Methods for Constraining Fine Structure Constant Evolution with OH Microwave Transitions

We investigate the constraints that OH microwave transitions in megamasers and molecular absorbers at cosmological distances may place on the evolution of the fine structure constant $\alpha =e^2/\hslash c$. The centimeter OH transitions are a combination of hyperfine splitting and lambda doubling that can constrain the cosmic evolution of $\alpha$ from a single species, avoiding systematic errors in $\alpha$ measurements from multiple species which may have relative velocity offsets. The most promising method compares the 18 and 6 cm OH lines, includes a calibration of systematic errors, and offers multiple determinations of $\alpha$ in a single object. Comparisons of OH lines to the HI 21 cm line and CO rotational transitions also show promise.