Speaker
Description
Predictions for the inclusive DIS total cross section at small $x$ are commonly obtained using the forward elastic scattering amplitude in the dipole picture. However, the usual dipole picture assumes an asymptotically large photon-proton center-of-mass energy $W$, such that the phase space of the produced partonic system at the unitarity cut remains unconstrained. In this work, we move away from the infinite-energy limit by implementing a finite-energy constraint that restricts the invariant mass of the produced partonic system by $W$. By explicitly integrating over the final-state phase space - which is possible when the optical theorem is not used - we derive the leading-order DIS cross section with a finite-energy constraint. We then quantify its phenomenological impact and find that, for $Q^2 = 1$ GeV$^2$, the constraint can modify the cross section by up to $\sim 35$% for charm quarks and $\sim 7$% for light quarks at $x = 0.01$, while the effect rapidly decreases at smaller $x$ or larger $Q^24. Our results are relevant for precision descriptions of HERA data and for future measurements at the EIC.