Constraining changes in the proton-electron mass ratio with inversion and rotational lines

We report deep Green Bank Telescope (GBT) spectroscopy in the redshifted NH$_3$~(1,1), CS~1-0 and H$_2$CO~0$_{\rm 00}$-1$_{\rm 01}$ lines from the $z \sim 0.685$ absorber towards B0218+357. The inversion (NH$_3$) and rotational (CS, H$_2$CO) line frequencies have different dependences on the proton-electron mass ratio $\mu$, implying that a comparison between the line redshifts is sensitive to changes in $\mu$. A joint 3-component fit to the NH$_3$, CS, and H$_2$CO lines yields $[\Delta \mu/\mu] = (-3.5 \pm 1.2) \times 10^{-7}$, from $z \sim 0.685$ to today, where the error includes systematic effects from comparing lines from different species and possible frequency-dependent source morphology. Two additional sources of systematic error remain, due to time variability in the source morphology and velocity offsets between nitrogen-bearing and carbon-bearing species. We find no statistically-significant ($\ge 3 \sigma$) evidence for changes in $\mu$, and obtain the stringent $3\sigma$ constraint, $[\Delta \mu/\mu] < 3.6 \times 10^{-7}$, over 6.2~Gyrs; this is the best present limit on temporal changes in $\mu$ from any technique, and for any lookback time, by a factor $\gtrsim 5$.