We study transition form factors for radiative and rare semi-leptonic B-meson decays into light pseudoscalar or vector mesons, combining theoretical constraints and phenomenological information from Lattice QCD, light-cone sum rules, and dispersive bounds. We pay particular attention to form factor parameterisations which are based on the so-called series expansion, and study the related systematic uncertainties on a quantitative level. In this context, we also provide the NLO corrections to the correlation function between two flavour-changing tensor currents, which enters the unitarity constraints for the coefficients in the series expansion.
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