Two distinct high-accuracy laboratory spectroscopic investigations of the ${\mathrm{H}}_2$ molecule are reported. Anchor lines in the $EF{}^1\Sigma _g^{+}-X{}^1\Sigma _g^{+}$ system are calibrated by two-photon deep-UV Doppler-free spectroscopy, while independent Fourier-transform spectroscopic measurements are performed that yield accurate spacings in the $B{}^1\Sigma _u^{+}-EF{}^1\Sigma _g^{+}$ and $I{}^1\Pi _g-C{}^1\Pi _u$ systems. From combination differences accurate transition wavelengths for the $B-X$ Lyman and the $C-X$ Werner lines can be determined with accuracies better than $\sim 5\times {10}^{-9}$, representing a major improvement over existing values. This metrology provides a practically exact database to extract a possible variation of the proton-to-electron mass ratio based on ${\mathrm{H}}_2$ lines in high-redshift objects. Moreover, it forms a rationale for equipping a future class of telescopes, carrying 30–40 m dishes, with novel spectrometers of higher resolving powers.

• Received 7 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.223001