Leading twist nuclear shadowing: uncertainties, comparison to experiments and higher twist effects

TL;DR

The paper develops and applies a leading twist theory of nuclear shadowing that links nuclear PDFs to nucleon diffraction via Gribov theory and QCD factorization. It delivers NLO predictions for $nPDFs$ at small $x$ (down to $10^{-5}$) with quantified uncertainties, and shows sizable shadowing, especially for gluons, alongside substantial higher twist contributions at fixed-target kinematics. The work emphasizes the role of diffractive PDFs, attenuation of multi-nucleon rescattering, and the impact parameter dependence, while identifying regions (notably $x>0.01$) where Reggeon effects and HT corrections become significant. It also offers practical guidance for neutron $F_2$ extraction and provides tabulated $nPDF$ sets for phenomenology at high-energy colliders.

Abstract

Using the leading twist approach to nuclear shadowing, which is based on the relationship between nuclear shadowing and diffraction on a nucleon, we calculate next-to-leading order nuclear parton distribution functions (nPDFs) and structure functions in the region $0.2 > x > 10^{-5}$ and $Q^2 \geq 4$ GeV$^2$. The uncertainties of our predictions due the uncertainties of the experimental input and the theory are quantified. We determine the relative role of the small ($\sim Q^2$) and large ($\gg Q^2$) diffractive masses in nuclear shadowing as a function of $x$ and find that the large mass contribution, which is an analog of the triple Pomeron exchange, becomes significant only for $x \le 10^{-4}$. Comparing our predictions to the available fixed-target nuclear DIS data, we argue, based on the current experimental studies of the leading twist diffraction, that the data at moderately small $x\sim 0.01$ and $Q^2 \sim 2$ GeV$^2$ could contain significant higher twist effects hindering the extraction of nPDFs from that data. Also, we find that the next-to-leading order effects in nuclear shadowing in the ratio of the nucleus to nucleon structure functions $F_2$ are quite sizable. Within the same formalism, we also present results for the impact parameter dependence of nPDFs. We also address the problem of extracting of the neutron $F_{2n}(x,Q^2)$ from the deuteron and proton data. We suggest a simple and nearly model-independent procedure of correcting for nuclear shadowing effects using $F_2^A/F_2^D$ ratios.

Figures (18)

• Figure 1: Gribov's theorem Gribov: The forward hadron-deuteron rescattering amplitude, which gives rise to nuclear shadowing, is proportional to the differential hadron-nucleon diffractive cross section at $t\sim 0$.
• Figure 2: The forward $\gamma^{\ast}$-nucleus rescattering amplitude that gives the principal contribution to nuclear shadowing.
• Figure 3: The forward $\gamma^{\ast}$-nucleus triple scattering amplitude.
• Figure 4: The effective cross section $\sigma_{{\rm eff}}$ for the anti $u$-quark and gluon channels at $Q_0^2=4$ GeV$^2$. The error bands represent the uncertainty in the predictions discussed in the text.
• Figure 5: The ratio $R$ at $Q_0^2=4$ GeV$^2$. The solid curves correspond to $\beta_{{\rm max}}=0.5$; the dashed curves correspond to $\beta_{{\rm max}}=0.1$; the dotted curves correspond to $\beta_{{\rm max}}=0.01$; the dot-dashed curves correspond to $\beta_{{\rm max}}=0.001$.