Convergence of Heavy-Flavor PDFs at Small x and Its Impact on Future ep Colliders

Abstract

We present the first quantitative demonstration of the statistical convergence of heavy-flavor parton distribution functions at small x across modern NNLO global fits. Using the latest NNPDF4.0, CT18, and MSHT20 sets, we find a maximal relative deviation of 16.8 percent at x = 1e-6 and Q = 100 GeV, corresponding to nearly a factor-of-two improvement over the approximately 30 percent spread in pre-2013 determinations. This convergence, stabilized by consistent alpha_s and scale treatments, marks a transition of the heavy-flavor sector into a statistically controlled regime of small-x QCD. We further show that this precision directly reduces PDF-driven uncertainties in heavy-quark electroproduction at future ep colliders (LHeC and FCC-eh) by about a factor of two and enhances the theoretical stability of leptophilic new-physics searches such as a neutral Z_l gauge boson. These findings establish a link between the precision frontier of QCD and the discovery potential of next-generation lepton-hadron facilities.