Testing Lorentz invariance in orbital electron capture

Searches for Lorentz violation were recently extended to the weak sector, in particular neutron and nuclear $\beta$ decay [Noordmans, Wilschut, and Timmermans, Phys. Rev. C 87, 055502 (2013)]. From experiments on forbidden $\beta$-decay transitions, strong limits in the range of ${10}^{-6}$ to ${10}^{-8}$ were obtained on Lorentz-violating components of the $W$-boson propagator [Noordmans, Wilschut, and Timmermans, Phys. Rev. Lett. 111, 171601 (2013)]. In order to improve on these limits, strong sources have to be considered. In this Brief Report we study isotopes that undergo orbital electron capture and allow experiments at high decay rates and low dose. We derive the expressions for the Lorentz-violating differential decay rate and discuss the options for competitive experiments and their required precision.

Figure 1

The oscillation of the asymmetries in Eqs. (6) and (8) as function of sidereal time, for $|{\chi }^{\mu \nu }|=0.1,A=1$, and colatitude $\zeta ={45}^{\circ }$. To avoid a constant offset of the signal, we assumed polarization in the east-west $\left(\widehat{y}\right)$ direction. For ${\mathcal{A}}_{Ir},\widehat{\mathbf{k}}$ was taken in the laboratory $\widehat{z}$ direction, i.e., perpendicular to Earth's surface.