Electromagnetic transitions of ##\psi(2S)##

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The discussion focuses on the electromagnetic transitions of the ##\psi(2S)## particle, specifically the decays into two channels: ##\psi(2S) \rightarrow \gamma + \eta({1}^S_0)## and ##\psi(2S) \rightarrow \gamma + \chi_{c0}({3}^P_0)##. The branching fraction for the decay into the eta meson is approximately ##3.4 \times 10^{-3}##, while the decay into the chi meson has a branching fraction of about ##9.7 \times 10^{-2}##. The discussion raises questions regarding the underlying reasons for the significant difference in branching fractions between these two transitions.

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When the ##\psi(2s)## particle decays also the following two transitions are observed

$$\psi(2S) \rightarrow \gamma + \eta({1}^S_0)$$
$$\psi(2S) \rightarrow \gamma + \chi_{c0}({3}^P_0)$$

The branching fraction for the first decay is about ##3.4*10^{-3}## while it's ##9.7*10^{-2}## for the second one.
Where does the difference come from?
 
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Why do you think it should be the same?
 
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