A Test of CP Symmetry in Positronium

The aim of this CP symmetry test in positronium is to measure the CP violation amplitude parameter \ccp. This is derived from the measurement of the asymmetry in an angular distribution of the photons from the decay of the ortho-positronium in a magnetic field. The Standard Model prediction for \ccp\ is a value of the order of $10^{-9}$. Thus the observation of a larger \ccp\ value would be signal of physics beyond the Standard Model. A previous measurement has found \ccp consistent with zero, with an uncertainty of $\sim 10^{-2}$. We have investigated the possibility of using the existing ETHZ-INRM-IN2P3 BGO crystal detector, set-up for positronium physics studies, to improve the sensitivity on the \ccp measurement. Preliminary calculations indicate that, using such an apparatus, with some modification, in a magnetic field of 4 kGauss, \ccp could be measured with an uncertainty in the range between $\sim 10^{-4}$ and $\sim 10^{-3}$, depending mainly on the uncertainty in the asymmetry measurement and the angular resolution of the photon detectors. If \ccp is less than $\sim 10^{-4}$, the experimental technique outlined here appears to be inadequate to observe a CP violating effect and new techniques or different observables must be exploited for better sensitivity.