Assessment of the a₂(1320) tensor-meson contribution to η/η^→π⁰γγ decays

In light of the recent measurement of the η→π⁰γγ decay by the KLOE-2 Collaboration, a previous analysis including vector- and scalar-meson exchange contributions using the VMD and L$σ$M 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 mγγ² values. The total decay rate is calculated to be Γ(η→π⁰γγ)=0.154(22) eV, which corresponds to a branching ratio of BR(η→π⁰γγ)=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(11ₛₜₐₜ)(14syst)×10⁻⁴. In contrast, the total contribution of the a₂ is found to be negligible in η^→π⁰γγ, as this process is completely dominated by the exchange of an on-shell $ω$ vector resonance.