  The nuclear response theory for isospin-transfer modes in the relativistic
particle-vibration coupling framework is extended to include coupling of single
nucleons to isospin-flip (charge-exchange) phonons, in addition to the usual
neutral vibrations. This new coupling introduces dynamical pion and rho-meson
exchange, beyond the Hartree-Fock approximation, up to infinite order. We
investigate the impact of this new mechanism on the Gamow-Teller response of a
few doubly-magic neutron-rich nuclei, namely $^{48}$Ca, $^{78}$Ni, $^{132}$Sn
and $^{208}$Pb. It is found that the coupling to isospin-flip vibrations can
have a non negligible impact on the strength distribution and quenching of the
giant resonance, globally improving the agreement with the experimental data.
The corresponding beta-decay half-lives of $^{78}$Ni and $^{132}$Sn are also
calculated, and found to be decreased by a factor $\sim 2$ by the inclusion of
the new phonons.
