Dipole-pion cross section in the saturation regime

The scale-dependent dipole-pion cross section is analyzed as a function of the dipole size $r$ and the impact parameter $b$. This analysis relies on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in $\mu \sim 1\mathrm{/}r+{\mu }_0$ at the next-to-leading order (NLO) approximation, with a specific initial condition at ${\mu }_0$. The dipole-pion cross section at small Bjorken variable $\beta$ is being considered over a wide range of transverse separations $r$. Using the Laplace transformation technique, we describe the determination of the dipole-pion cross section based on the gluon distribution at the initial scale ${\mu }_0$ within a kinematic region characterized by low values of the Bjorken variable $\beta$. We found that geometric scaling for the dipole-pion cross section holds approximately within a wide kinematic region of $r{Q}_s$. The cross section saturates at large dipole sizes.