Effective Color Dipole Approach to Color Transparency in $\rho^0$ Electroproduction

Abstract

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 $\rho^0\to\pi^+\pi^-$ decay. The purely kinematic and nuclear mechanisms prove insufficient to account for the CLAS data: the DLE alone cannot generate the observed $Q^2$-dependent enhancement, and the inclusion of nuclear shadowing further deepens the disagreement, so that a compensating reduction of the in-medium attenuation -- the hallmark of color transparency (CT) -- is required. To incorporate the color dynamics of the initially compact $q\bar{q}$ configuration, we replace the empirical Quantum Diffusion Model (QDM) ansatz for the initial interaction cross section $\sigma_h(Q^2)$ of the point-like configuration (PLC) by an effective Color Dipole Model (CDM) boundary condition, evaluated through a normalized dipole-weighted $\gamma^*\to\rho^0$ transition overlap. Combined with the standard linear QDM transport at an effective in-medium expansion scale $\Delta m^2 = 0.3$~GeV$^2$, the CDM boundary condition reproduces both the magnitude and the $Q^2$ dependence of the data for both targets. A $\chi^2$ analysis quantifies the pronounced separation between the non-CT and CT-based descriptions and thereby supports the onset of color transparency in the $\rho^0$ channel beyond what kinematic decay-length effects can accommodate.