Isospin dependence of nuclear EMC effect from global QCD analysis

Abstract

We perform a new global QCD analysis of unpolarized parton distribution functions (PDFs) in the nucleon from proton, deuteron and $A=3$ data, including recent measurements of $^3$He/$D$ and $^3$H/$D$ cross section ratios from the MARATHON experiment at Jefferson Lab. Simultaneously inferring the PDFs and nucleon off-shell corrections allows both to be determined consistently, without theoretical assumptions about the isospin dependence of nuclear effects. The analysis provides strong evidence for the need of nucleon off-shell corrections to describe the $A=3$ data, and suggests the presence of both isoscalar and isovector nuclear effects in $A \leq 3$ nuclei. We find that the extracted EMC ratios of nuclear to nucleon structure functions for $A=2$ and 3 differ from those naively extrapolated from heavy nuclei down to low $A$.

Figures (10)

• Figure 1: Ratios $F_2^D/F_2^p$ (left), $F_2^{{^3 {\rm He}}}/F_2^{D}$ (middle), and $F_2^{{^3 {\rm H}}}/F_2^{D}$ (right) from MARATHON JeffersonLabHallATritium:2021usdJeffersonLabHallATritium:2024las (black circles) at the experimental kinematics $Q^2=14 x_B$ GeV$^2$ compared to the full JAM fit (red solid lines and 68% CI bands) and to the same fit but with all off-shell corrections removed (green dashed lines) and with only symmetric isoscalar off-shell corrections included as in scenario (ii) (blue solid lines). The bottom panels show the ratios of the results relative to the mean JAM results. The theory curves are normalized by the fitted values 1.017(4), 0.996(6), and 0.991(5) for the $D/p$, ${^3 {\rm He}}/D$, and ${^3 {\rm H}}/D$ ratios, respectively.
• Figure 2: Ratio $F_2^{{^3 {\rm He}}}/F_2^{D}$ from the Jefferson Lab MARATHON JeffersonLabHallATritium:2024las (red circles) and Hall C E03-103 Seely:2009gt (green open circles) experiments compared to the JAM fit (colored 68% CI bands). No normalizations have been applied to any of the data here, while the theory curves have been divided by the normalizations listed in Table \ref{['t.norms']}.
• Figure 3: Isoscalar nuclear EMC ratio $(F_2^{{^3 {\rm He}}} + F_2^{{^3 {\rm H}}})/2F_2^D$ at the MARATHON kinematics $Q^2 = 14 x_B$ GeV$^2$. The JAM result, unmodified by any normalizations, (red 68% CI band) is compared to the result directly from the MARATHON paper JeffersonLabHallATritium:2024las (green open circles) and the result where the 1.021 and 0.996 normalizations are removed from ${^3 {\rm He}}$ and ${^3 {\rm H}}$, respectively (black circles). The errors on the latter are computed using the quadrature sum of the uncorrelated errors on the $F_2^{{^3 {\rm He}}}/F_2^D$ and $F_2^{{^3 {\rm H}}}/F_2^D$ ratios. The result is also compared to that of the KP model with isoscalar OSE Kulagin:2010gdJeffersonLabHallATritium:2024las (green dotted line).
• Figure 4: Ratios of PDFs for $u$ (left) and $d$ (right) quarks relative to the mean JAM result, for the full JAM analysis (red 68% CI band) and the analysis with no MARATHON data included (yellow 68% CI band) at $Q^2=10$ GeV$^2$.
• Figure 5: Off-shell functions $x \delta q_i$ versus $x$ at $Q^2 = 10$ GeV$^2$: (top panel) isoscalar $x \delta q_0 \equiv x \delta u_0 = x \delta d_0$ (blue), isovector $x \delta u_1$ (green), and isovector $x \delta d_1$ (orange) distributions; (bottom panel) difference $x(\delta u_1 - \delta d_1)$ (red). The bands indicate 68% CIs.