Study of the up-down asymmetry in $B^+\to K^+π^+π^-γ$ using $K_1(1270)$ amplitudes constrained by semileptonic $D$ Decays

Using $K_1(1270)\to Kππ$ amplitude models constrained by the charmed-meson semileptonic decays $D^{+(0)}\to K^-π^+π^{0(-)} e^+ν_e$, we present a model-dependent estimate of the up-down asymmetry observed in $B^+\to K^+π^+π^-γ$ in the mass region $M_{K^+π^+π^-}\in[1.1,1.3]$~GeV/$c^2$. Estimates based on an isolated $K_1(1270)$ show significant model dependence, but systematically lie below the measured asymmetry $\bar{\mathcal{H}}_{\mathrm{ud}}=(0.092\pm0.023)$ when assuming $λ_γ=1$. We also explore interference with the $K_1(1400)$ tail and find that it can appreciably reduce the tension.