This Letter presents a study of the flavorchanging neutral current radiative $B^{\pm} \to K^{\pm}\pi^{\mp}\pi^{\pm}\gamma$ decays performed using data collected in protonproton collisions with the LHCb detector at $7$ and $8\,$TeV centerofmass 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 finalstate 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 $5.2\,\sigma$.
Mass distribution of the selected $ B ^+ \!\rightarrow K ^+ \pi ^ \pi ^+ \gamma $ candidates. The blue solid curve shows the fit results as the sum of the following components: signal (red solid), combinatorial background (green dotted), missing pion background (black dashed) and other partially reconstructed backgrounds (purple dashdotted). 
Fig1.pdf [15 KiB] HiDef png [284 KiB] Thumbnail [79 KiB] *.C file 

Backgroundsubtracted $ K ^+\pi ^\pi ^+$ mass distribution of the $ B ^+ \!\rightarrow K ^+ \pi ^ \pi ^+ \gamma $ signal. The four intervals of interest, separated by dashed lines, are shown. 
Fig2.pdf [19 KiB] HiDef png [183 KiB] Thumbnail [80 KiB] *.C file 

Distributions of $\cos\hat{{\theta}}$ for $ B ^+ \!\rightarrow K ^+ \pi ^ \pi ^+ \gamma $ signal in four intervals of $ K ^+\pi ^\pi ^+$ mass. The solid blue (dashed red) curves are the result of fits allowing all (only even) Legendre components up to the fourth power. 
Fig3_a.pdf [10 KiB] HiDef png [154 KiB] Thumbnail [55 KiB] *.C file 

Fig3_b.pdf [10 KiB] HiDef png [153 KiB] Thumbnail [55 KiB] *.C file 

Fig3_c.pdf [10 KiB] HiDef png [163 KiB] Thumbnail [56 KiB] *.C file 

Fig3_d.pdf [10 KiB] HiDef png [151 KiB] Thumbnail [54 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2014001.gif Thumbnail 
Legendre coefficients obtained from fits to the normalized backgroundsubtracted $\cos\hat{{\theta}}$ distribution in the four $ K ^+\pi ^\pi ^+$ mass intervals of interest. The updown asymmetries are obtained from Eq. 4. The quoted uncertainties contain statistical and systematic contributions. The $ K ^+\pi ^\pi ^+$ mass ranges are indicated in $ {\mathrm{\,Ge V\!/}c^2}$ and all the parameters are expressed in units of $10^{2}$. The covariance matrices are given in the supplementary material. 
Table_1.pdf [33 KiB] HiDef png [95 KiB] Thumbnail [17 KiB] tex code 

Legendre coefficients obtained from fits to the normalized backgroundsubtracted $\cos\hat{{\theta}}$ distribution, using the alternative normal $\vec{p}_{\pi ^ }\times\vec{p}_{\pi ^+ }$ for defining the direction of the photon, in the four $ K ^+\pi ^\pi ^+$ mass intervals of interest. The updown asymmetries are obtained from Eq. 4. The quoted uncertainties contain statistical and systematic contributions. The $ K ^+\pi ^\pi ^+$ mass ranges are indicated in $ {\mathrm{\,Ge V\!/}c^2}$ and all the parameters are expressed in units of $10^{2}$. The covariance matrices are given in the supplementary material. 
Table_2.pdf [40 KiB] HiDef png [99 KiB] Thumbnail [18 KiB] tex code 

Covariance matrices (in units of $10^{3}$) for the fitted values of $c_1$, $c_2$, $c_3$ and $c_4$ of Table 1, for the four $ K ^+\pi ^\pi ^+ $ mass intervals. 
Table_3.pdf [41 KiB] HiDef png [18 KiB] Thumbnail [3 KiB] tex code 

Covariance matrices (in units of $10^{3}$) for the fitted values of $c^{\prime}_1$, $c^{\prime}_2$, $c^{\prime}_3$ and $c^{\prime}_4$ of Table 2, for the four $ K ^+\pi ^\pi ^+ $ mass intervals. 
Table_4.pdf [41 KiB] HiDef png [17 KiB] Thumbnail [3 KiB] tex code 
This ZIP file contains supplementary material for the publication LHCbPAPER2014001. The files are: LHCbPAPER2014001supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps *.C : The figures in various formats 
Fig4.pdf [53 KiB] HiDef png [125 KiB] Thumbnail [30 KiB] *C file 

Fig5.pdf [13 KiB] HiDef png [105 KiB] Thumbnail [50 KiB] *C file 

Fig6.pdf [13 KiB] HiDef png [106 KiB] Thumbnail [50 KiB] *C file 

LHCbP[..].pdf [379 KiB] HiDef png [299 KiB] Thumbnail [71 KiB] *C file 
Created on 20 April 2019.Citation count from INSPIRE on 25 April 2019.