Do radio core-halos and cold fronts in non-major-merging clusters originate from the same gas sloshing?

We show an interesting correlation between the surface brightness and temperature structure of the relaxed clusters RX J1720.1 + 2638 and MS 1455.0 + 2232, hosting a pair of cold fronts, and their central core-halo radio source. We discuss the possibility that the origin of this diffuse radio emission may be strictly connected with the gas sloshing mechanism suggested to explain the formation of cold fronts in non-major-merging clusters. We show that the radiative lifetime of the relativistic electrons is much shorter than the timescale on which they can be transported from the central galaxy up to the radius of the outermost cold front. This strongly indicates that the observed diffuse radio emission is likely produced by electrons reaccelerated via some kind of turbulence generated within the cluster volume limited by the cold fronts during the gas sloshing.