Proposed Test of Charge-Conjugation Invariance in Positronium Decay

Abstract

If the electromagnetic interactions are invariant under charge conjugation, $C$, then singlet positronium (Ps) can only decay into an even number of photons, while triplet Ps can only decay into an odd number of photons. In this paper we consider a model Hamiltonian which violates $C$ invariance but conserves parity. If $\ensuremath{\lambda}$ is the coupling constant in the proposed $C$-noninvariant interaction, then the branching ratio of the forbidden decay, $1^{3}S_{1}\ensuremath{\rightarrow}4\ensuremath{\gamma}$, to the allowed decay, $1^{3}S_{1}\ensuremath{\rightarrow}3\ensuremath{\gamma}$, has been found to be ${F}_{T}^{4\ensuremath{\gamma}}=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\ensuremath{\lambda}}^{2}$.An experimental upper limit on ${F}_{T}^{4\ensuremath{\gamma}}$ would provide a novel check of $C$ invariance in electromagnetic interactions, and would also yield new information on the $\overline{e}e\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ interaction. At present, indirect limits on ${F}_{T}^{4\ensuremath{\gamma}}$ show it to be less than about ${10}^{\ensuremath{-}2}$. We are now working on an experiment which is designed to reduce this upper limit to ${10}^{\ensuremath{-}5}$-${10}^{\ensuremath{-}6}$. If successful, it will subject the proposed interaction, or any similar interaction leading to $1^{3}S_{1}\ensuremath{\rightarrow}4\ensuremath{\gamma}$, to a stringent test. An outline of the experiment is included in this paper.