Further consistency tests of the stability of fundamental couplings

In a recent publication Ferreira et al. , Phys. Rev. D 89, 083011 (2014) we tested the consistency of current astrophysical tests of the stability of the fine-structure constant and the proton-to-electron mass ratio =m₏/m₄ (mostly obtained in the optical/ultraviolet range) with combined measurements of, and the proton gyromagnetic ratio g₏ (mostly in the radio band). Given the significant observational progress made in the past year, we now revisit and update this analysis. We find that apparent inconsistencies, at about the two-sigma level, persist and are in some cases enhanced, especially for matter era measurements (corresponding to redshifts z>1). Although hidden systematics may be the more plausible explanation, we briefly highlight the importance of clarifying this issue, which is within the reach of state-of-the-art observational facilities such as ALMA and ESPRESSO.