Gyromagnetic factors and atomic clock constraints on the variation of fundamental constants

We consider the effect of the coupled variations of fundamental constants on the nucleon magnetic moment. The nucleon g-factor enters into the interpretation of the measurements of variations in the fine-structure constant, α, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to α. However, in specific models, particularly unification models, changes in α are always accompanied by corresponding changes in other fundamental quantities such as the QCD scale, Λ_QCD. This work tracks the changes in the nucleon g-factors induced from changes in Λ_QCD and the light quark masses. In principle, these coupled variations can improve the bounds on the variation of α by an order of magnitude from existing atomic clock and astrophysical measurements. Unfortunately, the calculation of the dependence of g-factors on fundamental parameters is notoriously model-dependent.