Ruling out color transparency in quasi-elastic $^{12}$C(e,ep) up to $Q^2$ of 14.2 (GeV/c)$^2$

Quasielastic $^{12}$C$(e,ep)$ scattering was measured at space-like 4-momentum transfer squared $Q^2$~=~8, 9.4, 11.4, and 14.2 (GeV/c)$^2$, the highest ever achieved to date. Nuclear transparency for this reaction was extracted by comparing the measured yield to that expected from a plane-wave impulse approximation calculation without any final state interactions. The measured transparency was consistent with no $Q^2$ dependence, up to proton momenta of 8.5~GeV/c, ruling out the quantum chromodynamics effect of color transparency at the measured $Q^2$ scales in exclusive $(e,ep)$ reactions. These results impose strict constraints on models of color transparency for protons.