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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, alpha, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21 cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to alpha. However, in specific models, particularly unification models, changes in alpha are always accompanied by corresponding changes in other fundamental quantities such as the QCD scale, Lambda_QCD. This work tracks the changes in the nucleon g-factors induced from changes in Lambda_QCD and the light quark masses. In principle, these coupled variations can improve the bounds on the variation of alpha 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.