Using an amplitude analysis to measure the photon polarisation in B rightarrow Kpi pi gamma decays

Abstract

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 Kpi 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.