Using an amplitude analysis to measure the photon polarisation in [Formula: see text] decays

A method is proposed to measure the photon polarisation parameter [Formula: see text] in [Formula: see text] transitions using an amplitude analysis of [Formula: see text] decays. Simplified models of the [Formula: see text] system are used to simulate [Formula: see text] and [Formula: see text] decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the [Formula: see text] parameter irrespective of the model parameters. Similar sensitivities to [Formula: see text] are obtained with both the charged and neutral hadronic systems. In the absence of any background and distortion due to experimental effects, the statistical uncertainty expected from an analysis of [Formula: see text] decays in an LHCb data set corresponding to an integrated luminosity of 9 [Formula: see text] is estimated to be 0.009. A similar measurement using [Formula: see text] decays in a Belle II data sample corresponding to an integrated luminosity of 5 [Formula: see text] would lead to a statistical uncertainty of 0.018.