Chiral restoration from pionic atoms?

Abstract

We evaluate widths and shifts of pionic atoms using a theoretical microscopical potential in which the pion decay constant $f_\pi$ is changed by an in--medium density dependent one ($f_\pi(\rho)$), predicted by different partial Chiral restoration calculations. We show that the results obtained for shifts and widths are worse than if this modification were not implemented. On the other hand, we argue that in microscopic many body approaches for the pion selfenergy, based on effective Lagrangians, the mechanisms responsible for the change of $f_\pi$ in the medium should be automatically incorporated. Therefore, the replacement of $f_\pi$ by $f_\pi(\rho)$ in the many body derivation of the microscopic potential would be inappropriate.