A new constraint on the time dependence of the proton-to-electron mass ratio -: Analysis of the Q 0347-383 and Q 0405-443 spectra

A new limit on the possible cosmological variation of the proton-to-electron mass ratio mu = m(p)/m(e) is estimated by measuring wavelengths of H-2 lines of Lyman and Werner bands from two absorption systems at z(abs) = 2.5947 and 3.0249 in the spectra of quasars Q 0405-443 and Q 0347-383, respectively. Data are of the highest spectral resolution (R = 53 000) and S/N ratio (30 divided by 70) for this kind of study. We search for any correlation between z(i), the redshift of observed lines, determined using laboratory wavelengths as references, and K-i, the sensitivity coefficient of the lines to a change of mu, that could be interpreted as a variation of mu over the corresponding cosmological time. We use two sets of laboratory wavelengths, the first one, Set ( A) (Abgrall et al. 1993, J. Mol. Spec., 157, 512), based on experimental determination of energy levels and the second one, Set (P) (Philip et al. 2004, Can. J. Chem., 82, 713), based on new laboratory measurements of some individual rest-wavelengths. We find Delta mu/mu = (3.05 +/- 0.75) x 10(-5) for Set (A), and Delta mu/mu = (1.65 +/- 0.74) x 10(-5) for Set (P). The second determination is the most stringent limit on the variation of mu over the last 12 Gyr ever obtained. The correlation found using Set (A) seems to show that some amount of systematic error is hidden in the determination of energy levels of the H-2 molecule.