Enhanced sensitivity to variation of me/mp in molecular spectra

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio mu equivalent to 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 Cs-2, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in mu.