Testing the time-invariance of fundamental constants using microwave spectroscopy on cold diatomic radicals

The recently demonstrated methods to cool and manipulate neutral molecules offer new possibilities for precision tests of fundamental physics theories. We here discuss the possibility of testing the time-invariance of fundamental constants using near degeneracies between rotational levels in the fine structure ladders of molecular radicals. We show that such a degeneracy occurs between the J = 6, Omega = 1 and the J = 8, Omega = 0 levels of the various natural isotopomers of carbon monoxide in its a(3)Pi state. As a result, the 2-photon transition that connects these states is 300 times more sensitive to a variation of m(p)/m(e) than a pure rotational transition. We present a molecular beam apparatus that might be used to measure these transitions with a fractional accuracy of 10(-12). Ultimately, the precision of an experiment on metastable CO will be limited by the lifetime of the a(3)Pi state. We will discuss other possible molecules that have a suitable level structure and can be cooled using one of the existing methods.