Momentum fraction and hard scale dependence of double parton scattering

Abstract: The effective cross section of double parton scattering in high-energy hadron collisions has been measured in proton--proton collisions, with significant variation among final-state observables, contrary to the idea of a universal value. Building upon our previous work, we incorporate the dependence on both the parton longitudinal momentum fraction $x$ and the process energy hard scale $\mu$ into the transverse part of the double parton distributions, using a Gaussian profile. Employing the experimental data from the LHC and Tevatron experiments (covering different processes, kinematic configurations, and center--of--mass energies), we perform a global fit of the model, extracting the parameters that describe the proton structure. With this result, it becomes possible to calculate the effective cross section for others observables, and we provide predictions for future measurements at the LHC.