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 ${\gamma }^{\ast }\to {\rho }^0$ 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.

Comments: 7 pages, 4 figures