Superfast quarks in deuterium

An extension to our previous study on nuclear parton distribution functions (nPDFs) [Kim and Miller, Phys. Rev. C 106, 055202 (2022)] using light-front holographic quantum chromodynamics (LFHQCD) [Brodsky, de Teramond, Dosch, and Erlich, Phys. Rep. 584, 1 (2015)] is presented. We apply the effects of nucleon motion inside the nucleus (Fermi motion/smearing) to deuterium, extending our deuterium nPDFs to the superfast, $x>1$, region [Frankfurt and Strikman, Phys. Rep. 160, 235 (1988)] where we estimate our results to be reasonable up to $x\approx 1.7$. We utilize four different deuteron wave functions (AV18, NijmI, NijmII, Nijm93). We find that our model, with no additional new parameters, shows very good agreement with deuterium EMC ratio data obtained from the BONuS experiment [Fenker et al., Nucl. Instrum. Methods Phys. Res. A 592, 273 (2008); Baillie et al. (CLAS Collaboration), Phys. Rev. Lett. 108, 142001 (2012); Phys. Rev. Lett. 108, 199902(E) (2012); Tkachenko et al. (CLAS Collaboration), Phys. Rev. C 89, 045206 (2014); Phys. Rev. C 90, 059901(E) (2014); Griffioen et al., Phys. Rev. C 92, 015211 (2015)]. Looking beyond conventional nuclear physics, and in anticipation of 12 GeV experiments at Jefferson Lab, we use a LFHQCD ansatz to predict the contributions of an exotic six-quark state to the deuteron $F_2$ structure function, $F_2^D$, in the superfast region. We find that the effects of using other potentials are about the same magnitude as six-quark effects—both have small effects in $x<1$, but have significant contributions at $x>1$.

Figure 1

A plot of the interpolated AV18 nucleon momentum distribution in deuterium in the region $0<k<10{\mathrm{fm}}^{-1}$.

Figure 2

The proton and neutron LF density matrices for deuterium, divided by $\alpha$, as a function of $\alpha$, the momentum fraction of the nucleon in the nucleus weighted by $A$.

Figure 3

DIS $F_2$ structure functions on a logarithmic $y$-axis, evaluated at $Q^2=1.12{\mathrm{GeV}}^2$. The solid black line is the sum of the free proton and neutron structure functions and the solid red line was obtained by using Eq. (1).

Figure 4

(Top) Results for $F_2^D$, Eq. (1), using different deuteron wave functions. The sold red line uses the AV18 wave function and the dashed, dotted, and dot-dashed red lines use the NijmI, NijmII, and Nijm93 wave functions, respectively. (Bottom) The ratios of the Nijm $F_2^D$ results with respect to the AV18 results. Note that NijmI and NijmII lines are overlapped.

Figure 5

All DIS $F_2$ quantities are evaluated at $Q^2=1.12{\mathrm{GeV}}^2$. The solid red line is the convolution model nLFHQCD result using Eq. (1), the dot-dashed blue line was obtained by using free nucleon structure functions in Eq. (1), where the superscript $CV$ means ‘convolution’, and the filled black points are experimental results obtained from the BONuS experiment [32, 33, 34, 35].

Figure 6

Comparison between $x{q}_3(x,Q^2)$ distribution used in bound-nucleon PDFs in Eqs. (9), (10), and the six-quark PDF ansatz used in Eq. (19), $x{q}_6(x/2,Q^2)/2$, evaluated at $Q^2=1.12{\mathrm{GeV}}^2$.

Figure 7

(Top) DIS $F_2$ structure functions on a logarithmic $y$ axis. All $F_2$ quantities are evaluated at $Q^2=1.12{\mathrm{GeV}}^2$. (Bottom) The ratios $F_2^D\left(P_{6q}\right)/F_2^D(P_{6q}=0\%)$. The predicted six-quark contribution is displayed as a filled-in red volume, but is difficult to discern on the top plot with the given axis scaling. The lower boundary of the volume is $P_{6q}=0\%$ and the upper boundary is $P_{6q}=0.15\%$. The red dotted and dashed lines display $P_{6q}=0.05\%$ and $P_{6q}=0.005\%$, respectively, and are shown to clarify the trend of $F_2^D$ with varying $F_2^{6q}$ contributions.

Figure 8

(Top) DIS $F_2$ structure functions on a logarithmic $y$-axis, as a function of the Nachtmann variable, $\xi$, evaluated at $Q^2=10{\mathrm{GeV}}^2$. (Bottom) The ratios $F_2^D\left(P_{6q}\right)/F_2^D(P_{6q}=0\%)$. The predicted six-quark contribution is displayed as a filled-in red volume, but is difficult to discern on the top plot with the given axis scaling. The lower boundary of the volume is $P_{6q}=0\%$ and the upper boundary is $P_{6q}=0.15\%$. The red dotted and dashed lines display $P_{6q}=0.05\%$ and $P_{6q}=0.005\%$, respectively, and are shown to clarify the trend of $F_2^D$ with varying $F_2^{6q}$ contributions.