A modeldependent amplitude analysis of $B^{\pm} \rightarrow D K^{\pm}$ with $D \rightarrow K_S^0 \pi^+ \pi^$ decays is performed using protonproton collision data, corresponding to an integrated luminosity of $1$ fb$^{1}$, recorded by LHCb at a centreofmass energy of $7$ TeV in $2011$. Values of the $CP$ violation observables $x_{\pm}$ and $y_{\pm}$, which are sensitive to the CKM angle $\gamma$, are measured to be \begin{align*} x_ &= +0.027 \pm 0.044 ^{+0.010}_{0.008} \pm 0.001, \\ y_ &= +0.013 \pm 0.048 ^{+0.009}_{0.007} \pm 0.003, \\ x_+ &= 0.084 \pm 0.045 \pm 0.009 \pm 0.005, \\ y_+ &= 0.032 \pm 0.048 ^{+0.010}_{0.009} \pm 0.008, \end{align*} where the first uncertainty is statistical, the second systematic and the third arises from the uncertainty of the $D \rightarrow K_S^0 \pi^+ \pi^$ amplitude model. The value of $\gamma$ is determined to be $(84^{+49}_{42})^\circ$, including all sources of uncertainty. Neutral $D$ meson mixing is found to have negligible effect.
Invariant mass distributions for (a) $ B ^\pm \rightarrow D (\rightarrow K ^0_{\rm\scriptscriptstyle S} \pi ^+ \pi ^ ) K ^\pm $ {\it long}, (b) $ B ^\pm \rightarrow D (\rightarrow K ^0_{\rm\scriptscriptstyle S} \pi ^+ \pi ^ ) \pi ^\pm $ {\it long}, (c) $ B ^\pm \rightarrow D (\rightarrow K ^0_{\rm\scriptscriptstyle S} \pi ^+ \pi ^ ) K ^\pm $ {\it downstream} and (d) $ B ^\pm \rightarrow D (\rightarrow K ^0_{\rm\scriptscriptstyle S} \pi ^+ \pi ^ ) \pi ^\pm $ {\it downstream} candidates. The fit results, including signal and background components, are superimposed. The lower plots are normalised residual distributions. 
Fig1a.pdf [44 KiB] HiDef png [469 KiB] Thumbnail [133 KiB] *.C file 

Fig1b.pdf [44 KiB] HiDef png [490 KiB] Thumbnail [128 KiB] *.C file 

Fig1c.pdf [44 KiB] HiDef png [491 KiB] Thumbnail [136 KiB] *.C file 

Fig1d.pdf [44 KiB] HiDef png [498 KiB] Thumbnail [130 KiB] *.C file 

Dalitz plot and its projections, with fit result superimposed, for $B^ \rightarrow D \pi^$ candidates; $m_{\pm}^2 \equiv m_{ K ^0_{\rm\scriptscriptstyle S} \pi ^\pm }^2$ and $m_{0}^2 \equiv m_{\pi ^+ \pi ^ }^2$. The lower parts of the figures are normalised residual distributions. 
Fig2a.pdf [173 KiB] HiDef png [383 KiB] Thumbnail [149 KiB] *.C file 

Fig2b.pdf [26 KiB] HiDef png [231 KiB] Thumbnail [78 KiB] *.C file 

Fig2c.pdf [29 KiB] HiDef png [278 KiB] Thumbnail [93 KiB] *.C file 

Fig2d.pdf [30 KiB] HiDef png [288 KiB] Thumbnail [96 KiB] *.C file 

Dalitz plot and its projections, with fit result superimposed, for $B^+ \rightarrow D \pi^+$ candidates; $m_{\pm}^2 \equiv m_{ K ^0_{\rm\scriptscriptstyle S} \pi ^\pm }^2$ and $m_{0}^2 \equiv m_{\pi ^+ \pi ^ }^2$. The lower parts of the figures are normalised residual distributions. 
Fig3a.pdf [177 KiB] HiDef png [384 KiB] Thumbnail [148 KiB] *.C file 

Fig3b.pdf [30 KiB] HiDef png [278 KiB] Thumbnail [94 KiB] *.C file 

Fig3c.pdf [27 KiB] HiDef png [231 KiB] Thumbnail [78 KiB] *.C file 

Fig3d.pdf [30 KiB] HiDef png [292 KiB] Thumbnail [97 KiB] *.C file 

Dalitz plot and its projections, with fit result superimposed, for $B^ \rightarrow D K^$ candidates; $m_{\pm}^2 \equiv m_{ K ^0_{\rm\scriptscriptstyle S} \pi ^\pm }^2$ and $m_{0}^2 \equiv m_{\pi ^+ \pi ^ }^2$. The lower parts of the figures are normalised residual distributions. 
Fig4a.pdf [52 KiB] HiDef png [203 KiB] Thumbnail [89 KiB] *.C file 

Fig4b.pdf [28 KiB] HiDef png [244 KiB] Thumbnail [81 KiB] *.C file 

Fig4c.pdf [29 KiB] HiDef png [275 KiB] Thumbnail [101 KiB] *.C file 

Fig4d.pdf [29 KiB] HiDef png [293 KiB] Thumbnail [104 KiB] *.C file 

Dalitz plot and its projections, with fit result superimposed, for $B^+ \rightarrow D K^+$ candidates; $m_{\pm}^2 \equiv m_{ K ^0_{\rm\scriptscriptstyle S} \pi ^\pm }^2$ and $m_{0}^2 \equiv m_{\pi ^+ \pi ^ }^2$. The lower parts of the figures are normalised residual distributions. 
Fig5a.pdf [52 KiB] HiDef png [198 KiB] Thumbnail [87 KiB] *.C file 

Fig5b.pdf [29 KiB] HiDef png [278 KiB] Thumbnail [101 KiB] *.C file 

Fig5c.pdf [28 KiB] HiDef png [236 KiB] Thumbnail [81 KiB] *.C file 

Fig5d.pdf [29 KiB] HiDef png [285 KiB] Thumbnail [104 KiB] *.C file 

Likelihood contours at 39.35%, 86.47%, 98.89% and 99.97% confidence level for $(x_{+},y_{+})$ (blue) and $(x_{},y_{})$ (red). 
Fig6.pdf [19 KiB] HiDef png [316 KiB] Thumbnail [80 KiB] *.C file 

Projections of the pvalue regions onto the $(\gamma, \delta_{ B })$ and $(\gamma, r_{ B })$ planes with all sources of uncertainty taken into account. 
Fig7a.pdf [1 MiB] HiDef png [1 MiB] Thumbnail [135 KiB] *.C file 

Fig7b.pdf [223 KiB] HiDef png [526 KiB] Thumbnail [127 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2014017.gif Thumbnail 
Signal and background yields for components contributing to the $ C\!P$ asymmetry fit, in the region $\pm 50 {\mathrm{\,Me V\!/}c^2} $ around the known $ B ^\pm$ meson mass. 
Table_1.pdf [64 KiB] HiDef png [111 KiB] Thumbnail [17 KiB] tex code 

Absolute values of systematic uncertainties. The $ C\!P$ asymmetry fit bias is considered as a onesided uncertainty and is included in the quadrature sum on that side only. 
Table_2.pdf [65 KiB] HiDef png [110 KiB] Thumbnail [16 KiB] tex code 

Model related systematic uncertainties for each alternative model. The relative signs indicate full correlation or anticorrelation. 
Table_3.pdf [52 KiB] HiDef png [150 KiB] Thumbnail [23 KiB] tex code 
Supplementary material full pdf 
supple[..].pdf [1 MiB] 

This ZIP file contains supplementary material for the publication LHCbPAPER2014017. The files are: Supplementary.pdf : An overview of the extra figures (colour versions of Figure 7 of the paper) *.pdf, *.png, *.eps, *.C : The figures in various formats 
Fig1_g[..].pdf [1 MiB] HiDef png [2 MiB] Thumbnail [186 KiB] *C file 

Fig1_g[..].pdf [217 KiB] HiDef png [1 MiB] Thumbnail [188 KiB] *C file 
Created on 19 April 2019.Citation count from INSPIRE on 19 April 2019.