Nuclear structure functions at a future electron-ion collider

The quantitative knowledge of heavy nuclei’s partonic structure is currently limited to rather large values of momentum fraction $x$—robust experimental constraints below $x\sim {10}^{-2}$ at low resolution scale $Q^2$ are particularly scarce. This is in sharp contrast to the free proton’s structure which has been probed in Deep Inelastic Scattering (DIS) measurements down to $x\sim {10}^{-5}$ at perturbative resolution scales. The construction of an electron-ion collider (EIC) with a possibility to operate with a wide variety of nuclei, will allow one to explore the low-$x$ region in much greater detail. In the present paper we simulate the extraction of the nuclear structure functions from measurements of inclusive and charm reduced cross sections at an EIC. The potential constraints are studied by analyzing simulated data directly in a next-to-leading order global fit of nuclear Parton Distribution Functions based on the recent EPPS16 analysis. A special emphasis is placed on studying the impact an EIC would have on extracting the nuclear gluon parton distribution function, the partonic component most prone to nonlinear effects at low $Q^2$. In comparison to the current knowledge, we find that the gluon parton distribution function can be measured at an EIC with significantly reduced uncertainties.

Figure 1

The kinematic acceptance in $x$ and $Q^2$ of an EIC compared to completed fixed target $\ell +A$ DIS and Drell-Yan (DY) experiments.

Figure 2

Left: A depiction of inclusive DIS. Right: $c\overline{c}$ production through photon-gluon fusion.

Figure 3

Fraction of statistical uncertainty over the total uncertainty of the simulated reduced cross section measurement at an EIC, for each $x$ and $Q^2$ bin, at different c.o.m. energies, assuming a combined collected luminosity of $10{\mathrm{fb}}^{-1}$.

Figure 4

The reduced cross section (left) in $e+\mathrm{Au}$ collisions at an EIC is plotted as a function of $Q^2$ and $x$, the kinematic space covered by currently available experimental data is marked on the plot by the green area. The measured reduced cross section points are shifted by $-{\log }_{10}(x)$ for visibility. Two examples of the ${\sigma }_r$ (right) at $Q^2$ values of $4.4{\mathrm{GeV}}^2$ and $139{\mathrm{GeV}}^2$ are plotted versus $x$, with the ratio between the widths of the experimental and theoretical uncertainties shown in the bottom panel. In both plots the statistical and systematic uncertainties are added in quadrature and compared to the theoretical uncertainty (gray bands) from CT14NLO+EPPS16. The overall 1.4% systematic uncertainty on the luminosity determination in not shown on the plots. Points that correspond to different energy configurations are horizontally offset in $Q^2$ for visibility.

Figure 5

Left: The distribution of the momentum of a decay $K$ from $c\overline{c}$ production events versus pseudorapidity. Right: The vertex position of $K$ in inclusive DIS (blue line) compared to $c\overline{c}$ production events (red line).

Figure 6

The reduced cross section (left) of $c\overline{c}$ production in $e$+Au collisions at an EIC is plotted as a function of $Q^2$ and $x$. The points are shifted by $-{\log }_{10}(x)/10$ for visibility. Two examples of the ${\sigma }_r^{c\overline{c}}$ (right) at $Q^2$ values of $4.4{\mathrm{GeV}}^2$ and $139{\mathrm{GeV}}^2$ are plotted versus $x$, with the ratio between the widths of the experimental and theoretical uncertainties shown in the bottom panel. In both plots the statistical and systematic uncertainties are added in quadrature and compared to the theory uncertainty (gray bands) from CT14NLO+EPPS16. The overall 1.4% systematic uncertainty on the luminosity measurement in not shown on the plots. Points that correspond to different energy configurations are horizontally offset in $Q^2$ for visibility.

Figure 7

The energy (left) and polar angle (right) distribution of radiative photons emitted in $\mathrm{e}+\mathrm{Au}$ collision events.

Figure 8

The radiative correction factor to the inclusive reduced cross section (left) and the reduced cross section for charm production (right) as a function of the inelasticity, estimated for 20 GeV electrons off 100 GeV Au-ions collision events, at different $Q^2$ values.

Figure 9

The reduced cross section for $e+\mathrm{Au}$ collisions at $\sqrt{s}=63.2$, 77.5 and 89.4 GeV versus $Y^{+}$ for $Q^2=7.81{\mathrm{GeV}}^2$ for three values of $x$. Fitting the slope of each data set with fixed $x$ gives the negative of $F_L$.

Figure 10

Inclusive $F_L$ (left) and $F_L^{c\overline{c}}$ (right) as a function of $x$ for several values of $Q^2$. The vertical bars represent statistical and systematic uncertainties added in quadrature. The grey bands represent the theoretical predictions based on EPPS16.

Figure 11

Illustration of the rigidity/flexibility of the small-$x$ fit functions used in EPPS16 analysis (upper) and in the present work (lower).

Figure 12

Results for the nuclear modifications of Pb at $Q^2=1.69{\mathrm{GeV}}^2$. The hatched bands correspond to the baseline fit, the blue bands are the results from fits with no charm data included, and the black error bands denote the full analysis with inclusive and charm data.

Figure 13

As Fig. 12 but at $Q^2=10{\mathrm{GeV}}^2$.

Figure 14

As Fig. 12, but for average valence (upper panels) and average light sea quarks (lower panels). The upper set of four panels corresponds to $Q^2=1.69{\mathrm{GeV}}^2$ and the lower set of panels to $Q^2=10{\mathrm{GeV}}^2$.

Figure 15

The inclusive EIC pseudodata (in $E_e=20\mathrm{GeV}$, $E_{\mathrm{p},\mathrm{C},\mathrm{Au}}=20\mathrm{GeV}$ setup) for carbon (upper panels) and gold (lower panels) compared with the baseline fit (hatched bands), the fit with inclusive low-energy data only (gray bands), and the fit with the inclusive low- and high-energy data (blue bands). The assumed overall 1.4% data normalization uncertainty is not shown.

Figure 16

The charm-tagged EIC pseudodata (in $E_e=20\mathrm{GeV}$, $E_{\mathrm{p},\mathrm{C},\mathrm{Au}}=20\mathrm{GeV}$ setup) for carbon (upper panels) and gold (lower panels) compared with the baseline fit (hatched bands), the fit with inclusive EIC data included (gray bands), and charm data included (blue bands). The overall 1.4% normalization uncertainty is not shown.

Figure 17

The LHC p–Pb and RHIC D–Au data for Z (two upper left panels), ${\mathrm{W}}^{\pm }$ (two lower left panels), dijet production (lower right panel), and inclusive pion production [58] (upper right panel) compared with the baseline fit (hatched bands) and the full high-energy EIC analysis (blue bands).