Standard Model Collision Laboratory · Validation report · September 2026

How Hadronica compares with MadGraph, PYTHIA, Herwig and Sherpa

Hadronica was tested against the established particle-physics event generators on the same inputs and the same published measurements. Its own physics engine reproduces MadGraph to 0.13 %, its PYTHIA mode is identical to PYTHIA run directly, and against real LEP and LHC data it matches or beats Herwig 7.3 and Sherpa 3.0 on five of six benchmarks. Soft (minimum-bias) collisions are where it falls behind.

Summary

Own engine vs MadGraph≤ 0.13 % largest difference over 25 cross sections, 11 processes, same conventions

PYTHIA mode vs PYTHIAidentical bit-for-bit the same Rivet histograms for the same events

Best on data1.82 χ²/ndf on CMS top-pair data with NLO + MadSpin + tune (Herwig 15.6, Sherpa 15.4)

Weakest area36.3 χ²/ndf on ATLAS minimum bias, against Herwig's 7.1

Against measured data

Each generator ran Hadronica's six validation benchmarks, analysed with the same Rivet analyses and scored with the same code. The score is the median χ²/ndf over each measurement's distributions: 1 means agreement within the uncertainties, and lower is better. The first three columns are like for like: leading order with a parton shower (Sherpa also merges extra jets). The last column is Hadronica's best mode, which uses next-to-leading-order samples.

Benchmark	Hadronica LO	Herwig 7.3	Sherpa 3.0	Hadronica best
LEP event shapesALEPH, e⁺e⁻ → hadrons at 91.2 GeV; Phys. Rept. 294 (1998) 1	2.48	19.48 ^†	4.57	2.48same as LO
Minimum biasATLAS, charged particles at 13 TeV; Phys. Lett. B 758 (2016) 67	36.33	7.10	n/c ^‡	36.33same as LO
Z transverse momentumATLAS, Z → ℓℓ at 13 TeV; Eur. Phys. J. C 80 (2020) 616	4.23	4.62	9.45	1.65NLO FxFx + Hadronica tune
Top pairs, lepton + jetsCMS, event variables at 13 TeV; JHEP 06 (2018) 002	7.92	15.59	15.44	1.82NLO + MadSpin + tune
Top pairs, dileptonATLAS, eμ channel at 13 TeV; Eur. Phys. J. C 80 (2020) 528	11.34	22.19	15.53	0.97NLO + MadSpin
Inclusive jetsCMS, jet cross section at 13 TeV; Eur. Phys. J. C 76 (2016) 451	5.68	8.55	6.27	5.68same as LO

^† Herwig on LEP is unconfirmed. Its charged multiplicity is 19.48 against ALEPH's 20.91 ± 0.22 (Phys. Rept. 294 (1998) 1). Herwig's authors document that its tune cannot describe LEP spectra and multiplicities well at the same time (D. Reichelt, P. Richardson, A. Siodmok, Eur. Phys. J. C 77 (2017) 876, arXiv:1708.01491), but its event shapes are surprisingly poor for a generator tuned to LEP. This Herwig build needed nine workarounds for Ubuntu 26.04's compilers and tools, so a build problem cannot be ruled out.

^‡ Sherpa on minimum bias is not comparable. Sherpa's official minimum-bias example covers non-diffractive collisions only, while the ATLAS measurement includes diffraction. It predicts 62 % too many particles per event, which says more about the setup than about Sherpa.

Limited by simulation statistics. In the dilepton top-pair and Z transverse-momentum measurements the data are more precise than 60 000 to 150 000 simulated events. There a χ²/ndf near 1 means consistent within the simulation's statistics rather than agreement at the data's precision; large values still mean real disagreement.

Fairness fixes. Herwig's LEP setup radiated photons off the incoming beams, which the data are corrected for; it now runs without initial-state radiation (checked: no beam photons in 300 events). Sherpa's default left K⁰_S and Λ undecayed, which the LEP measurement counts; its LEP run now decays particles with cτ < 300 mm, the LEP convention. Herwig and Sherpa ran at leading order because their NLO modes need OpenLoops, which is not installed.

Hadronica's own engine against MadGraph

Hadronica's built-in engine computes Born cross sections from its own formulas. MadGraph5_aMC@NLO is the standard for tree-level calculations. With Hadronica's couplings switched to MadGraph's conventions (α = 1/132.04, on-shell mixing angle, no QCD factor) every cross section agrees within MadGraph's precision, which checks the formulas themselves. As shipped, Hadronica uses a running α(s), the effective mixing angle and a QCD factor for quarks; those choices move cross sections by a few percent and are what reproduce LEP's measured asymmetries.

Process	√s (GeV)	MadGraph σ (pb)	Hadronica / MG, same scheme	Hadronica / MG, as shipped
e⁺e⁻ → μ⁺μ⁻	20.0	233.8	1.0003	1.0143
e⁺e⁻ → μ⁺μ⁻	91.2	2006	1.0000	0.9887
e⁺e⁻ → μ⁺μ⁻	250.0	1.775	1.0001	1.0556
e⁺e⁻ → μ⁺μ⁻	500.0	0.4303	1.0005	1.0733
e⁺e⁻ → τ⁺τ⁻	91.2	2002	0.9997	0.9884
e⁺e⁻ → τ⁺τ⁻	250.0	1.774	1.0006	1.0561
e⁺e⁻ → uū	91.2	6901	0.9998	1.0162
e⁺e⁻ → uū	250.0	3.016	0.9996	1.0639
e⁺e⁻ → dd̄	91.2	8840	0.9998	1.0208
e⁺e⁻ → dd̄	250.0	1.764	0.9988	1.0260
e⁺e⁻ → bb̄	91.2	8765	0.9998	1.0207
e⁺e⁻ → bb̄	250.0	1.763	0.9987	1.0258
e⁺e⁻ → tt̄	365.0	0.4972	0.9997	1.0859
e⁺e⁻ → tt̄	500.0	0.5515	0.9995	1.0868
e⁺e⁻ → ν_μν̄_μ	91.2	3944	1.0001	0.9943
e⁺e⁻ → ν_μν̄_μ	250.0	0.5229	0.9991	0.9932
e⁺e⁻ → ν_eν̄_e	91.2	3959	1.0001	0.9942
e⁺e⁻ → ν_eν̄_e	250.0	42.72	1.0003	0.9961
e⁺e⁻ → ZH	240.0	0.2393	1.0001	0.9942
e⁺e⁻ → ZH	365.0	0.1171	0.9999	0.9941
e⁺e⁻ → ZH	500.0	0.05715	0.9997	0.9938
Bhabha (QED)	91.2	3858	1.0008	1.0008
Bhabha (QED)	250.0	513.3	1.0007	1.0007
e⁺e⁻ → γγ (QED)	91.2	60.91	1.0000	1.0000
e⁺e⁻ → γγ (QED)	250.0	8.103	1.0001	1.0001

√s (GeV)	MadGraph A_FB	Hadronica, same scheme	Hadronica, shipped
20.0	-0.0175 ± 0.0071	-0.0273	-0.0271
91.2	0.0380 ± 0.0071	0.0331	0.0161
250.0	0.5315 ± 0.0060	0.5301	0.5175
500.0	0.4839 ± 0.0062	0.4897	0.4743

Forward–backward asymmetry of e⁺e⁻ → μ⁺μ⁻ (MadGraph from 20 000 events). At the Z pole, Hadronica as shipped gives 0.0161, close to LEP's measured 0.0169 ± 0.0013 (PDG 2026 Electroweak review, Table 10.3); MadGraph's tree-level scheme gives about twice that.

Hadronica's PYTHIA mode against PYTHIA itself

A stand-alone C++ program ran PYTHIA with exactly the settings Hadronica uses, handing events to Rivet through PYTHIA's own converter and skipping every Hadronica layer. For the same events, both routes produce bit-identical histograms. With independent random seeds they agree within statistics; the minimum-bias figure reflects strongly correlated bins, since a control comparing PYTHIA with itself gives 1.14 on the same measure.

Benchmark	Hadronica vs data	PYTHIA direct vs data	Hadronica vs PYTHIA
LEP event shapes	2.48	2.47	1.02
Minimum bias	36.33	36.68	1.74
Z transverse momentum	4.23	4.09	1.00
Top pairs, lepton + jets	7.92	8.67	0.70
Inclusive jets	5.68	6.33	1.01

Method

All runs used the same beams, energies and generation cuts as Hadronica's validation: 60 000 to 150 000 events per benchmark, generated in parallel chunks with independent seeds and merged with rivet-merge. Herwig 7.3.0 was built from source with herwig-bootstrap; Sherpa 3.0.0 came from conda-forge; both used their authors' example inputs, changing only beams, energy, cuts and output. Rivet 4.1.4 supplied the analyses and the published reference data.

The scripts are in hep/compare/ of the Hadronica repository: builtin_vs_madgraph.py, pythia_direct.py, other_generators.py and summary.py. Every number on this page is read from their saved outputs, and Hadronica's test suite checks the numbers quoted in its audit against the same files.

Generators: MadGraph5_aMC@NLO, J. Alwall et al., JHEP 07 (2014) 079, arXiv:1405.0301; PYTHIA 8.3, C. Bierlich et al., SciPost Phys. Codebases 8 (2022), arXiv:2203.11601; Herwig 7.3, G. Bewick et al., Eur. Phys. J. C 84 (2024) 1053, arXiv:2312.05175; Sherpa 3, E. Bothmann et al., JHEP 12 (2024) 156, arXiv:2410.22148. Analysis: Rivet 4, C. Bierlich et al., SciPost Phys. Codebases 36 (2024), arXiv:2404.15984; reference data from HEPData (E. Maguire, L. Heinrich, G. Watt, J. Phys. Conf. Ser. 898 (2017) 102006).

Sources: D. Reichelt, P. Richardson, A. Siodmok, Improving the Simulation of Quark and Gluon Jets with Herwig 7, Eur. Phys. J. C 77 (2017) 876; MCPlots, Z → hadrons, Herwig.