Enhanced Sensitivity to Variation ofme/mpin Molecular Spectra

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio $\mu \equiv m_e/m_p$. We consider a nearly degenerate pair of molecular vibrational levels, each associated with a different electronic potential. With respect to a change in $\mu$, the change in the splitting between such levels can be large both on an absolute scale and relative to the splitting. We demonstrate the existence of such pairs of states in ${\mathrm{Cs}}_2$, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in $\mu$.