Test of Charge Conjugation Invariance

We report on the first determination of upper limits on the branching ratio ($BR$) of $\eta$ decay to ${\pi }^0{\pi }^0\gamma$ and to ${\pi }^0{\pi }^0{\pi }^0\gamma$. Both decay modes are strictly forbidden by charge conjugation ($C$) invariance. Using the Crystal Ball multiphoton detector, we obtained $BR(\eta \to {\pi }^0{\pi }^0\gamma )<5\times {10}^{-4}$ at the 90% confidence level, in support of $C$ invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured $BR(\eta \to {\pi }^0{\pi }^0{\pi }^0\gamma )<6\times {10}^{-5}$ at the 90% confidence level, in support of $C$ invariance of isovector electromagnetic interactions.

Figure 1

Distributions for the events selected as ${\pi }^{-}p\to 2{\pi }^0\gamma n\to 5\gamma n$: kinematic-fit CL (row 1), $z$-vertex coordinate (row 2), parameter $\rho$ vs cluster energy $E$ for the decay photon (row 3), and invariant mass of the ${\pi }^0{\pi }^0\gamma$ system (row 4) obtained with $\mathrm{C}\mathrm{L}>20\%,|z|<7\mathrm{c}\mathrm{m}$ , and $\rho$ cut. Distributions are shown for ${\mathrm{L}\mathrm{H}}_2$ (column 1) and empty-target (column 2) data, MC simulation for $1.6\times {10}^7$ ${\pi }^{-}p\to \eta n\to 3{\pi }^{0}n$ events (column 3), MC for $4\times {10}^7$ ${\pi }^{-}p\to {\pi }^0{\pi }^{0}n$ events (column 4), and MC for $4\times {10}^5$ ${\pi }^{-}p\to \eta n\to 2{\pi }^0\gamma n$ events (column 5). The curve in the plots shows the cut on the parameter $\rho$. The cut requires all events in which $\rho$ lies above the curve to be discarded.

Figure 2

Distributions for the kinematic-fit CL and the decay-photon momentum $p_{\gamma }^{*}$ (in the $\eta$ rest frame) obtained from testing the ${\pi }^{-}p\to n\eta \to n3{\pi }^0\gamma \to n7\gamma$ hypothesis for: (a), (b) experimental ${\mathrm{L}\mathrm{H}}_2$ data, (c), (d) MC simulation for $3\times {10}^7$ ${\pi }^{-}p\to \eta n\to 3{\pi }^{0}n$ events, (e), (f) MC for $4\times {10}^5$ ${\pi }^{-}p\to \eta n\to 3{\pi }^0\gamma n$ events.