The papers this lab stands on

Colibri: a new tool for fast-flying PDF fits

Costantini, Mantani, Moore, Schutze Sanchez, Ubiali (HEP-PBSP, Cambridge) · arXiv:2510.03391 · Oct 2025

The framework this whole lab runs on: explicit Bayesian posteriors for PDFs via nested sampling (UltraNest), with pluggable parametrizations (abstract PDFModel: any JAX function θ → PDF grid) and Hessian/Monte-Carlo modes in the same chassis, so methodology comparisons share data, cuts, theory and code. Likelihood: Gaussian χ² with t0 covariance (Eq. 2.3); positivity/integrability as penalties (Eqs. 2.4–2.5); DIS predictions linear in the PDF (Eq. 2.6), hadronic quadratic (Eq. 2.7). Validated by L0/L1 closure tests on a 13-parameter benchmark parametrization (Sec. 3, Table 3.1) — the table we replicated 6/6.

Used in: everything. Replication: PPDF-1 PPDF-3 PPDF-4 PPDF-5 PPDF-6; real data PPDF-7–PPDF-9.

NNPDF4.0: the path to proton structure at 1% accuracy

Ball et al. (NNPDF) · arXiv:2109.02653 · EPJC 82 (2022) 428 · 139 pp

The state-of-the-art global fit and the ecosystem our fits consume: ~4,600 points from 80+ datasets (DIS, Drell-Yan, W/Z, jets, top…), neural-net parametrization (2–25–20–8 architecture in the evolution basis), 1000-replica uncertainty propagation, closure + future tests for validation. Companion infrastructure: YAML commondata with full correlated systematics, FK tables via PineAPPL→EKO, validphys analysis layer — the first global-fit framework ever fully open-sourced.

Used in: every dataset, cut, t0 reference and theory table we fit; the replica method we benchmarked in PPDF-5; the χ²/N ≈ 1.1–1.2 global benchmark our PPDF-9 floor question is calibrated against.

MSHT20: PDFs from LHC, HERA, Tevatron and fixed-target data

Bailey, Cridge, Harland-Lang, Martin, Thorne · arXiv:2012.04684 · EPJC 81 (2021) 341 · PDF ↗

One of the big-three global fits, and the source of the parametrization Maria pointed us at: x f(x,Q₀²) = A(1−x)^η x^δ (1 + Σᵢ aᵢ Tᵢ(y(x))) with Chebyshev polynomials in y = 1 − 2x^k, fitted in the basis u_V, d_V, S, s₊, s₋, d̄/ū, g (+c₊) — 52 free parameters after analytic sum rules. Hessian uncertainties with dynamic tolerance. The "real parametrization" successor to our Les Houches toy.

Used in: the coming MSHT20-in-Colibri port — target of the next phase; will be judged against the PPDF-7 evidence baseline.

FPPDF: assessing fitting-methodology impact at aN³LO (Hessian, open source)

Cruz-Martinez, Giani, Harland-Lang · arXiv:2602.07118 · Feb 2026 · github.com/FPPDF/fppdf · PDF ↗

Open tool running the MSHT20 fixed parametrization with Levenberg–Marquardt + dynamic-tolerance Hessian errors on the NNPDF data stack (sole dependency: nnpdf). Global χ²/N ≈ 1.13–1.17 over 4,616 points at NNLO/aN³LO. Headline finding: aN³LO and MHOU impacts on PDFs and benchmark cross-sections are largely methodology-insensitive; residual genuine differences sit in valence shapes and how uncertainty is distributed between data and extrapolation regions. Contains no Bayesian inference — which is precisely our opening.

Used in: exact parametrization code (pdfs.py, chebyshevs.py) and published starting parameters for our port; the Hessian counterpart for the future Bayesian-vs-Hessian MSHT20 comparison; parity-test reference implementation.

A critical study of the Monte Carlo replica method

Costantini, Madigan, Mantani, Moore · arXiv:2404.10056 · 2024

The theoretical spine of the whole Bayesian argument: proves the NNPDF-style replica ensemble coincides with Bayesian posterior sampling only for linear models with Gaussian likelihoods, and quantifies the bias beyond that. Leans on it: the motivation framing across the site and study guide; context for PPDF-5/PPDF-6.

A linear PDF model for Bayesian inference

Costantini, Mantani, Moore, Ubiali · arXiv:2507.16913 · 2025

The Colibri companion (cited there as the first realistic Bayesian fit): builds a linear PDF model from neural-net-derived basis vectors, making Bayesian PDF inference fast and exactly tractable. Leans on it: a candidate model class for our evidence-ladder after MSHT20 — linear models make the Bayes-vs-replica comparison exact.

A stress test of global PDF fits: closure testing MSHT & first direct NN comparison

Harland-Lang, Cridge, Thorne · arXiv:2407.07944 · 2024

Predecessor of FPPDF (the then-private code): closure-tests the MSHT20 fixed parametrization and compares directly to the NNPDF neural-net approach. Leans on it: evidence that the 52-param form is flexible enough to pass closure — the reason a Bayesian MSHT20 fit is meaningful at all.

UltraNest — a robust, general purpose Bayesian inference engine

Buchner · arXiv:2101.09604 · JOSS 6(60) 3001, 2021

The nested sampler inside every Bayesian fit we run: live-point contours, evidence integration with error budget, slice-sampling for high dimensions. Leans on it: every logZ we quote; the slice-sampler lesson of PPDF-8 is an UltraNest operational fact.

Fitting parton distribution data with multiplicative normalization uncertainties

Ball et al. (NNPDF) · arXiv:0912.2276 · 2009

The t0 paper: shows naive treatment of normalization errors biases fits low (d'Agostini bias) and introduces the t0 covariance prescription. Leans on it: the use_t0_covmat + t0pdfset lines in every runcard on this site; wiki entry t0 method.

LHAPDF6: parton density access in the LHC precision era

Buckley et al. · arXiv:1412.7420 · EPJC 75 (2015) 132

The community-standard PDF grid format and access library. Leans on it: our truth PDFs are read through it (PPDF-2); our posteriors export to it, making every fit usable by standard collider tools.

HERA and the LHC workshop proceedings — DGLAP evolution & parton-fit benchmarks

Alekhin, Blümlein, Böttcher et al. · arXiv:hep-ph/0601012 (Part A, pp. 119–159) · 2005

Where our "Les Houches" toy actually comes from: the HERA-LHC benchmark chapter defining common evolution settings and simple benchmark parametrizations for cross-group comparison. Leans on it: the 13-parameter form behind PPDF-1–PPDF-7.

An open-source machine learning framework for global analyses of parton distributions

Ball et al. (NNPDF) · arXiv:2109.02671 · 2021

The NNPDF4.0 code paper — n3fit, hyperoptimization, validphys, and the data infrastructure as software. Leans on it: the stack underneath Colibri; the citation Colibri's own README requests; reference for how commondata/FK tables are structured.