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.
