Simultaneous Extraction of Unpolarized PDFs and Nuclear Effects

We present a new global QCD analysis of unpolarized parton distribution functions (PDFs) and nuclear effects including for the ﬁrst time data from the SeaQuest and MARATHON experiments in addition to high-energy weak-boson-production data from the Tevatron and Large Hadron Collider. Simultaneously extracting the PDFs and nuclear effects, we ex-amine the impact of the SeaQuest and MARATHON data on the light-quark sea asymmetry and the EMC ratios of deuterium, helium, and tritium.


Introduction
Over the past few decades, experiments from lepton-nucleon deep-inelastic scattering (DIS), Drell-Yan, and weak boson production have revealed much about the one-dimensional structure of the proton (p), encoded in PDFs. However, there are still gaps in our knowledge, particularly for the down quark (d) at large momentum fraction x and the asymmetry of up and down antiquarks (ū andd) above x ≈ 0.3. Questions also remain concerning the nuclear effects within the light nuclei deuterium (D), helium ( 3 He), and tritium ( 3 H).
Recent experiments have attempted to provide insight on these questions. The MARATHON experiment at Jefferson Lab Hall A [1] measured DIS off of 3 He and 3 H targets in order to extract information on the ratio of down to up quarks d/u at high x as well as nuclear effects. These nuclear effects can be summed up by a non-trivial EMC ratio [2], which is defined as the ratio of the structure function F 2 for the nuclear target to the sum of F 2 for the constituent nucleons. The EMC ratio would be unity in the absence of nuclear effects. Meanwhile, the NuSea [3,4] and SeaQuest [5] experiments at Fermilab have measured the Drell-Yan process for proton and deuterium targets in order to extract information on thed/ū ratio at values of x up to 0.3 and 0.4, respectively.

098.1
We present an analysis using the JAM Monte Carlo global QCD framework including for the first time the latest measurements from SeaQuest and MARATHON , in addition to hadroncollider data from the Tevatron and LHC, and DIS data from fixed-target and collider experiments. With this data, we are able to extract the PDF ratios d/u andd/ū as well as the nuclear effects in A = 2, 3 nuclei [6, 7].

Methodology
Our theoretical framework is based on the JAM iterative Monte Carlo approach to QCD global analysis, which utilizes Bayesian inference sampling methodology that allows thorough exploration of the parameter space and robust error quantification. In this analysis, we parameterize the unpolarized PDFs at the input scale µ 2 0 = m 2 c , with m c the mass of the charm quark, using the standard form, where N , α, β, γ, and η are the parameters to be fit. We discriminate the valence and sea components through parameterizations for the quantities where the dependence on x and µ 2 0 has been suppressed. The input distributions u v , d v ,ū 0 , d 0 , s 0 , ands 0 , characterizing the quark distributions in the valence region, and the gluon PDF are parameterized individually as in Eq. (1). The S 1 and S 2 distributions describe the light and strange sea quarks, respectively, at low x by restricting the α in Eq. (1) so that the resulting distribution is more divergent than the valence PDFs. Furthermore, γ and η are free parameters for all distributions except s 0 ,s 0 , S 1 , and S 2 where they are set to zero.
The PDFs are evolved using the DGLAP evolution equation, and the renormalization group equation (RGE) is solved numerically for the strong coupling α S at two loops making use of the boundary condition α S (M Z ) = 0.118. The boundary conditions for the RGE are parameterized at the scale µ 2 0 and inferred from data. The evolution equations are solved using the zero-mass variable-flavor-number scheme with splitting kernels evaluated at O(α 2 S ). The values of the heavy-quark mass thresholds for the evolution of the PDFs and α S are taken from the PDG values m c = 1.28 GeV and m b = 4.18 GeV in the MS scheme [8]. All hard-scattering kernels are expanded to NLO in the strong coupling, with the NLO expressions for Drell-Yan and Wlepton production taken from [9] and [10], respectively.
For a nuclear target, nuclear effects such as binding, Fermi motion, and off-shell effects become relevant at x 0.2. In the weak-binding approximation, appropriate for light nuclei, nuclear PDFs can be expressed in terms of convolutions of light-cone momentum distributions of nucleons inside nuclei and nucleon PDFs [11,12]. The off-shell effects, which take into account the fact that a nucleon of mass M and 4-momentum k in a nucleus typically has k 2 = M 2 , can be parameterized in a similar manner using off-shell light-cone momentum distributions [7].

Quality of Fit
In addition to the new MARATHON data and SeaQuest data we fit also 2694 data points for the structure function F 2 measured in fixed-target DIS experiments on p and D targets as well as 1185 data points on reduced neutral and charged-current proton DIS cross sections, all with 098.2 Figure 1: Comparison of the JAM PDFs (red bands) with the results from NNPDF3.1 [13] (gold), ABMP16 [14] (blue), CJ15 [16] (cyan), and CT18 [15] (gray) at the scale Q 2 = 10 GeV 2 . All bands represent 1σ uncertainty and all results are at NLO. Note that the gluon PDF has been divided by 10.
the kinematic constraints W 2 > 3.0 GeV 2 and Q 2 > m 2 c . We fit also 199 Drell-Yan data points from NuSea [3,4], 97 data points on W ± asymmetries, 56 data points on reconstructed Z/γ * cross sections, and 200 data points on jet production.
The quality of our analysis is summarized by the global average χ 2 /N dat = 1.10 for a total of 4466 data points, with a χ 2 /N dat of 1.10 for DIS, 1.20 for Drell-Yan, 0.94 for W /Z boson production, and 1.09 for jet production. For the MARATHON experiment, we find a χ 2 /N dat of 0.99 for the measurement of the D/p structure function ratio and 0.67 for the measurement of the 3 He/ 3 H ratio, with the latter improving significantly with the inclusion of off-shell corrections. For the SeaQuest experiment, we find a χ 2 /N dat of 1.10, along with some tension with the NuSea data for x 0.2, as has been seen in previous analyses [5].

Results for PDFs and Nuclear Effects
The results for the PDFs are shown in Fig. 1. Most notably, we see that thed/ū ratio is larger than one up to x ≈ 0.4; a consequence of the inclusion of the SeaQuest data in our analysis that brings our results in agreement with those from CT18 and ABMP16 but in slight disagreement with those from NNPDF3.1 and CJ15. The inclusion of the SeaQuest data significantly reduces the errors on thed/ū ratio, up to around 50% for x 0.3. For the d/u ratio our result agrees with CJ15 and is consistent with NNPDF3.1, but disagreements are seen with CT18 and especially ABMP16. In the valence sector the resulting PDFs are generally slightly larger compared to other groups and, correlated with this result, we find a relatively suppressed strange distribution.  : Results from this analysis (red bands) for the deuteron EMC ratio R(D) at Q 2 = 10 GeV 2 (left) and the super-ratio R at the MARATHON kinematics Q 2 = 14x GeV 2 (right). The deuteron EMC ratio R(D) is also compared with that from CJ15 [16] (green band) and AKP17 [17] (light blue band). The super ratio R is compared with the KP model [18] (gray band).
the uncertainty on R across the entire range of x, from 50% at high x to 70% at low x, the resulting errors are still much larger than those from the KP model, suggesting that the latter may be underestimated.

Conclusions
We have presented the resulting PDFs and EMC ratios of a global QCD analysis including for the first time data from the SeaQuest and MARATHON experiments. The inclusion of the SeaQuest data causes some slight tension with the NuSea data, but reduces the uncertainty of thed/ū ratio by roughly 50% at high x and reveals that the ratio must remain larger than one up to x ≈ 0.4. The MARATHON data drastically decreases the uncertainties on the super ratio R. To some extent, our results for the EMC ratios disagree with those from the KP model. In particular, we find R(D) < 1 at x = 0.31.
In the future, combining this analysis with semi-inclusive DIS data could provide even more information on thed/ū ratio. Additional information on the nuclear EMC effects in 3 He and 3 H separately will come from 3 He/D and 3 H/D ratios measured by MARATHON , which are expected to be analyzed in the near future. Beyond this, constraints on neutron structure, and the d/u PDF ratio at large x, will come from the BONuS experiment at Jefferson Lab, which tags spectator protons in semi-inclusive DIS from the deuteron.