Stability of fundamental couplings: A global analysis

Astrophysical tests of the stability of fundamental couplings are becoming an increasingly important probe of new physics. Motivated by the recent availability of new and stronger constraints we update previous works testing the consistency of measurements of the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $\mu=m_p/m_e$ (mostly obtained in the optical/ultraviolet) with combined measurements of $\alpha$, $\mu$ and the proton gyromagnetic ratio $g_p$ (mostly in the radio band). We carry out a global analysis of all available data, including the 293 archival measurements of {\it Webb et al.} and 66 more recent dedicated measurements, and constraining both time and spatial variations. While nominally the full datasets show a slight statistical preference for variations of $\alpha$ and $\mu$ (at up to two standard deviations), we also find several inconsistencies between different sub-sets, likely due to hidden systematics and implying that these statistical preferences need to be taken with caution. The statistical evidence for a spatial dipole in the values of $\alpha$ is found at the 2.3 sigma level. Forthcoming studies with facilities such as ALMA and ESPRESSO should clarify these issues.