writeup.
PROGRAM SUMMARY
HELAC-Onia 2.0 is a Unix-like-platform program for heavy-quarkonium simulations within NRQCD, combining automated helicity-amplitude calculations with event-generation and analysis capabilities.
- The program is implemented in Python, Fortran 77, Fortran 90, and C++ for Unix-like platforms.
- Heavy-quarkonium production probes QCD's poorly known non-perturbative regime and requires complex high-multiplicity computations plus collider-environment simulations.
- The program uses recursion relations to calculate helicity amplitudes for high-multiplicity heavy-quarkonium-production processes.
- Dedicated modules interface parton-shower Monte Carlo programs, simulate spin-correlated quarkonium decays, estimate theoretical uncertainties, and analyze events during computation.
1 Introduction
Heavy-quarkonium production offers broad QCD and collider-physics applications, but reliable simulation tools remain limited despite NRQCD's established framework. HELAC-Onia 2.0 addresses this need with features motivated by practical phenomenological simulations and user experience.
- Heavy-quarkonium processes probe perturbative and non-perturbative QCD and inform measurements of fundamental parameters, PDFs, CP violation, and multiple-parton interactions.
- Heavy-quarkonium studies also support investigations of quark-gluon plasma, cold nuclear matter effects, and beyond-Standard-Model particles.
- Monte Carlo tools for heavy-quarkonium production are limited, while production-mechanism puzzles persist within the NRQCD framework.
- HELAC-Onia 2.0 introduces new features motivated by practical phenomenological simulations and user experience.
2 Methodology, algorithm and new features
HELAC-Onia 2.0 combines recursive heavy-quarkonium amplitude computation with flexible event generation, showering, decay, uncertainty estimation, plotting, and parallel execution.
- Amplitude computation: Off-shell recursion constructs higher-level currents from lower-level currents, beginning with external legs and ending with the full n-leg helicity amplitude.
- NRQCD framework: NRQCD factorization separates perturbative short-distance coefficients from non-perturbative long-distance matrix elements, with projection onto specified spin, orbital, angular-momentum, and color states.
- Event generation: Two independent PHEGAS- and VEGAS-based generators produce unweighted events for 2 →n processes with n ≥2, while VEGAS also handles 2 →1 hadron-collider processes.
- Simulation features: The program interfaces with LHAPDF, Pythia 8, and QEDPS, supports fixed-target frames and initial e± photon showering, and generates analysis plots during computation.
- Uncertainties and workflow: Reweighting estimates renormalization/factorization-scale and PDF uncertainties without recalculating cross sections, while Python scripts enable multicore or cluster computations.
- Decay simulation: Spin-entangled and cascade decays are implemented, including processes such as J/ψ →ℓ+ℓ− and χc →J/ψ + γ.
3 How to use the program
HELAC-Onia 2.0 supports standalone and Python-script workflows for generating, configuring, running, and analyzing heavy-quarkonium calculations. The Python interface enables cluster or multicore execution and integrates decays, parton showers, and on-the-fly analysis.
- Running modes: HELAC-Onia 2.0 offers direct executable and Python-script modes for cross-section computations.The Python-script workflow is recommended for accessing most new features.
- Process setup: Users configure processes and decays, then generate one or multiple subprocesses through interactive commands.The workflow supports examples including J/ψ-pair production and higher-order subprocesses.
- Parallel computation: Generated subprocesses can use multiple cores on clusters or multicore machines, with adjustable integration and Monte Carlo settings.The program supports addon processes and VEGAS configuration.
- Decay configuration: The decay interface specifies decay channels and branching ratios through Python commands before job submission.Examples include charmonium decay to muon pairs with a 6% branching ratio and W decay with 100% probability.
- Showering and analysis: HELAC-Onia 2.0 interfaces with Pythia8 and QEDPS for showering, while analysis files can produce event outputs or plots during processing.Pythia8 requires configured paths and shower parameters; compilation problems are reported through the absence of Pythia8.exe and can be investigated in shower.log.
4 Examples
The examples demonstrate HELAC-Onia 2.0 on complex heavy-quarkonium production, parton-shower effects, and spin-correlated decay validation. They show its use for high-multiplicity calculations, differential observables, and agreement with analytical decay distributions.
- NNLO⋆-level production: The pp → ψ + 3-jets color-singlet calculation is organized into 13 independent subprocesses, with options to include additional quark flavors and combine factors.The quarksumQ and iqnum settings include initial quark PDFs in a three-light-quark-flavor scheme.
- NNLO⋆-level production: HELAC-Onia 2.0 handles complex quarkonium processes, including a 2 → 4 calculation involving more than 2000 Feynman diagrams.The example studies pp → J/ψ + J/ψ + c¯c with gluon-gluon initial states.
- NNLO⋆-level production: The J/ψ-pair example uses differential azimuthal, rapidity, invariant-mass, and transverse-momentum distributions to distinguish DPS and SPS mechanisms.Feeddown from ψ(2S) increases the differential cross section by a factor of 1.89.
- Parton-shower effects: The inclusive J/ψ example uses parton showers to study small-pT production, where showering significantly smears the leading-order distribution.The example uses the color-singlet contribution at leading order with Pythia8.186 and without primordial kT or multiple interactions in the stated setup.
- Decay validation: HELAC-Onia 2.0 decay implementations agree with analytical angular distributions for J/ψ → ℓ+ℓ− and χc1,2 → J/ψ + γ validation examples.The comparisons include selected λθ values and normalized total cross sections.
5 Conclusions
HELAC-Onia 2.0 adds practical interfaces and simulation capabilities for heavy-quarkonium production studies, including cluster execution, parton showers, spin-entangled decays, uncertainty reweighting, and on-the-fly analysis.
- Python scripts provide a user-friendly interface for submitting calculations with multithreading or cluster processors.
- HELAC-Onia 2.0 interfaces with QEDPS and Pythia 8 for parton-shower simulations.
- A decay module performs spin-entangled cascade decays of heavy quarkonia and includes several dedicated decay processes.
- Automatic reweighting estimates renormalization-scale, factorization-scale, and PDF uncertainties.
- One-dimensional and two-dimensional histograms can be generated on the fly alongside analysis tools.
- The upgrades provide a flexible framework for future heavy-quarkonium studies, including heavy-ion collisions and transverse-momentum factorization.
A Program structure
HELAC-Onia 2.0 is organized into input, source, integration, event-generation, shower, analysis, PDF, decay, cluster, and output components. Its structure separates helicity-amplitude generation from phase-space integration and event production while supporting external simulation and analysis tools.
- The program is divided into subdirectories for input, source code, phase-space integration, PDFs, showers, analysis, decays, clusters, and outputs.
- The src directory separates matrix-element generation from phase-space integration and event generation.
- HELAC-Onia computes helicity amplitudes using off-shell currents generated through recursion relations.
- Adapted Monte Carlo programs provide phase-space integration for hadron and electron-positron colliders.
- The shower directory contains interfaces for QEDPS and Pythia 8, while additional Pythia and Herwig directories are reserved for future use.
- The analysis directory provides plotting, histogram, Root-tree, event-file, and tagging tools.
B Particle symbols in HELAC-Onia via Python script
Appendix B documents the particle identity numbers and symbols used by HELAC-Onia 2.0’s Python scripts, covering Standard Model particles and quarkonia in multiple flavor and Fock-state categories.
- Table 3 covers Standard Model elementary particles.
- Table 4 covers charmonia in various Fock states.
- Table 5 covers bottomonia in various Fock states.
- Table 6 covers the mixed-flavor quarkonium B±.
C New input parameters
HELAC-Onia 2.0 introduces input parameters controlling beam setup, helicity sampling, PDFs, uncertainty reweighting, plotting, initial-state radiation, and parton showers.
- Beam energies and the fixtarget flag specify collider energies and fixed-target operation.
- The ranhel parameter controls Monte Carlo helicity sampling, with ranhel=4 selecting helicity eigenstates for subsequent spin-entangled decays.
- PDF settings select PDF sets and can enable LHAPDF-based PDF uncertainty reweighting.
- Scale reweighting estimates renormalization- and factorization-scale dependence through configurable variation bounds.
- Plotting flags generate histograms and output files in TopDrawer, Gnuplot, or Root formats on the fly.
- Parameters control QEDPS initial-state radiation and parton-shower activation, with parton shower=0 denoting fixed-order calculation.
D Addon codes
HELAC-Onia 2.0 includes addon codes for dedicated phenomenological studies, listed in the addon/addon process.dat file.
- Addon codes for dedicated studies are implemented in HELAC-Onia 2.0.Their available processes are listed in addon/addon process.dat.
D.1 Single-quarkonium hadroproduction with crystal ball function
This section introduces a crystal-ball-function approach for data-driven single-quarkonium hadroproduction, including its cross-section formulation and fitted parameters.
- Single-quarkonium production remains theoretically challenging, motivating data-driven empirical descriptions for collider phenomenology.The approach is also presented as an economical way to generate single-quarkonium events.
- The initial-averaged squared amplitude for single-quarkonium production is modeled with a crystal ball function under gluon-gluon-channel dominance.
- The proton-proton cross section combines the modeled production amplitude with the gluon PDF and Lorentz-invariant phase space.
- The parameters λ, κ, n, and ⟨P_T⟩ are determined by fitting the model to experimental data.
D.1.1 Fit codes
HELAC-Onia 2.0 provides fitting codes driven by Minuit and demonstrates them with a combined fit to multiple collider datasets for prompt ψ(2S).
- Dedicated fitting codes support ψ(1S, 2S) and Υ(1S, 2S, 3S) crystal-ball fits.
- The fitting workflows are driven by Minuit using configurable state, fit-parameter, and experimental-data input files.
- κ = 0.543 and λ = 0.118 were obtained for prompt ψ(2S) with ⟨P_T⟩ = 4.5 GeV and n = 2.The combined fit used ATLAS, CMS, LHCb, and CDF data, with χ2 = 242 for 90 experimental data.
D.1.2 A simple event generator for single-quarkonium hadroproduction
The addon suite extends single-quarkonium event generation through fitted crystal-ball models and implements pocket-formula DPS calculations for quarkonium, diphoton, and dijet production.
- Fitted crystal-ball parameters can generate events for multiple single-quarkonium states, including J/ψ, ψ(2S), Υ states, and χc or χb states.The generator supports proton-proton and proton-antiproton collisions.
- Users can configure the quarkonium species, polarization, and crystal-ball parameters through dedicated input files.
- The DPS addon calculates double-quarkonium production with a pocket formula based on single-quarkonium cross sections and σeff.σeff characterizes an effective spatial area of parton-parton interactions.
- The first-order assumption that σeff is process- and energy-independent should be checked case by case.The passage notes that σeff may vary with initial-parton species and Bjorken x.
- The addon suite also supports data-driven heavy-flavor pair production and unweighted event generation.
- DPS diphoton and dijet production uses implemented leading-order matrix elements for γγ, γj, and jj subprocesses, including a loop-induced gluon-gluon diphoton channel.Users can select subprocesses or generate corresponding non-DPS samples for cross-checks and global K-factor specification.