Addendum: A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ η ′ → π + π - γ and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$ η ′ → ℓ + ℓ - γ

Abstract In this addendum to Ref. [1] we show that the mismatch between the $$\rho $$ ρ – $$\omega $$ ω mixing parameter $$\epsilon _{\rho \omega }$$ ϵ ρ ω as extracted from $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ η ′ → π + π - γ and $$e^+e^-\rightarrow \pi ^+\pi ^-$$ e + e - → π + π - can be resolved by including higher orders in the expansion in $$e^2$$ e 2 in the description of the $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ η ′ → π + π - γ decay. We repeat the analysis in this extended framework and update the numerical results accordingly.