Effective Color Dipole Approach to Color Transparency in \texorpdfstring{$ρ^0$}{rho^0} Electroproduction

We investigate nuclear transparency in exclusive $\rho^{0}$ electroproduction on $^{12}$C and $^{56}$Fe nuclei within a multi-channel final-state interaction (FSI) framework that explicitly incorporates the kinematic decay length effect (DLE) arising from the short-lived $\rho^{0}\rightarrow\pi^{+}\pi^{-}$ decay. A realistic treatment of the deuteron reference state using the Paris potential wave function, which incorporates the short-range repulsive core and tensor correlations, provides a physically reliable normalization for the transparency ratio $T_A/T_D$. The conventional DLE and nuclear shadowing mechanisms together remain insufficient to account for the observed $Q^2$-dependent enhancement, systematically underestimating the measured transparency throughout the CLAS kinematic range. To address this, we introduce an effective Color Dipole Model (CDM) boundary condition for the initial PLC interaction cross section $\sigma_{\text{h}}(Q^2)$, evaluated as a dipole-weighted average over the $\gamma^*$--$\rho^0$ transition wave functions, in place of the purely empirical Quantum Diffusion Model (QDM) ansatz. This CDM-inspired initial condition, combined with the standard linear QDM transport, yields a consistent description of the $Q^2$-dependent CLAS data for both targets with an effective in-medium expansion scale $\Delta m^2 = 0.3~\mathrm{GeV}^2$. Although the present analysis does not provide definitive evidence for the onset of Color Transparency, it demonstrates that a CDM-inspired PLC boundary condition, together with a realistic treatment of the underlying reaction dynamics, yields a physically consistent and quantitatively improved description of the CLAS data.