In light of the recent measurement of the ηπ^0γγ decay by the KLOE-2 Collaboration, a previous analysis including vector- and scalar-meson exchange contributions using the VMD and LσM frameworks, respectively, is extended in the present study to incorporate the effects of the a₂ (1320) tensor meson within a chiral context. Although the individual contribution of the a₂ is negligible, its destructive interference with the vector-meson resonances is found to be significant, representing approximately 18\% of the total signal and substantially affecting the diphoton invariant-mass distribution, especially at low m⏒⏒^2 values. The total decay rate is calculated to be Γ (ηπ^0γγ) =0. 154 (22) eV, which corresponds to a branching ratio of BR (ηπ^0γγ) =1. 17 (17) 10^-4. This result is approximately 5σ below the reported value of the PDG, 2. 55 (22) 10^-4, while it is in very good agreement with the KLOE-2 measurement, 0. 98 (11 ₒₓ₀ₓ) (14 ₒₘₒₓ) 10^-4. In contrast, the total contribution of the a₂ is found to be negligible in η^π^0γγ, as this process is completely dominated by the exchange of an on-shell ω vector resonance.
Escribano et al. (Wed,) studied this question.