Perspective: Tipping the scales - search for drifting constants from molecular spectra

Transitions in atoms and molecules provide an ideal test ground for constraining or detecting a possible variation of the fundamental constants of nature. In this Perspective, we review molecular species that are of specific interest in the search for a drifting proton-to-electron mass ratio $\mu$. In particular, we outline the procedures that are used to calculate the sensitivity coefficients for transitions in these molecules and discuss current searches. These methods have led to a rate of change in $\mu$ bounded to $6 \times 10^{-14}$/yr from a laboratory experiment performed in the present epoch. On a cosmological time scale the variation is limited to $|\Delta\mu/\mu| < 10^{-5}$ for look-back times of 10-12 billion years and to $|\Delta\mu/\mu| < 10^{-7}$ for look-back times of 7 billion years. The last result, obtained from high-redshift observation of methanol, translates into $\dot{\mu}/\mu = (1.4 \pm 1.4) \times 10^{-17}$/yr if a linear rate of change is assumed.