The other three groups on this site each hand the world a finished product: a set of proton distributions with an error band, ready to download. Colibri hands the world a workshop instead. It is an open-source code in which you supply the model of the proton, and it will fit it — and, crucially, it will compute the uncertainty on that fit three different ways within the same program: Hessian, Monte-Carlo replicas, and Bayesian nested sampling. That is the whole point, and it is the reason this project exists: it is the only way to find out whether those three answers agree.
If you read nothing else on this page.
Every group that measures the proton has to answer two separate questions: what shape is it, and how sure are we. The second question has three standard answers in this field, and they are genuinely different pieces of mathematics. Until now, nobody could tell whether those three answers actually agree, because each group uses only one of them — and a different dataset, and a different model of the proton, and different code. Change four things at once and you learn nothing about any one of them.
Colibri is a program that holds everything else fixed and changes only the uncertainty method. That is its entire scientific value. It is a measuring instrument for measuring instruments.
It comes from Cambridge, from Maria Ubiali's group, funded by a European Research Council grant called PBSP — "Physics Beyond the Standard Proton". The paper describing it was published in the European Physical Journal C in January 2026.
A small university group, not a large international collaboration.
This is the clearest structural difference from the other three. MSHT, CT and NNPDF are long-running collaborations spanning many institutions and, in NNPDF's case, dozens of authors. Colibri is a five-author paper from one research group, built inside a single funded project.
| author | affiliation as published |
|---|---|
| Mark N. Costantini | DAMTP, University of Cambridge |
| Luca Mantani | IFIC, Universidad de Valencia–CSIC, Spain |
| James M. Moore | Lucy Cavendish College, Cambridge |
| Valentina Schütze Sánchez | DAMTP, University of Cambridge |
| Maria Ubiali | DAMTP, University of Cambridge |
| full name | Physics Beyond the Standard Proton |
| funder | European Research Council — ERC Starting Grant, Horizon 2020 |
| grant ID | 950246 |
| value | €1,473,463 |
| host | DAMTP, University of Cambridge |
| principal investigator | Maria Ubiali |
| dates | 1 October 2020 — 30 September 2026 |
| website | pbsp.org.uk |
Maria Ubiali is Professor of Theoretical Particle Physics and Phenomenology at DAMTP, Cambridge, a title she has held since 2022. Her research spans QCD and beyond-the-Standard-Model phenomenology, with a focus on determining proton structure using machine-learning techniques. She is a long-standing member of the NNPDF collaboration — which matters for reading this page: Colibri is built by someone from inside the Monte-Carlo tradition, deliberately building the tools to check it.
Why "just compare the published sets" does not answer the question.
Suppose you want to know whether the Hessian method gives a smaller error bar than the Monte-Carlo method. The obvious move is to download MSHT20 (Hessian) and NNPDF4.0 (Monte-Carlo) and compare the bands. But those two sets differ in every respect at once:
Any difference you observe is the sum of all five. The methodological question is confounded with everything else, and no amount of comparing published sets will un-confound it.
The framing above is our own gloss, not a quotation from the Colibri authors. What the paper itself states is the positive version: that its modularity lets a user "benchmark different parametrisations under identical statistical conditions", and that applying the methods "to the same dataset and parametrisation" allows one to "systematically study the assumptions and limitations of each method". The confounding argument follows from that, but the paper does not use the word.
Open-source Python, JAX under the hood, standing on NNPDF's public data.
| language | Python (≥ 3.11), structured as a reportengine application |
| numerical core | JAX — array operations, automatic differentiation, optional GPU via CUDA |
| optimiser | Optax — gradient-based minimisation |
| sampler | UltraNest — nested sampling for the Bayesian mode |
| data & theory | experimental data and fast theory predictions (FK tables) taken from the public NNPDF code |
| output | writes fits in LHAPDF format, so results plug into standard machinery |
| licence | GPL-3.0 · github.com/HEP-PBSP/colibri |
Automatic differentiation means the code can compute exact gradients of the fit quality with respect to every parameter, without anyone hand-deriving them. That is what makes gradient-based fitting and curvature (Hessian) calculations practical on the same model that the sampler explores — and it is why all three uncertainty methods can share one implementation instead of three.
The relationship to NNPDF is a real dependency, not a passing resemblance: Colibri takes its experimental data and fast theory predictions from NNPDF's public code, and is built on the same reportengine framework that underpins NNPDF's validphys. What it changes is that the parametrisation and the inference method both become things the user plugs in, rather than fixed choices.
This is the feature everything else serves.
| method | what it does | what it assumes |
|---|---|---|
| Hessian | Finds the best fit by gradient descent, then measures the curvature of the fit quality around that point and inverts it to get a covariance. Supports a tolerance factor T>1, rescaling the covariance by T². | That the fit quality is a well-behaved bowl near its minimum — i.e. a Gaussian approximation. |
| Monte-Carlo replicas | Generates many pseudo-datasets by jiggling the real data within its error bars, and fits each one independently. The spread of the resulting fits is the uncertainty. | Formally equivalent to the Bayesian posterior only for linear models with Gaussian likelihoods — the paper says so explicitly. |
| Bayesian | Nested sampling (via UltraNest) — maps the full posterior probability over the parameter space, given an explicit prior. | That the sampler has actually converged. Makes the prior explicit rather than implicit. |
A fourth mode, analytic, is available for models where the posterior has a closed form — a linear model with a Gaussian likelihood. That is the case where all methods provably coincide, so it serves as an exact reference for validating the other three.
These are not three equally-good options. The Bayesian posterior is the reference answer; Hessian and Monte-Carlo are approximations to it that are exact only under conditions that a real PDF fit does not satisfy. The value of running all three on one fit is that it tells you how badly those approximations fail in practice — which is a question nobody could previously answer.
Being precise here matters more than being impressive.
The paper is a tool paper with a proof-of-concept validation. It is important not to overstate what has been demonstrated:
| model fitted | the Les Houches parametrisation — a simple polynomial form with 13 free parameters covering gluon, Σ, uv and dv |
| data used | deep-inelastic scattering only, the DIS subset of NNPDF4.0 — no collider data |
| tests run | Level-0 and Level-1 closure tests — fitting synthetic data generated from a known "true" answer, without and then with noise |
| result | all three methods reproduce the known truth, and agree with each other |
No global PDF fit. No neural-network fit. No Level-2 closure test. No hadron-collider data. The 13-parameter polynomial is a well-behaved, near-Gaussian problem — which is precisely the regime where the three methods should agree. Their agreement validates the machinery; it does not establish that they agree for a realistic fit with dozens of parameters and flat directions.
That last point is not a criticism — it is the open door. The paper's own framing is that Colibri is "a living project… under active development", and that for Bayesian PDF determination "a full-fledged PDF fit is yet to be produced, in part due to the absence of accessible, general-purpose tools."
There is no Colibri PDF set. This is deliberate, and worth stating plainly.
The other three pages on this site end with a list of downloadable grids. This one cannot, and it would be wrong to imply otherwise. We checked the official LHAPDF set index directly: there is no Colibri set, and no PBSP set. By comparison, the same index lists MSHT20, CT18 and NNPDF4.0 many times over.
| group | releases a public PDF set? | what you actually get |
|---|---|---|
| MSHT20 | yes | LHAPDF grids you can download and use |
| CT18 | yes | LHAPDF grids you can download and use |
| NNPDF4.0 | yes | LHAPDF grids you can download and use |
| Colibri | no | source code you run to produce fits |
Colibri writes its output in LHAPDF format, so a fit you run with it slots into the standard tooling. But the project ships no grid of its own, and it does not compete with or supersede the other three as a deliverable. It is infrastructure.
Taking the idea past the 13-parameter demonstration.
Colibri establishes that the three methods can be run under identical conditions, and shows that they agree on a well-behaved 13-parameter problem. The obvious next question is what happens when the problem is not well-behaved — a realistic parametrisation, with many more parameters, on real data.
That is what the figure below is. It is one fit — the MSHT20 parametrisation, 52 free parameters, on real deep-inelastic-scattering data — with the uncertainty computed all three ways. The answer is that in this regime the three methods do not agree at all.
Band width relative to the Bayesian answer. If the three methods agreed, all three lines would sit on top of each other at 1.
This is our own run, not a result published by the Colibri authors, and not a claim about their work. It is a methodology test on deep-inelastic-scattering data only — not a measurement of the proton, and these bands should not be used as physics. The full read-out is on the Explorer and in the August deck.
Everything on this page traces to one of these.