Using an amplitude analysis to measure the photon polarisation in $B \rightarrow K\pi \pi \gamma $ decays
Résumé
A method is proposed to measure the photon polarisation parameter $\lambda _{\gamma }$ in ${{b}} \!\rightarrow {s} {\gamma } $ transitions using an amplitude analysis of $B\!\rightarrow K\pi \pi {\gamma } $ decays. Simplified models of the ${K} {\pi } {\pi } $ system are used to simulate ${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $ and ${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $ decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the $\lambda _{\gamma }$ parameter irrespective of the model parameters. Similar sensitivities to $\lambda _{\gamma }$ 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 ${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $ decays in an LHCb data set corresponding to an integrated luminosity of 9 $\,\hbox {fb}^{-1}$ is estimated to be 0.009. A similar measurement using ${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $ decays in a Belle II data sample corresponding to an integrated luminosity of 5 $\hbox {\,ab}^{-1}$ would lead to a statistical uncertainty of 0.018.