Quantifying the interplay of experimental constraints in analyses of parton distributions

Parton distribution functions (PDFs) play a central role in calculations for the LHC. To gain a deeper understanding of the emergence and interplay of constraints on the PDFs in the global QCD analyses, it is important to examine the relative significance and mutual compatibility of the experimental datasets included in the PDF fits. Toward this goal, we discuss the <math display="inline"><msub><mi>L</mi><mn>2</mn></msub></math> sensitivity, a convenient statistical indicator for exploring the statistical pulls of individual datasets on the best-fit PDFs and identifying tensions between competing datasets. Unlike the Lagrange multiplier method, the <math display="inline"><msub><mi>L</mi><mn>2</mn></msub></math> sensitivity can be quickly computed for a range of PDFs and momentum fractions using the published Hessian error sets. We employ the <math display="inline"><msub><mi>L</mi><mn>2</mn></msub></math> sensitivity as a common metric to study the relative importance of datasets in the recent ATLAS, CTEQ-TEA, MSHT, and reduced PDF4LHC21 PDF analyses at next-to-next-to-leading-order and approximate next-to-next-to-next-to-leading-order. We illustrate how this method can aid the users of PDFs to identify datasets that are important for a PDF at a given kinematic point, to study quark flavor composition and other detailed features of the PDFs, and to compare the data pulls on the PDFs for various perturbative orders and functional forms. We also address the feasibility of computing the sensitivities using Monte Carlo error PDFs. Together with the article, we present a companion interactive website with a large collection of plotted <math display="inline"><msub><mi>L</mi><mn>2</mn></msub></math> sensitivities for eight recent PDF releases and a C++ program to plot the <math display="inline"><msub><mi>L</mi><mn>2</mn></msub></math> sensitivities.