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This Letter presents a study of the flavor-changing neutral current radiative $B^{\pm} \to K^{\pm}\pi^{\mp}\pi^{\pm}\gamma$ decays performed using data collected in proton-proton collisions with the LHCb detector at $7$ and $8\,$TeV center-of-mass energies.
- In this sample, corresponding to an integrated luminosity of $3\,\text{fb}^{-1}$, nearly $14\,000$ signal events are reconstructed and selected, containing all possible intermediate resonances with a $K^{\pm}\pi^{\mp}\pi^{\pm}$ final state in the $[1.1, 1.9]\,$GeV/$c^{2}$ mass range.
- The distribution of the angle of the photon direction with respect to the plane defined by the final-state hadrons in their rest frame is studied in intervals of $K^{\pm}\pi^{\mp}\pi^{\pm}$ mass and the asymmetry between the number of signal events found on each side of the plane is obtained.
- The first direct observation of the photon polarization in the $b \to s\gamma$ transition is reported with a significance of $5.2\,\sigma$.
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