New apparatus for the measurement of the electron and positron $g$-factors to test the Standard Model

The comparison of the measurement of the electron magnetic moment with its predicted value from the Standard Model yields the most precise test of the Standard Model [1, 2]. This 0.9 parts per trillion comparison between measurement and theory reveals a 2.4 $\sigma $ discrepancy which warrants further investigation [3, 4]. Additionally, a comparison between the electron and positron magnetic moments provides a strong test of CPT symmetry. An apparatus currently being constructed has the goal of improving on the previous measurement of the electron and positron $g$-factors. A Penning trap has been designed with careful consideration of the microwave cavity mode structure with the aim of cooling the axial state via cavity-assisted sideband cooling. The apparatus includes a low field region about 40 cm from the electron trap for implementation of a SQUID detector. A proposed measurement procedure will be presented. 1. D. Hanneke, S. Fogwell, and G. Gabrielse, \textit{Physical Review Letters} 100 (2008) 120801 2. R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. M\"{u}ller, \textit{Science} 360 (2018) 191 3. G. Gabrielse, S.E. Fayer, T.G. Myers, X. Fan,~ \textit{Atoms} 2019, 7, 45. 4. T. Aoyama, T. Kinoshita,~ M. Nio, \textit{Atoms} 2019, 7, 28.