The behavior of the heavy-quarks structure functions at small-$x$

TL;DR

This paper investigates the small-$x$ behavior of charm and bottom structure functions in heavy quarks, comparing predictions from hard-Pomeron and saturation models, and analyzing their impact on reduced cross sections and effective exponents.

Contribution

It provides a detailed comparison of unshadowed and shadowed corrections in heavy-quark structure functions at small-$x$, highlighting the independence of effective exponents from $x$ and $Q^{2}$.

Findings

Effective exponents are independent of $x$ and $Q^{2}$.

Effective coefficients depend on $ ext{ln}Q^{2}$.

Behavior aligns with predictions from DL and CD models.

Abstract

The behavior of the charm and bottom structure functions ($F_{k}^{i}(x,Q^{2})$, i=c,b; k=2,L) at small-$x$ is considered with respect to the hard-Pomeron and saturation models. Having checked that this behavior predicate the heavy flavor reduced cross sections concerning the unshadowed and shadowed corrections. We will show that the effective exponents for the unshadowed and saturation corrections are independent of $x$ and $Q^{2}$, and also the effective coefficients are dependent to $\ln{Q^{2}}$ compared to Donnachie-Landshoff (DL) and color dipole (CD) models.