Study · Topic 3
The global-fitting machine — from measurements to PDFs
The engineering: parametrizations, sum-rule algebra, FK tables, and the χ² done right. Each section below is a full chapter: complete mathematical treatment, derivations, diagrams, and worked examples.
3.1The inverse problem and parametrizationsLH toy, MSHT20 Chebyshev form in full, NNPDF nets, grids — with the MSHT20 basis written out.
3.2Sum rules analytically: the Euler-Beta machineryEvery normalization integral derived — the exact algebra our MSHT20 port runs.
3.3FK tables and the theory pipelineFrom PineAPPL grids through EKO to the linear/quadratic contractions fits evaluate.
3.4The χ², correlated systematics, and t0Covariance anatomy, nuisance-parameter equivalence derived, the d'Agostini bias and its fix.
3.5The global-fitting landscape: MSHT, CT, NNPDFThe three collaborations, the Hessian/Monte-Carlo/Bayesian trichotomy, the PDF4LHC combination, and where this lab's controlled comparison sits.
3.6MSHT — fixed forms and the dynamic toleranceThe MRS→MRST→MSTW→MMHT→MSHT lineage, the Chebyshev fixed form, and the Hessian dynamic-tolerance method whose parametrization backs our fits.
3.7CT (CTEQ-TEA) — Hessian errors and toleranceThe CTEQ tradition, Bernstein forms, the two-tier Δχ²≈100 tolerance, and the Lagrange-multiplier cross-check.
3.8NNPDF — neural nets and Monte-Carlo replicasNo-fixed-form neural-net PDFs, the Monte-Carlo replica method and closure tests, and the open-source ecosystem Colibri is built on.