Colibri: A new tool for fast-flying PDF fits

TL;DR

Colibri presents a modular, open-source platform for global PDF fits that unifies multiple inference strategies under a single framework. By providing a generic PDFModel interface, fast forward maps via FK-tables, and Bayesian, Hessian, and Monte Carlo approaches, Colibri enables straightforward benchmarking and principled model comparison across parametrisations. The paper demonstrates closure tests with the Les Houches parametrisation, highlighting consistent results across inference methods and showcasing Bayesian posterior samples for detailed correlation studies. The work emphasizes Colibri's potential for future joint fits with Standard Model parameters and Beyond-the-Standard-Model coefficients, aiming to deliver robust, reproducible PDF determinations with a principled treatment of uncertainties.

Abstract

We present Colibri, an open-source Python code that provides a general and flexible tool for PDF fits. The code is built so that users can implement their own PDF model, and use the built-in functionalities of Colibri for a fast computation of observables. It grants easy access to experimental data, several error propagation methodologies, including the Hessian method, the Monte Carlo replica method, and an efficient numerical Bayesian sampling algorithm. To demonstrate the capabilities of Colibri, we consider its simplest application: a polynomial PDF parametrisation. We perform closure tests using a full set of DIS data and compare the results of Hessian and Monte Carlo fits with those from a Bayesian fit. We further discuss how the functionalities illustrated in this example can be extended to more complex PDF parametrisations. In particular, the Bayesian framework in Colibri provides a principled approach to model selection and model averaging, making it a valuable tool for benchmarking and combining different PDF parametrisations on solid statistical grounds.

Figures (4)

• Figure 1: Colibri's workflow: the code takes as input (i) a PDF model, which may be any arbitrary parametrisation implemented by the user, makes use of (ii) JAX jax2018github, which provides high-performance array operations and native GPU support for fast computations, and inherits (iii) data and theory predictions from the NNPDF public code nnpdfcodeNNPDF:2021uiq. The code then performs a fit using a given inference method, which is specified by the user. At the time of release, the options are a Monte Carlo, Hessian, Bayesian or analytic fit. In each case, the result is outputted in the LHAPDF format Buckley:2014anaLHAPDFurl.
• Figure 1: A gluon PDF fit resulting from a level 0 closure test computed with the Monte Carlo replica method (blue), Bayesian inference (orange), and the Hessian method (red). The green line shows the underlying law to be recovered, which in this case is the Les Houches parametrisation with best-fit parameter values from Ref. Alekhin:2005xgg. The right-hand panel shows the ratio to the underlying law.
• Figure 2: A $\Sigma$ PDF fit resulting from a level 1 closure test computed with the Monte Carlo replica method (blue), Bayesian inference (orange), and the Hessian method (pink). The green line shows the underlying law to be recovered, which in this case is the Les Houches parametrisation with best-fit parameter values from Ref. Alekhin:2005xgg. The right-hand panel shows the ratio to the underlying law.
• Figure 3: Example corner plots of posterior samples. The left panel shows the parameters associated with the $u$ valence quark, and the right panel those of the $d$ valence quark. In principle, analogous plots could be produced for all 13 parameters, but here we restrict to subsets for clarity and illustration.