Abstract
In the development of atomic clocks, some atomic transition frequencies are measured with remarkable precision. These measured spectra may include the effects of a new force mediated by a weakly interacting boson. Such effects might be distilled out from possible violation of a linear relation in isotope shifts between two transitions, as known as King’s linearity, with relatively suppressed theoretical uncertainties. We discuss the experimental sensitivity to a new force in the test of the linearity as well as the linearity violation owing to higher-order effects within the Standard Model. The sensitivity to new physics is limited by such effects. We have found that, for hbox {Yb}^{+}, the higher-order effect is in the reach of future experiments. The sensitivity to a heavy mediator is also discussed. It is analytically clarified that the sensitivity becomes weaker than that in the literature. Our numerical results of the sensitivity are compared with other weak force search experiments.
Highlights
We study the violation of King’s linearity by a new force which is mediated by a light new boson
We argue how the field-shift non-linearity limits the experimental sensitivity to the new physics
The expected bounds on the new force in future experiments are compared with the other known constraints
Summary
We review King’s linearity and discuss its violation . Two sources of the linearity violation are examined. The isotope shift of a transition, which is represented by δν, is described by the leading orders of the mass shift and the field shift, and the other contributions as δν = Gδμ + Fδ r2 + X. If the last term is independent of the mass numbers, the modified isotope shifts satisfy the linear relation, that is, King’s linearity [2]. In the rest of this section, we firstly study the higher-order correction of the field shift. Since it contributes X , the sensitivity to the new particle is limited by the size of its contribution. Afterwards, the violation of the linearity is discussed in detail for both of the shifts
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