The study of heavy quarks pair production at the LHeC and FCC-eh in the collinear generalized double asymptotic scaling (DAS) approach

In this paper, the main idea is the prediction of the linear and nonlinear behavior of heavy quarks pair production cross section at the deep inelastic scattering leptoproduction at the future electron–proton colliders, i.e., the Large Hadron electron Collider (LHeC) and the Future Circular Collider electron-hadron (FCC-eh) at the leading order (LO) and the next-to-leading order (NLO) approximation in perturbative quantum chromodynamics (pQCD) at small x . By considering the nonlinear corrections to the gluon distribution function in the framework of the nonlinear GLR-MQ-ZRS evolution equation and using the Laplace transform technique, based on the parametrization method of structure function F_2(x,Q^2) and its derivatives, we determine the linear and nonlinear evolution of production cross section and structure functions F_2(x,Q^2) and F_L(x,Q^2) and their ratio with respect to variables x and Q^2 for heavy quarks of charm and beauty. To study the heavy quark production processes, we use the collinear generalized double asymptotic scaling (DAS) approach in kinematics range of the LHeC and FCC-eh colliders. The computed results are compared with experimental data from HERA and the results of NNPDF4.0 and CT18 Collaborations.