  Experimental measurements in deep-inelastic scattering and lepton-pair
production on deuterium targets play an important role in the flavor separation
of $u$ and $d$ (anti)quarks in global QCD analyses of the parton distribution
functions (PDFs) of the nucleon. We investigate the impact of theoretical
corrections accounting for the light-nuclear structure of the deuteron upon the
fitted $u, d$-quark, gluon, and other PDFs in the CJ15 and CT18 families of
next-to-leading order CTEQ global analyses. The investigation is done using the
$L_2$ sensitivity statistical method, which provides a common metric to
quantify the strength of experimental constraints on various PDFs and ratios of
PDFs in the two distinct fitting frameworks. Using the $L_2$ sensitivity and
other approaches, we examine the compatibility of deuteron data sets with other
fitted experiments under varied implementations of the deuteron corrections. We
find that freely-fitted deuteron corrections modify the PDF uncertainty at
large momentum fractions and will be relevant for future PDFs affecting
electroweak precision measurements.
