CONSTRAINTS ON THE VARIATIONS OF FUNDAMENTAL CONSTANTS

Abstract

In many theories beyond the standard model, gauge and Yukawa couplings can be thought of as dynamical variables. Indeed, such is the case in string theory, where the gauge and Yukawa couplings are set by ratios of the dilaton and moduli field vacuum expectation values to the string tension. Thus until these vevs are fixed, the fundamental coupling constants could vary in time. A considerable amount of interest in the possibility of time-varying constants has been generated by recent observations of quasar absorption systems. These data, analyzed using the many-multiplet method, suggest a time variation in the fine structure constant by an amount Aa/a = (0.54 ± 0.12) x 10~ over a redshift range of 0.5 3.5. Alternatively, much of this data may be explained by isotopic anomalies (in Mg) in these systems. There are several constraints on the possible variation of the fine-structure constant, which interestingly enough do not directly conflict with the claimed observation. Significantly stronger constraints on the variation of the fine structure constant can be obtained in the context of theories in which the change in a scalar field vev which induces a change in the fine structure constant also induces a change in the other gauge and Yukawa couplings. In any unified theory in which the gauge fields have a common origin, variations in the fine structure constant will be accompanied by similar variations in the other gauge couplings. For example, the running of the strong coupling constant has dramatic consequences for the low energy hadronic parameters, including the masses of nucleons. Indeed the masses are determined by the QCD scale, A, which is related to the ultraviolet scale, Muv, by dimensional transmutation. Clearly, changes in gs will induce (exponentially) large changes in A. On the other hand, the electromagnetic coupling a never experiences significant running from Muv to A and thus AA/A ;§> Aa/a. A more elaborate treatment of the renormalization group equations above