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Electromagnetic moments of particles carry important information on theirinternal structure, as well as on the structure of the effective Lagrangiandescribing their underlying field theory. One of the cleanest observable ofsuch kind is the electric dipole moment (EDM), since Standard Model estimateswould imply very small, much less then 10^-30 ecm value for that quantity,whereas several Beyond Standard Model (BSM) theories happen to predict of theorder of 10^-28 ecm EDM for elementary or hadronic particles. So far, precisionEDM upper bounds are mainly available for neutrons via cold neutronexperiments, and indirect measurements for electrons. Therefore, in the recentyear there has been a growing interest for direct measurement of EDM forcharged particles, such as electrons, protons, muons or light nuclei. Suchmeasurements become possible in relativistic storage rings, called frozen spinstorage rings. Many environmental factors give systematic backgrounds to theEDM signal, including General Relativity (GR), due to the gravitational fieldof the Earth. It turns out that, depending of the experimental scenario, the GReffect can be well above the planned EDM sensitivity. Therefore, it is both ofconcern as a source of systematics, as well as it can serve as a spin-offexperiment for an independent test of GR. There are a handful of theoreticalpapers quantifying the GR systematics, delivering slightly different results.The aim of this paper is to clarify these claims, eventually try to reconcilethese predictions, and to deduce their experimental implications. The closingsection of the paper quantifies the field imperfection systematic errorcancellation in the case of a so-called doubly-frozen spin storage ringsetting, in the idealized axial symmetric limit.

Clarification on theoretical predictions for general relativistic effects in frozen spin storage rings