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

TL;DR

This paper measures $CP$ violation in $B^{ m ext{±}} ightarrow D K^{ m ext{±}}$ decays to constrain the CKM angle $oldsymbol{oldsymbol{ extit{ extgamma}}}$, using amplitude analysis of $D ightarrow K_S^0 \pi^+\pi^-$ decays with proton-proton collision data.

Contribution

It provides the first measurement of $CP$ violation observables and the CKM angle $ extit{ extgamma}$ using a model-dependent amplitude analysis with LHCb data.

Findings

Measured $x_{ m ext{±}}$, $y_{ m ext{±}}$ with uncertainties

Determined $ extit{ extgamma} = (84^{+49}_{-42})^ ext{o}$

Found negligible effect of $D$ meson mixing

Abstract

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-proton collision 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 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.