Mapping data sensitivities in global QCD analysis with linear response and influence functions

TL;DR

This paper introduces a linear response and influence function framework to interpret how experimental data constrains non-perturbative functions in global QCD analyses, enhancing understanding of information flow.

Contribution

The authors develop a gradient-based sensitivity analysis method to clarify data influence on fitted QCD quantities, improving interpretability of complex fits.

Findings

Quantifies how data constrains hadron structure functions.

Reveals local data influence on uncertainties and correlations.

Provides a transparent framework for diagnosing information flow.

Abstract

Global QCD analyses provide the primary framework for extracting hadron structure from experimental data, yet the mechanisms by which data constrain non-perturbative functions remain difficult to interpret due to the high dimensionality and complexity of these fits. Here we develop a framework based on linear response and influence functions, which are gradient-based sensitivity measures that directly quantify how experimental information propagates to fitted quantities and observables. These quantities cleanly expose how data locally determines the central values and uncertainties of quantum correlation functions, as well as the correlations between them, providing a transparent and general framework for diagnosing information flow in inverse problems in QCD.