Dynamical model of antishadowing of the nuclear gluon distribution

We explore the theoretical observation that within the leading twist approximation, the nuclear effects of shadowing and antishadowing in nonperturbative nuclear parton distribution functions (nPDFs) at the input QCD evolution scale involve diffraction on nucleons of a nuclear target and originate from merging of two parton ladders belonging to two different nucleons, which are close in the rapidity space. It allows us to propose that for a given momentum fraction $x_{IP}$ carried by the diffractive exchange, nuclear shadowing and antishadowing should compensate each other in the momentum sum rule for nPDFs locally on the interval $ln(x/x_{IP})\le 1$. We realize this by constructing an explicit model of nuclear gluon antishadowing, which has a wide support in $x,{10}^{-4}<x<0.2$, peaks at $x=0.05\text{–}0.1$ at the level of $\approx 15\%$ for ${}^{208}\mathrm{Pb}$ at $Q_0^2=4{\mathrm{GeV}}^2$ and rather insignificantly depends on details of the model. We also studied the impact parameter $b$ dependence of antishadowing and found it to be slow.

Figure 1

The multiple scattering series for the nuclear parton distribution $f_{j/A}(x,Q_0^2)$.

Figure 2

Hard diffractive DIS at the leading order.

Figure 3

Merging of two ladders coupled to two different nucleons in the $2IP\to IP$ process in the nucleus infinite momentum frame. This process corresponds both to nuclear shadowing and antishadowing.

Figure 4

Pattern of $x$ and $x_{IP}$ dependence of the gluon shadowing and antishadowing.

Figure 5

$\delta x{g}_A^{\mathrm{anti}}(x,Q_0^2)/\left[Ax{g}_N(x,Q_0^2)\right]$ (left) and $x{g}_A(x,Q_0^2)/\left[Ax{g}_N(x,Q_0^2)\right]$ (right) as a function of $x$ for ${}^{208}\mathrm{Pb}$ at $Q_0^2=4{\mathrm{GeV}}^2$. See text for details.

Figure 6

Comparison of $x{g}_A(x,Q_0^2)/\left[Ax{g}_N(x,Q_0^2)\right]$, when antishadowing is modeled using Eqs. (10) and (11) with $B_0=3x_{IP}$ (the upper shaded band) with the case when it is modeled using Eq. (6) (the lower shaded band labeled “$x_{IP}$-indep.”).

Figure 7

Impact parameter dependent gluon nuclear distribution of ${}^{208}\mathrm{Pb}$ at $Q_0^2=4{\mathrm{GeV}}^2$. The $x{g}_A(x,b,Q_0^2)/\left[A{T}_A\left(b\right)x{g}_N(x,Q_0^2)\right]$ ratio as a function of $x$ at $b=0$ in the dynamical approach to antishadowing.

Figure 8

Comparison of the prediction of the leading twist nuclear shadowing and the dynamical model of antishadowing for $x{g}_A(x,Q_0^2)/\left[Ax{g}_N(x,Q_0^2)\right]$ (same as in Fig. 6) with results of the EPPS16 (left panel) and nCTEQ15 (right panel) fits. The shaded error bands around the EPPS16 and nCTEQ15 curves give their uncertainties.

Figure 9

Impact parameter dependent gluon nuclear shadowing and antishadowing. Comparison of $x{g}_A(x,b,Q_0^2)/\left[A{T}_A\left(b\right)x{g}_N(x,Q_0^2)\right]$ predicted in the leading twist model of nuclear shadowing and the dynamical model of antishadowing (same as in Fig. 7) to the EPS09s result. The shaded areas show uncertainties of the respective predictions.