Using an amplitude analysis to measure the photon polarisation in $$B \rightarrow K\pi \pi \gamma $$ B→Kππγ decays

• Published in: The European physical journal. C, Particles and fields Vol. 79; no. 7; pp. 1 - 15
• Main Authors: V. Bellée, P. Pais, A. Puig Navarro, F. Blanc, O. Schneider, K. Trabelsi, G. Veneziano
• Format: Journal Article
• Language: English
• Published: SpringerOpen 01-07-2019
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-019-7127-3

Abstract A method is proposed to measure the photon polarisation parameter $$\lambda _{\gamma }$$ λγ in $${{b}} \!\rightarrow {s} {\gamma } $$ b→sγ transitions using an amplitude analysis of $$B\!\rightarrow K\pi \pi {\gamma } $$ B→Kππγ decays. Simplified models of the $${K} {\pi } {\pi } $$ Kππ system are used to simulate $${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $$ B+→K+π-π+γ and $${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $$ B0→K+π-π0γ decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the $$\lambda _{\gamma }$$ λγ parameter irrespective of the model parameters. Similar sensitivities to $$\lambda _{\gamma }$$ λγ 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 $${{{B} ^+}} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^+} {\gamma } $$ B+→K+π-π+γ decays in an LHCb data set corresponding to an integrated luminosity of 9 $$\,\hbox {fb}^{-1}$$ fb-1 is estimated to be 0.009. A similar measurement using $${{B} ^0} \!\rightarrow {{K} ^+} {{\pi } ^-} {{\pi } ^0} {\gamma } $$ B0→K+π-π0γ decays in a Belle II data sample corresponding to an integrated luminosity of 5 $$\hbox {\,ab}^{-1}$$ ab-1 would lead to a statistical uncertainty of 0.018.