Nuclear Structure Functions and Heavy Flavour Leptoproduction Off the Nucleus at Small x in Perturbative QCD

TL;DR

This work advances a perturbative QCD treatment of nuclear structure functions and heavy flavour leptoproduction at small $x$ using the color-dipole framework and nonlinear BFKL (BK-like) evolution in the large-$N_c$ limit. Starting from a GBW-saturation-inspired initial dipole–nucleus cross-section at $x=0.01$, it solves the evolution equation for the dipole density to obtain the nuclear structure function $F_2$ and the associated gluon density, then computes heavy-flavour production via photon–gluon fusion. The results show $F_{2A}$ rising as $ ext{ln}^2(1/x)$ and a substantial $A$-dependence ($F_{2A} o A^{oldsymbol{ extalpha}}F$ with $oldsymbol{ extalpha}$ dropping below 1/2 at very small $x$), along with sizeable heavy-quark transverse momentum distributions extending beyond the naive hard scale. The findings illustrate saturation-driven growth patterns at small $x$ and provide a framework to connect nonlinear small-$x$ evolution to observable leptoproduction on nuclei, while acknowledging that $1/N_c^2$ corrections could become relevant at the lowest $x$.

Abstract

Nuclear structure functions and cross-sections for heavy flavour production in lepton-nucleus collisions are investigated in the low $x$ region accessible now or in the near future. The scattering on a heavy nucleus is described by the sum of fan diagrams of BFKL pomerons, which is exact in the high-colour limit. The initial condition for the evolution at $x=0.01$ is taken from a saturation model, which reproduces the experimental data on the proton. The $A$ dependence of the structure functions is well described by a power factor $A^α$, with $α$ reaching values as low as 1/2 at extremely low $x$. The total cross-sections for heavy flavour production reach values of the order of mb, and the corresponding transverse momentum distributions are sizeable up to transverse momenta larger than the initial large scale $\sqrt{Q^2+4m_f^2}$.

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