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 $\Delta\mu/\mu = (1.5 \pm 1.5)
\times 10^{-7}$ 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 $\Delta\mu/\mu = (-1.0 \pm
0.8_{\rm stat} \pm 1.0_{\rm sys}) \times 10^{-7}$.
