Resolution of the SU(3) Puzzle:Γ(η→γγ)Γ(π0→γγ)

Abstract

Using the Duffin-Kemmer-Petiau (DKP) description of mesons, we are able to render simple SU(3) theory consistent with the supposedly "large" experimental value of $\frac{\Gamma (\eta \to \gamma \gamma )}{\Gamma ({\pi }^0\to \gamma \gamma )}=129\mathrm{}\pm 33$. After discussing $\eta -{\eta }^{\prime }$ mixing we make a prediction [uncertain because of large errors in ${\Gamma }_{\mathrm{tot}}^{\mathrm{expt}}\left({\pi }^0\right)$ and ${\Gamma }_{\mathrm{tot}}^{\mathrm{expt}}\left(\eta \right)$] of ${\Gamma }^{\mathrm{DKP}}({\eta }^{\prime }\to \gamma \gamma )={0.32}_{-0.32\mathrm{}}^{+0.99\mathrm{}}$ keV. This is at least 1-2 orders of magnitude lower than the Klein-Gordon (KG) prediction, ${\Gamma }^{\mathrm{KG}}({\eta }^{\prime }\to \gamma \gamma )=52\mathrm{}\pm 24$ keV, which in fact is almost ruled out by upper limits set by recent experiments.