Using an amplitude analysis to measure the photon polarisation in decays

A method is proposed to measure the photon polarisation parameter $$ in $$ transitions using an amplitude analysis of $$ decays. Simplified models of the $$ system are used to simulate $$ and $$ decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the $$ parameter irrespective of the model parameters. Similar sensitivities to $$ 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 $$ decays in an LHCb data set corresponding to an integrated luminosity of 9  $$ is estimated to be 0.009. A similar measurement using $$ decays in a Belle II data sample corresponding to an integrated luminosity of 5  $$ would lead to a statistical uncertainty of 0.018.