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 = 53000) and S/N ratio (30\div70) 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.), based on experimental determination of energy levels and the second one, Set (P) (Philip et al.), based on new laboratory measurements of some individual rest-wavelengths. We find \Delta\mu/\mu = (3.05+-0.75)10^-5 for Set (A), and \Delta\mu/\mu = (1.65+-0.74)10^-5 for Set (P). The second determination is the most stringent limit on the variation of \mu over the last 12 Gyrs 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.