Examining the EMC effect using the $F_2^n$ neutron structure function

The persistently mysterious deviations from unity of the ratio of nuclear target structure functions to those of deuterium as measured in deep inelastic scattering (often termed the “EMC effect”) have become the canonical observable for studies of nuclear medium modifications to free nucleon structure in the valence regime. The structure function of the free proton is well known from numerous experiments spanning decades. The free neutron structure function, however, has remained difficult to access. Recently it has been extracted in a systematic study of the global data within a parton distribution function extraction framework and is available from the CTEQ–Jefferson Lab (CJ) Collaboration. Here, we leverage the latter to introduce a new method to study the EMC effect in nuclei by reexamining existing data in light of the the magnitude of the medium modifications to the free neutron and proton structure functions independently. From the extraction of the free neutron from world data, it is possible to examine the nuclear effects in deuterium and their contribution to our interpretation of the EMC effect. In this study, we observe that the ratio of the deuteron to the sum of the free neutron and proton structure functions has some $x_B$ and $Q^2$ dependencies that impact the magnitude of the EMC effect as typically observed. Specifically, different EMC slopes are obtained when data from different $x_B$ and $Q^2$ values are utilized. While a linear correlation persists between the EMC and short range correlation effects, the slope is modified when deuteron nuclear effects are removed.

Figure 1

(a) The kinematics of the SLAC E139 experiment are shown as they span $x_B$ and $Q^2$ for various target nuclei. (b) $x_B$ is shown per nuclei in the SLAC E139 experiment.

Figure 2

The theoretical extraction of the ratio of $F_2^d/F_2^N$, where $N$ indicates per nucleon. The deuteron exhibits some $x_B$ dependence such that the ratio is modified by as much as $6\%$ in the regime of $x_B$ between 0.3 and 0.7 of interest to the EMC effect [6].

Figure 3

Theoretically derived deuteron $F_2$ ratios with respect to the free neutron and proton. These results are shown for fixed $Q^2=5{\mathrm{GeV}}^2/c^2$.

Figure 4

(a) The extracted CJ $F_2^n$ DIS data are shown in blue circles, and the $F_2^p$ from the NMC global fit are shown in red squares for the same corresponding $x_B$ and $Q^2$ [10]. (b) The ratio $F_2^n/F_2^p$ from the (a) is shown as a function of $x_B$ in the blue triangles. A comparison to a previous extraction of the $F_2^n/F_2^p$ ratio from [11] is shown by the red circles and line.

Figure 5

(a) The proton structure function from CJ15 is shown as a function of $x_B$ for various fixed $Q^2$ (as indicated). (b) The neutron structure function from CJ15 is shown as a function of $x_B$ for various fixed $Q^2$. (c) The deuteron structure function from CJ15 is shown as a function of $x_B$ for various fixed $Q^2$. All are shown without uncertainty to better reflect the $Q^2$ dependence of each.

Figure 6

(a) The deuteron structure function divided by the sum of the free proton and free neutron structure functions from the CJ15 fit is shown for various $Q^2$. This ratio reflects the magnitude of the nuclear effects in the deuteron. The $Q^2$ dependence shows significant spread above $x_B=0.6$, where the ratio begins to increase. (b) The Whitlow deuterium data from SLAC [13] are shown divided by the sum of the free proton and free neutron structure functions from the CJ15 fit. In both cases, uncertainties are not shown in order to emphasize the general kinematic dependence.

Figure 7

(a) The deuterium structure function from the CJ15 fit is shown as a ratio to the proton structure function from CJ15 for various $Q^2$. (b) The deuterium structure function from the CJ15 fit is shown as a ratio to the neutron structure function from CJ15 for various $Q^2$. Uncertainties are not shown to emphasize the kinematic dependence of the structure functions.

Figure 8

(a) $F_2^A$ calculated from the published SLAC E139 cross sections is taken as a ratio per nucleon to $F_2^n$ and $F_2^p$, separately. The published ratios for carbon and gold [18] are shown for reference as $F_2^A/F_2^d$ per nucleon. Theory predictions for the $F_2^A$ structure function per nucleon as a ratio to $F_2^p$ are also shown [7, 8, 9]. The nuclei from the SLAC E139 experiment are shown as ratios per nucleon relative to $F_2^p$ (bottom) and $F_2^n$ (top). (b) $F_2^A$ calculated from the published SLAC E139 cross sections is taken as a ratio per neutron or proton and $F_2^n$ and $F_2^p$, separately. The published EMC ratios for carbon and gold [18] are shown for reference. Different from the plot on the left (a), the nuclei from the SLAC E139 experiment are shown as ratios per proton relative to $F_2^p$ (bottom) and per neutron $F_2^n$ (top). A larger spread in the nuclei is observed per neutron than per proton for $x_B$.

Figure 9

Linear fits to the deuterium target data with cuts on $Q^2$ and $x_B$. The blue solid points show the ratio of the E139 deuterium data relative to the CJ15 deuterium while the red open points show the ratio of the E139 deuterium data relative to the sum of the free proton and free neutron (excludes nuclear effects of deuterium). (a) Data taken for $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) Data taken for all $Q^2$ but excluding the data at $x_B=0.7$. (c) All data taken through $x_B=0.7$.

Figure 10

Linear fits to the $C$ target data with cuts on $Q^2$ and $x_B$. The blue solid data points show the ratio of the nucleus relative to deuterium while the red open data points show the ratio of the nucleus relative to the sum of the free proton and free neutron (excluding the nuclear effects of deuterium). The linear fit to the data is taken for all $Q^2$, where $5<Q^2<15$ ${\mathrm{GeV}}^2/c^2$. No data were taken in the E139 experiment for carbon at $x_B=0.7$.

Figure 11

The slopes to the fits of the $F_2$ ratios versus $x_B$ are shown as a function of the target $A$. (a) The slope comparisons are made using all data with $Q^2=5$ ${(\mathrm{GeV}/c)}^2$. (b) The slopes are compared with no cut on $Q^2$ but requiring that $x_B<0.7$. (c) The slopes are compared with no cut on $Q^2$ and $x_B<0.8$.

Figure 12

The slopes are compared for the different cuts in $Q^2$ and $x_B$. The inclusion of larger $Q^2$ and $x_B$ points in the fit generates a somewhat shallower slope.

Figure 13

The slopes of the fit to the data for $Q^2=5{\mathrm{GeV}}^2/c^2$ are shown versus the $a_2$ SRC factor from [23]. The points shown in blue (solid) are the slopes from the ratios taken with respect to deuterium, and the points in red (open) are from the slopes with respect to the free neutron and free proton denominator. The slope value for deuterium taken with respect to itself (blue) is set to 0.

Figure 14

Linear fits to the Au target data with cuts on $Q^2$ and $x_B$. The blue solid data points show the ratio of the nucleus relative to deuterium while the red data points show the ratio of the nucleus relative to the sum of the free proton and free neutron (excluding nuclear effects of deuterium). (a) Linear fit to the data taken for $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) Linear fit to the data taken for all $Q^2$ but excluding the data at $x_B=0.7$. (c) Linear fit to all data taken through $x_B=0.7$.

Figure 15

Linear fits to the He target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. (c) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ up to $x_B<0.8$.

Figure 16

Linear fits to the Be target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. (c) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ up to $x_B<0.8$.

Figure 17

Linear fits to the Al target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. (c) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ up to $x_B<0.8$.

Figure 18

Linear fits to the Ca target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. No data were taken on $Ca$ beyond $x_B=0.6$.

Figure 19

Linear fits to the Fe target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. (c) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ up to $x_B<0.8$.

Figure 20

Linear fits to the Ag target data with cuts on $Q^2$ and $x_B$ from the E139 experiment. (a) The ratios are constructed requiring that $Q^2=5{\mathrm{GeV}}^2/c^2$. (b) The ratios include all data $5<Q^2<15{\mathrm{GeV}}^2/c^2$ where $x_B<0.7$. No data were taken on Ag beyond $x_B=0.6$.