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A model-dependent amplitude analysis of $B^{\pm} \rightarrow D K^{\pm}$ with$D \rightarrow K_S^0 \pi^+ \pi^-$ decays is performed using proton-protoncollision data, corresponding to an integrated luminosity of $1$ fb$^{-1}$,recorded by LHCb at a centre-of-mass energy of $7$ TeV in $2011$. Values of the$CP$ violation observables $x_{\pm}$ and $y_{\pm}$, which are sensitive to theCKM 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} \pm0.003, \\ x_+ &= -0.084 \pm 0.045 \pm 0.009 \pm 0.005, \\ y_+ &= -0.032 \pm0.048 ^{+0.010}_{-0.009} \pm 0.008, \end{align*} where the first uncertainty isstatistical, the second systematic and the third arises from the uncertainty ofthe $D \rightarrow K_S^0 \pi^+ \pi^-$ amplitude model. The value of $\gamma$ isdetermined to be $(84^{+49}_{-42})^\circ$, including all sources ofuncertainty. Neutral $D$ meson mixing is found to have negligible effect.

nuclear physics b

Measurement of $CP$ violation and constraints on the CKM angle $\gamma$  in $B^{\pm}\rightarrow D K^{\pm}$ with $D \rightarrow K_S^0 \pi^+ \pi^-$  decays