The DIS dipole picture cross section in exact kinematics

We implement a finite energy constraint in the dipole picture of deep inelastic scattering by restricting the invariant mass of the produced partonic system by the virtual photon-target center of mass energy. We show that, for $Q^2=1$GeV$^2$, the effect of this constraint can reach up to $\sim$35% for charm quarks and $\sim$7% for light quarks at $x=0.01$, but then rapidly decreases at smaller $x$ or larger $Q^2$.