Methanol as a tracer of fundamental constants

The methanol molecule CH3OH has a complex microwave spectrum with a large number of very strong lines. This spectrum includes purely rotational transitions as well as transitions with contributions of the internal degree of freedom associated with the hindered rotation of the OH group. The latter takes place due to the tunneling of hydrogen through the potential barriers between three equivalent potential minima. Such transitions are highly sensitive to changes in the electron-to-proton mass ratio, mu = m_e/m_p, and have different responses to mu-variations. The highest sensitivity is found for the mixed rotation-tunneling transitions at low frequencies. Observing methanol lines provides more stringent limits on the hypothetical variation of mu than ammonia observation with the same velocity resolution. We show that the best quality radio astronomical data on methanol maser lines constrain the variability of mu in the Milky Way at the level of |Delta mu/mu| < 28x10^{-9} (1sigma) which is in line with the previously obtained ammonia result, |Delta mu/mu| < 29x10^{-9} (1\sigma). This estimate can be further improved if the rest frequencies of the CH3OH microwave lines will be measured more accurately.