Detailed study of the nuclear dependence of the EMC effect and short-range correlations

Background: The density of the nucleus has been important in explaining the nuclear dependence of the quark distributions, also known as the EMC effect, as well as the presence of high-momentum nucleons arising from short-range correlations (SRCs). Recent measurements of both of these effects on light nuclei have shown a clear deviation from simple density-dependent models.

Purpose: A better understanding of the nuclear quark distributions and short-range correlations requires a careful examination of the experimental data on these effects to constrain models that attempt to describe these phenomena.

Methods: We present a detailed analysis of the nuclear dependence of the EMC effect and the contribution of SRCs in nuclei, comparing to predictions and simple scaling models based on different pictures of the underlying physics. We also make a direct, quantitative comparison of the two effects to further examine the connection between these two observables related to nuclear structure.

Results: We find that, with the inclusion of the new data on light nuclei, neither of these observables can be well explained by common assumptions for the nuclear dependence. The anomalous behavior of both effects in light nuclei is consistent with the idea that the EMC effect is driven by either the presence of high-density configurations in nuclei or the large virtuality of the high-momentum nucleons associated with these configurations.

Conclusions: The unexpected nuclear dependence in the measurements of the EMC effect and SRC contributions appear to suggest that the local environment of the struck nucleon is the most relevant quantity for explaining these results. The common behavior suggests a connection between the two seemingly disparate phenomena, but the data do not yet allow for a clear preference between models which aim to explain this connection.

Figure 1

EMC ratio, $({\sigma }_A/A)/({\sigma }_D/2)$, for carbon [32]. The solid line is a linear fit for $0.35<x<0.7$.

Figure 2

Magnitude of the EMC effect, $|d{R}_{\mathrm{EMC}}/dx|$, vs the average nucleon separation energy. The empty circle indicates the known (zero) deuteron EMC slope.

Figure 3

Magnitude of the EMC effect vs $A$ (top) and $A^{-1/3}$ (bottom). The bottom plot includes a linear fit for $A\ge 12$.

Figure 4

Magnitude of the EMC effect vs average nuclear density.

Figure 5

Magnitude of the EMC effect (solid circles) vs scaled nuclear density. The solid triangles and hollow squares show the calculated average $2N$ overlap from Eq. (5) minus the deuteron value, i.e., ${\langle O_N\rangle }_A-{\langle O_N\rangle }_D$ (right-hand scale; see text for details). Overlap points are offset on the $x$ axis for clarity.

Figure 6

Per nucleon cross section ratios for ${}^3$He/${}^2$H and ${}^{12}$C/${}^2$H measured at JLab [9] at 18${}^{\circ }$. In the region dominated by 2$N$ SRCs the ratios become independent of $x$. The dip around $x=1$ is the result of $A>2$ nuclei having wider quasielastic peaks and the solid line indicates the region used to extract the ratio $a_2$.

Figure 7

Momentum distribution for the free deuteron and an $np$ pair in iron, taken as the sum of a mean-field (Gaussian) contribution and the convolution of the high-momentum deuteron tail with the c.m. motion of the pair in iron.

Figure 8

$R_{2N}$ vs $A^{-1/3}$.

Figure 9

$R_{2N}$ vs scaled nuclear density (solid circles). The solid triangles and hollow squares show the calculated 2$N$ overlap minus the deuteron value (right-hand scale) from Eq. (5). Points are offset on the $x$ axis for clarity.

Figure 10

Size of the EMC effect ($|d{R}_{\mathrm{EMC}}/dx|$ as well as the relative measure of SRCs ($R_{2N}$) shown as a function of $A$ (top) and scaled nuclear density (bottom).

Figure 11

Comparison of EMC slopes and SRC observables from world data where both observables are available for the same nuclei. The top plot shows the EMC slope vs $a_2$, testing the high-virtuality interpretation, and the bottom plot shows the EMC slope vs $R_{2N}$ scaled by $N_{\mathrm{tot}}/N_{\mathrm{iso}}$, testing the local density interpretation (as discussed in the text), along with fits.

Figure 12

EMC slopes vs $a_2$ (top) and $R_{2N}$ scaled by $N_{\mathrm{tot}}/N_{\mathrm{iso}}$ and normalized to the deuteron (bottom). The solid line is the one-parameter fit, constrained to yield zero for the deuteron (grey point). The dashed red line shows the result of the two-parameter (Fig. 11) for comparison. The fits are almost indistinguishable for the LD tests.