Molecular hydrogen transitions in the sub-damped Lyman alpha absorber at redshift z = 2.69, toward the background quasar SDSS J123714.60+064759.5, were analyzed in order to search for a possible variation of the proton-to-electron mass ratio mu over a cosmological time-scale. The system is composed of three absorbing clouds where 137 H2 and HD absorption features were detected. The observations were taken with the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of 32 per 2.5 km/s pixel, covering the wavelengths from 356.6 to 409.5 nm. A comprehensive fitting method was used to fit all the absorption features at once. Systematic effects of distortions to the wavelength calibrations were analyzed in detail from measurements of asteroid and `solar twin spectra, and were corrected for. The final constraint on the relative variation in mu between the absorber and the current laboratory value is dmu/mu = (-5.4 pm 6.3 stat pm 4.0 syst) x 10^(-6), consistent with no variation over a look-back time of 11.4 Gyrs.
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