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.
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"title": "Using an amplitude analysis to measure the photon polarisation in $$B \\rightarrow K\\pi \\pi \\gamma $$ <math><mrow><mi>B</mi><mo>\u2192</mo><mi>K</mi><mi>\u03c0</mi><mi>\u03c0</mi><mi>\u03b3</mi></mrow></math> decays"
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"value": "A method is proposed to measure the photon polarisation parameter $$\\lambda _{\\gamma }$$ <math><msub><mi>\u03bb</mi><mi>\u03b3</mi></msub></math> in $${{b}} \\!\\rightarrow {s} {\\gamma } $$ <math><mrow><mi>b</mi><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><mi>s</mi><mi>\u03b3</mi></mrow></math> transitions using an amplitude analysis of $$B\\!\\rightarrow K\\pi \\pi {\\gamma } $$ <math><mrow><mi>B</mi><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><mi>K</mi><mi>\u03c0</mi><mi>\u03c0</mi><mi>\u03b3</mi></mrow></math> decays. Simplified models of the $${K} {\\pi } {\\pi } $$ <math><mrow><mi>K</mi><mi>\u03c0</mi><mi>\u03c0</mi></mrow></math> system are used to simulate $${{{B} ^+}} \\!\\rightarrow {{K} ^+} {{\\pi } ^-} {{\\pi } ^+} {\\gamma } $$ <math><mrow><msup><mrow><mi>B</mi></mrow><mo>+</mo></msup><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><msup><mrow><mi>K</mi></mrow><mo>+</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>-</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>+</mo></msup><mi>\u03b3</mi></mrow></math> and $${{B} ^0} \\!\\rightarrow {{K} ^+} {{\\pi } ^-} {{\\pi } ^0} {\\gamma } $$ <math><mrow><msup><mrow><mi>B</mi></mrow><mn>0</mn></msup><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><msup><mrow><mi>K</mi></mrow><mo>+</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>-</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mn>0</mn></msup><mi>\u03b3</mi></mrow></math> decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the $$\\lambda _{\\gamma }$$ <math><msub><mi>\u03bb</mi><mi>\u03b3</mi></msub></math> parameter irrespective of the model parameters. Similar sensitivities to $$\\lambda _{\\gamma }$$ <math><msub><mi>\u03bb</mi><mi>\u03b3</mi></msub></math> 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 $${{{B} ^+}} \\!\\rightarrow {{K} ^+} {{\\pi } ^-} {{\\pi } ^+} {\\gamma } $$ <math><mrow><msup><mrow><mi>B</mi></mrow><mo>+</mo></msup><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><msup><mrow><mi>K</mi></mrow><mo>+</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>-</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>+</mo></msup><mi>\u03b3</mi></mrow></math> decays in an LHCb data set corresponding to an integrated luminosity of 9 $$\\,\\hbox {fb}^{-1}$$ <math><mrow><mspace width=\"0.166667em\"></mspace><msup><mtext>fb</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> is estimated to be 0.009. A similar measurement using $${{B} ^0} \\!\\rightarrow {{K} ^+} {{\\pi } ^-} {{\\pi } ^0} {\\gamma } $$ <math><mrow><msup><mrow><mi>B</mi></mrow><mn>0</mn></msup><mspace width=\"-0.166667em\"></mspace><mo>\u2192</mo><msup><mrow><mi>K</mi></mrow><mo>+</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mo>-</mo></msup><msup><mrow><mi>\u03c0</mi></mrow><mn>0</mn></msup><mi>\u03b3</mi></mrow></math> decays in a Belle II data sample corresponding to an integrated luminosity of 5 $$\\hbox {\\,ab}^{-1}$$ <math><mrow><mspace width=\"0.166667em\"></mspace><msup><mtext>ab</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> would lead to a statistical uncertainty of 0.018."
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