Constraint on a cosmological variation in the proton-to-electron mass ratio from electronic CO absorption

Carbon monoxide (CO) absorption in the sub-damped Lyman-\(\alpha\) absorber at redshift \(z_{abs} \simeq 2.69\), toward the background quasar SDSS J123714.60+064759.5 (J1237+0647), was investigated for the first time in order to search for a possible variation of the proton-to-electron mass ratio, \(\mu\), over a cosmological time-scale. The observations were performed with the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of 40 per 2.5 kms\(^{-1}\) per pixel at \(\sim 5000\) \AA. Thirteen CO vibrational bands in this absorber are detected: the A\(^{1}\Pi\) - X\(^{1}\Sigma^{+}\) (\(\nu'\),0) for \(\nu' = 0 - 8\), B\(^{1}\Sigma^{+}\) - X\(^{1}\Sigma^{+}\) (0,0), C\(^{1}\Sigma^{+}\) - X\(^{1}\Sigma^{+}\) (0,0), and E\(^{1}\Pi\) - X\(^{1}\Sigma^{+}\) (0,0) singlet-singlet bands and the d\(^{3}\Delta\) - X\(^{1}\Sigma^{+}\) (5,0) singlet-triplet band. An updated database including the most precise molecular inputs needed for a \(\mu\)-variation analysis is presented for rotational levels \(J = 0 - 5\), consisting of transition wavelengths, oscillator strengths, natural lifetime damping parameters, and sensitivity coefficients to a variation of the proton-to-electron mass ratio. A comprehensive fitting method was used to fit all the CO bands at once and an independent constraint of \(\Delta\mu/\mu = (0.7 \pm 1.6_{stat} \pm 0.5_{syst}) \times 10^{-5}\) was derived from CO only. A combined analysis using both molecular hydrogen and CO in the same J1237+0647 absorber returned a final constraint on the relative variation of \(\Delta\mu/\mu = (-5.6 \pm 5.6_{stat} \pm 3.1_{syst}) \times 10^{-6}\), which is consistent with no variation over a look-back time of \(\sim 11.4\) Gyrs.