Robust Constraint on a Drifting Proton-to-Electron Mass Ratio at z=0.89 from Methanol Observation at Three Radio Telescopes

A limit on a possible cosmological variation of the proton-to-electron mass ratio $mu$ is derived from methanol (CH$_3$OH) absorption lines in the benchmark PKS1830$-$211 lensing galaxy at redshift $z = 0.89$ observed with the Effelsberg 100-m radio telescope, the Institute de Radio Astronomie Millim{e}trique 30-m telescope, and the Atacama Large Millimeter/submillimeter Array. Ten different absorption lines of CH$_3$OH covering a wide range of sensitivity coefficients $K_{mu}$ are used to derive a purely statistical 1-$sigma$ constraint of $Deltamu/mu = (1.5 pm 1.5) times 10^{-7}$ for a lookback time of 7.5 billion years. Systematic effects of chemical segregation, excitation temperature, frequency dependence and time variability of the background source are quantified. A multi-dimensional linear regression analysis leads to a robust constraint of $Deltamu/mu = (-1.0 pm 0.8_{rm stat} pm 1.0_{rm sys}) times 10^{-7}$.