Figure 1

The one-step (a) and two-step (b) processes in DIS on a nucleus. If the scattering on nucleon $N_1$ is via Pomeron exchange, the one-step and two-step amplitudes are opposite in phase, thus diminishing the $\overline{q}$ flux reaching $N_2$. This causes shadowing of the charge and neutral current nuclear structure functions.Reuse & Permissions

Figure 2

Representation of leading-twist QCD contributions to the nuclear structure function as calculated from the absorptive part of the forward virtual Compton amplitude $ImT({\gamma }^{*}A\to {\gamma }^{*}A)$. (a) Illustration of a two-step contribution in the usual $q^{+}=0$, $a_{\perp }^2=Q^2$ parton model frame. The deep inelastic scattering of a lepton on a valence quark of a target proton is followed by the final-state two-gluon exchange Pomeron interaction of the outgoing quark on a neutron. (b) Illustration of the physics of the same two-step process illustrated in (a), but in the laboratory frame where $q^{+}>0$. The $u\overline{u}$ fluctuation of the virtual photon scatters elastically via two-gluon exchange on a neutron; this is then followed by the annihilation of the $\overline{u}$ quark on a proton. (c) Illustration of a doubly inelastic discontinuity of the same two-step process as (a) in the laboratory frame $q^{+}>0$. The $u\overline{u}$ fluctuation of the virtual photon first scatters inelastically on a neutron via a single-gluon exchange which produces an excited color state $8_C$ of the neutron. This is then followed by the annihilation of the $\overline{u}$ quark on a proton.Reuse & Permissions

Figure 3

Representation of leading-twist QCD contributions to the nuclear structure function from the absorptive part of the forward virtual Compton amplitude $ImT({\gamma }^{*}A\to {\gamma }^{*}A)$ involving Odderon exchange. (a) Illustration of a two-step contribution in the $q^{+}=0$, $q_{\perp }^2=Q^2$ parton model frame—deep inelastic lepton scattering on a valence quark of a target proton followed by the final-state three-gluon exchange Odderon interaction of the outgoing quark on a target neutron. (b) Illustration of the physics of the same two-step process shown in (a), but in the laboratory frame where $q^{+}>0$. The $u\overline{u}$ fluctuation of the virtual photon first scatters elastically via three-gluon exchange on a neutron; this is then followed by the annihilation of the $\overline{u}$ quark on a proton. (c) Illustration of a doubly inelastic discontinuity of the same two-step process as (a) in the laboratory frame $q^{+}>0$. The $u\overline{u}$ fluctuation of the virtual photon first scatters inelastically on a neutron via two-gluon exchange which produces an excited color state $8_C$ of the neutron. This is then followed by the annihilation of the $\overline{u}$ quark on a proton. The two-step amplitudes of (b) or (c) can interfere constructively with the Regge-behaved single-step annihilation amplitude on the proton alone, thus producing antishadowing. Similar processes occur in the case of the electroweak currents.Reuse & Permissions

Figure 4

The calculated nucleon structure function (biggest solid curve), valence (next solid curve at large $x$ values), and sea (smallest solid curve at large $x$ values) contributions to $F_2$, and the corresponding result of the MRST parametrization [43] (dashed curves), at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The experimental data are taken from Ref. 46.Reuse & Permissions

Figure 5

The calculated difference $F_2^p-F_2^n$ of the nucleon structure functions (solid curve) and the corresponding result of the MRST parametrization [43] (dashed curve), at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The experimental data are taken from Ref. 45.Reuse & Permissions

Figure 6

The calculated ratio $F_2^n/F_2^p$ of the nucleon structure functions (solid curve) and the corresponding result of the MRST parametrization [43] at energy scale 1 GeV (dashed curve). The experimental data are taken from Ref. 45.Reuse & Permissions

Figure 7

The quark contributions to the ratios of structure functions at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, for ${\gamma }^{*}$, $Z$, $W^{+}$, and $W^{-}$ currents [figures (a), (b), (c), (d), respectively]. The solid, dashed, and dotted curves correspond to the $u$, $d$, and $s$ quark contributions, respectively. This corresponds in our model to the nuclear dependence of the $\sigma (\overline{u}-A)$, $\sigma (\overline{d}-A)$, $\sigma (\overline{s}-A)$ cross sections, respectively. In order to stress the individual contribution of quarks, the numerator of the ratio $F_2^A/F_2^{N_0}$ shown in these two figures is obtained from the denominator by a replacement $q^{N_0}$ into $q^A$ for only the considered quark. As a result, the effect of antishadowing appears diminished.Reuse & Permissions

Figure 8

The antiquark contributions to ratios of the structure functions at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, for ${\gamma }^{*}$, $Z$, $W^{+}$, and $W^{-}$ currents [figures (a), (b), (c), (d), respectively]. The solid, dashed, and dotted curves correspond to $\overline{u}$, $\overline{d}$, and $\overline{s}$ quark contributions, respectively. This corresponds in our model to the nuclear dependence of the $\sigma (u-A)$, $\sigma (d-A)$, $\sigma (s-A)$ cross sections, respectively. In order to stress the individual contribution of quarks, the numerator of the ratio $F_2^A/F_2^{N_0}$ shown in these two figures is obtained from the denominator by a replacement ${\overline{q}}^{N_0}$ into ${\overline{q}}^A$ for only the considered antiquark.Reuse & Permissions

Figure 9

The nuclear shadowing and antishadowing effects at $⟨Q^2⟩=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The experimental data are taken from Refs. 47, 48.Reuse & Permissions

Figure 10

Our predictions for the ratio of $F_2$ structure functions $F_{2A}[\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{o}]/(18/5)F_{2A}[\mathrm{m}\mathrm{u}\mathrm{o}\mathrm{n}]$, measured in Ref. 50, at $Q^2=20{\mathrm{G}\mathrm{e}\mathrm{V}}^2$.Reuse & Permissions

Figure 11

Ratios $F_2^A/F_2^{N_0}$ (solid curves) and $F_3^A/F_3^{N_0}$ (dashed curves) for ${\gamma }^{*}$, $Z$, $W^{+}$, and $W^{-}$ current exchange interactions [figures (a), (b), (c), (d), respectively], at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$.Reuse & Permissions

Figure 12

The nuclear effect on the cross sections of CC and NC neutrino-nucleus DIS, at $Q^2=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The dotted and dashed curves almost overlap.Reuse & Permissions

Figure 13

The nuclear effect on the Paschos-Wolfenstein ratio of differential cross sections $R_A^{-}(x)/R_N^{-}(x)$, at $Q^2=20{\mathrm{G}\mathrm{e}\mathrm{V}}^2$.Reuse & Permissions

Figure 14

(a) The ${sin}^2{\theta }_W$ dependence in $R_{A/N}^{-}$; (b) The nuclear shadowing/antishadowing corrections to the ${sin}^2{\theta }_W$.Reuse & Permissions

Figure 15

Representation of leading-twist QCD “hidden-color” contributions to the nuclear structure function from the absorptive part of the forward virtual Compton amplitude $ImT({\gamma }^{*}A\to {\gamma }^{*}A)$. (a) Illustration of a two-step contribution in the $q^{+}=0$, $q_{\perp }^2=Q^2$ parton model frame—deep inelastic lepton scattering on a valence quark of a target proton followed by the final-state single-gluon interaction of the outgoing quark on a target neutron. The proton and neutron are both color excited to color-octet states. The amplitude requires the presence of hidden-color components in the nuclear wave function. (b) Illustration of the physics of the two-step process shown in (a), but in the laboratory frame where $q^{+}>0$. The $u\overline{u}$ fluctuation of the virtual photon first scatters via a single-gluon exchange on a neutron; this is then followed by the annihilation of the $\overline{u}$ quark on a proton. The proton and neutron are both color excited to color-octet states. The amplitude requires the presence of hidden-color components in the nuclear wave function. The two-step annihilation amplitude on the proton alone, thus producing antishadowing. Similar processes occur in the case of the weak currents.Reuse & Permissions