Unfolding with systematics benchmark datasets: Realistic datasets with detector and theory systematic variations

Three datasets with Systematic Variations for Unfolding This dataset provides three synthetic samples for unfolding R&D and systematic-aware machine-learning and statistical inference benchmarks. The release accompanies the publication arXiv:2510.15129. Toy examples - generation at run time Two toy examples are provided together with generators: Exponential distribution resembling a transverse momentum distribution Resonant distribution resembling a Z mass measurement Each of which include both signal and background components and each with various theory and systematic variations. The histograms corresponding to each process are included. Full Physics Example with Theory and Detector Variations Additionally 5M events simulated with Pythia 8.312 and showered through a modified ATLAS-like Delphes 3.5.1 fast detector simulation are included. See the included `WJETSDATASET.md` for the full specification. Generation Beams: pp at sqrt(s) = 13 TeV Hard processes: Pythia 8 LO 2 → 2 W+jet processes `WeakBosonAndParton:qqbar2Wg` and `qg2Wq` Parton-level cut: pTHatMin = 20 GeV W decay: W → e nu and W → mu nu (W → tau nu disabled) Pythia tune: Monash 2013 default; PDF set NNPDF2.3 LO (5-flavour scheme) Detector simulation: Delphes 3.5.1 ATLAS-like card, modified for consistent anti-kT R = 0.4 jet clustering at truth and reco level and with the GenJetFlavorAssociation module enabled for truth jet flavour Jet algorithm:** anti-kT, R = 0.4, p_T > 25 GeV (truth and reco) Selection: exactly one isolated lepton (p_T > 25 GeV, |eta| < 2.5), at least one jet (p_T > 25 GeV, |eta| < 4.5), MET > 25 GeV Truth ↔ reco match: leading reco jet within DeltaR < 0.4 of leading GenJet Process classification: inclusive any-jet, priority b > c > light Systematic variations 21 samples in total, each with 1 000 000 generated events: Detector (11 samples; same Pythia seed, varying Delphes cards nominal jet energy scale +/- 2% jet energy resolution +/- 10% electron ID efficiency +/- 4% (central eta) muon ID efficiency +/- 4% (central eta) b-tag efficiency +/- 10% (b, c and light mistag scaled together) Theory (10 samples; varying Pythia seed, nominal Delphes) renormalisation scale muR x {0.5, 2.0} factorisation scale muF x {0.5, 2.0} ISR alpha_s in {0.115, 0.140} FSR alpha_s in {0.115, 0.140} Pythia strange-quark fragmentation StringFlav:probStoUD in {0.19, 0.30} A 2% luminosity uncertainty is to be applied analytically by the user. Files Six compressed NumPy archives for the raw events: ```light_detector.npz light_theory.npzcharm_detector.npz charm_theory.npzbeauty_detector.npz beauty_theory.npz``` The detector files share a single truth array (the 11 detector variations are evaluated on the same hadron-level events) and contain 11 (reco, sel, matched) blocks. The theory files contain independent (truth, reco, sel, matched) blocks per variation. Each event record stores five observables (leading-jet p_T, jet multiplicity, scalar H_T, leading-jet |eta| and missing transverse energy) at both truth and reco level, plus the W+jets selection and truth-reco matching flags. Quick-start usage ```pythonimport numpy as np d = np.load("beauty_detector.npz")truth = d["truth"] # (N, 5) -- jet_pt, n_jets, ht, jet_abseta, metreco = d["reco_jes_up"] # (N, 5) -- JES +2% reconstructionmask = d["sel_jes_up"] & d["matched_jes_up"] # response matrix entries (for unfolding):truth_pt = truth[mask, 0]reco_pt = reco[mask, 0]``` For the full specification (PDF set, smearing formulas, b-tag efficiency parametrisations, processing pipeline, caveats) see `WJETSDATASET.md`. Caveats (please read before use) Pythia 8 does not have a W+bb̄ matrix element, so all W+beauty events in this sample originate from parton-shower g → bb̄ splittings. As a consequence, FSR variations produce a substantially larger relative shift on W+beauty yields than on W+light or W+charm. Analyses that require a realistic W+b model should generate a dedicated W+bb̄ sample with a higher-multiplicity matrix-element generator (MadGraph, POWHEG) and shower it through Pythia. No pile-up is included. Tau leptons in W decays are disabled. Citation If you use this dataset, please cite both the Zenodo record 10.5281/zenodo.20140091 and the companion paper arXiv:2510.15129. ```bibtex@dataset{systematic_unfold_2026, title = {Unfolding with systematics benchmark datasets: Realistic datasets with detector and theory systematic variations}, author = {Croft, Vincent A. and Brenner, Lydia and Burgard, Carsten}, year = {2026}, doi = {10.5281/zenodo.20140091}, url = {https://doi.org/10.5281/zenodo.20140091},}```