$\psi(2S)$ versus $J/\psi$ suppression in proton-nucleus collisions from factorization violating soft color exchanges.

We argue that the large suppression of the $\psi(2S)$ inclusive cross-section relative to the $J/\psi$ inclusive cross-section in proton-nucleus (p+A) collisions can be attributed to factorization breaking effects in the formation of quarkonium. These factorization breaking effects arise from soft color exchanges between charm-anticharm pairs undergoing hadronization and comoving partons that are long-lived on time scales of quarkonium formation. We compute the short distance pair production of heavy quarks in the Color Glass Condensate (CGC) effective field theory and employ an improved Color Evaporation model (ICEM) to describe their hadronization into quarkonium at large distances. The combined CGC+ICEM model provides a quantitative description of $J/\psi$ and $\psi(2S)$ data in proton-proton (p+p) collisions from both RHIC and the LHC. Factorization breaking effects in hadronization, due to additional parton comovers in the nucleus, are introduced heuristically by imposing a cutoff $\Lambda$, representing the momentum kick from soft color exchanges, in the ICEM model. Such soft exchanges have no perceptible effect on $J/\psi$ suppression in p+A collisions. In contrast, the interplay of the physics of these soft exchanges at large distances, with the physics of semi-hard rescattering at short distances, causes a significant additional suppression of $\psi(2S)$ yields relative to that of the $J/\psi$. A good fit of all RHIC and LHC $J/\psi$ and $\psi(2S)$ data, for transverse momenta $P_\perp\leq 5$ GeV in p+p and p+A collisions, is obtained for $\Lambda\sim 10$ MeV.