Lepton universality violation from neutral pion decays in $R_{K^{(*)}}$ measurements

I show that the neutral pion decay in $B \to K^{(*)} \pi^0 \gamma$, with $\pi^0 \to ee \gamma$, might generate large sources of lepton flavor universality violation (LFUV) in measurements of the ratios, $R_{K^{(*)}}$: If the photons in the $K^{(*)} e e \gamma \gamma$ final state are reconstructed as Bremsstrahlung, the recovered electron-positron invariant mass can be pushed into the $1$-$6$ GeV$^{2}$ signal region, artificially enhancing the measured $B \to K^{(*)} e e$ branching ratio compared to $B \to K^{(*)} \mu\mu$. I present a conservative estimate and simulation of the $B \to K \pi^0 \gamma$ LFUV background at LHCb, that together suggest this effect could reduce the recovered $R_K$ up to several percent. A reliable assessment of the size of this effect will require dedicated simulations within experimental frameworks themselves.