Deuterium scattering experiments in CTEQ global QCD analyses: a comparative investigation

TL;DR

This work compares CJ15 and CT18 global QCD fits to assess how deuteron nuclear corrections shape nucleon PDFs, using the L2 sensitivity metric to quantify cross-framework constraints and data compatibility. It demonstrates that freely fitted deuteron corrections significantly affect high-x PDFs, especially d and the gluon, with impacts on electroweak precision observables and the reliability of flavor separation. The analysis highlights that deuteron corrections can be as consequential as NNLO effects in some data regimes, and that allowing nuclear parameters to vary reduces tensions between datasets, motivating inclusion of nuclear corrections in future high-precision PDF determinations. The findings emphasize the importance of consistent treatment of light-nuclear effects for robust PDF predictions in upcoming collider and EW precision tests.

Abstract

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.

Figures (13)

• Figure 1: Hessian correlations Stump:2001guNadolsky:2001ygNadolsky:2008zw for the values of $\sin\theta_W$ extracted from $Z$ boson production at the LHC 8 TeV Armbruster:2018. Left: correlations with valence PDFs and PDF ratios at $Q=$81.45 GeV, plotted as a function of $x$ for CT14 NNLO PDFs. Right: the same, for correlations with PDFs of individual flavors.
• Figure 2: Lagrange Multiplier scans on $d_{val}(x=0.03,Q=85\, \mathrm{GeV})$ (left) and $u_{val}(x=0.03,Q=85\, \mathrm{GeV})$ (right), showing the changes in the $\chi^2$ for all data sets and most sensitive experimental data sets in the CT18Z NNLO global QCD analysis Hou:2019efy.
• Figure 3: We plot the nuclear correction ratio, $F^N_2/F^d_2$, calculated using the central CJ15 fit results for several selections of the $Q^2$ scale. Each of the four panels above highlights a given value of $Q^2$, while graying out the curves for other scales in order to retain visual information on the scale dependence of the correction factor at large $x$. In the upper two panels, which focus on lower scales, $Q^2=5, 10$ GeV$^2$, the dotted lines indicate the range of $x$ that is only accessible to CJ ($W^2\!>\!3$ GeV$^2$) but not CT ($W^2\!>\!12.25$ GeV$^2$), due to the more conservative cut of the latter.
• Figure 4: Kinematics of the DIS data included in the fits discussed in this paper. The HERA DIS collider data were taken on proton targets; the fixed-target SLAC, JLab, BCDMS and NMC experiments include both proton and deuterium target data at approximately the same kinematics. The $W^2=12.25$ GeV$^2$ and $W^2=3$ GeV$^2$ cuts adopted, respectively, by the CT and CJ fits are shown by dashed and dot-dashed lines, respectively. The figure is taken from Ref. Owens:2012bv.
• Figure 5: A comparison of the PDF pulls of the deuterium DIS data computed according to the $L_2$ method at 2 GeV for the CT fixed d.c. (left) and CJ fixed d.c. (right) fits; both cases are for the scenario with fixed deuteron corrections. Here and elsewhere, we place on the vertical axis a self-explanatory label of $\Delta \chi^2$ as we plot the $L_2$ sensitivity which approximates this quantity.