“…Precise measurements of their branching fractions (BFs) are important for a wide variety of physics topics. For example, the decay widths of 𝜂, 𝜂 ′ → 𝛾𝛾 are related to the quark content of the two mesons [3], the BFs of 𝜂, 𝜂 ′ → 3𝜋 decays can provide valuable information on light quark masses [4], the BFs of 𝜂, 𝜂 ′ → 𝜋 + 𝜋 − 𝛾 decays are related to details of chiral dynamics [5,6], and the BFs of some rare decays of the 𝜂 and 𝜂 ′ can test fundamental QCD symmetries [7] and probe for physics beyond the standard model [8]. As the BFs of the rare decays are obtained via normalization to the dominant decay modes, a precise determination of the BFs of the dominant decay modes of the 𝜂 and 𝜂 ′ is essential.…”