cern.ch

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

[to restricted-access page]

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.

Figures and captions

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 [387 KiB]
Thumbnail [121 KiB]
*.C file
Fig1a.pdf
Fig1b.pdf [44 KiB]
HiDef png [391 KiB]
Thumbnail [112 KiB] *.C file
Fig1b.pdf
Fig1c.pdf [44 KiB]
HiDef png [399 KiB]
Thumbnail [121 KiB] *.C file
Fig1c.pdf
Fig1d.pdf [44 KiB]
HiDef png [398 KiB]
Thumbnail [113 KiB] *.C file
Fig1d.pdf

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 [308 KiB]
Thumbnail [64 KiB]
*.C file
Fig2a.pdf
Fig2b.pdf [26 KiB]
HiDef png [221 KiB]
Thumbnail [76 KiB] *.C file
Fig2b.pdf
Fig2c.pdf [29 KiB]
HiDef png [260 KiB]
Thumbnail [90 KiB] *.C file
Fig2c.pdf
Fig2d.pdf [30 KiB]
HiDef png [268 KiB]
Thumbnail [95 KiB] *.C file
Fig2d.pdf

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 [308 KiB]
Thumbnail [63 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [30 KiB]
HiDef png [261 KiB]
Thumbnail [92 KiB] *.C file
Fig3b.pdf
Fig3c.pdf [27 KiB]
HiDef png [222 KiB]
Thumbnail [77 KiB] *.C file
Fig3c.pdf
Fig3d.pdf [30 KiB]
HiDef png [271 KiB]
Thumbnail [96 KiB] *.C file
Fig3d.pdf

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 [158 KiB]
Thumbnail [38 KiB]
*.C file
Fig4a.pdf
Fig4b.pdf [28 KiB]
HiDef png [233 KiB]
Thumbnail [80 KiB] *.C file
Fig4b.pdf
Fig4c.pdf [29 KiB]
HiDef png [259 KiB]
Thumbnail [99 KiB] *.C file
Fig4c.pdf
Fig4d.pdf [29 KiB]
HiDef png [275 KiB]
Thumbnail [101 KiB] *.C file
Fig4d.pdf

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 [154 KiB]
Thumbnail [37 KiB]
*.C file
Fig5a.pdf
Fig5b.pdf [29 KiB]
HiDef png [261 KiB]
Thumbnail [100 KiB] *.C file
Fig5b.pdf
Fig5c.pdf [28 KiB]
HiDef png [227 KiB]
Thumbnail [79 KiB] *.C file
Fig5c.pdf
Fig5d.pdf [29 KiB]
HiDef png [269 KiB]
Thumbnail [102 KiB] *.C file
Fig5d.pdf

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 [272 KiB]
Thumbnail [78 KiB]
*.C file
Fig6.pdf

Projections of the p-value 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 [903 KiB]
Thumbnail [76 KiB]
*.C file
Fig7a.pdf
Fig7b.pdf [223 KiB]
HiDef png [408 KiB]
Thumbnail [67 KiB] *.C file
Fig7b.pdf

Animated gif made out of all figures.

PAPER-2014-017.gif
Thumbnail
thumbnail_PAPER-2014-017.gif

Tables and captions

Signal and background yields for components contributing to the $ C\!P$ asymmetry fit, in the region $\pm 50 {\mathrm{\,MeV\!/}c^2} $ around the known $ B ^\pm$ meson mass.

Table_1.pdf [64 KiB]
HiDef png [86 KiB]
Thumbnail [13 KiB]
tex code
Table_1.pdf

Absolute values of systematic uncertainties. The $ C\!P$ asymmetry fit bias is considered as a one-sided uncertainty and is included in the quadrature sum on that side only.

Table_2.pdf [65 KiB]
HiDef png [87 KiB]
Thumbnail [12 KiB]
tex code
Table_2.pdf

Model related systematic uncertainties for each alternative model. The relative signs indicate full correlation or anti-correlation.

Table_3.pdf [52 KiB]
HiDef png [116 KiB]
Thumbnail [18 KiB]
tex code
Table_3.pdf

Supplementary Material [file]

Supplementary material full pdf

supple[..].pdf [1 MiB]
supplementary.pdf

This ZIP file contains supplementary material for the publication LHCb-PAPER-2014-017. 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 [199 KiB]
*C file
Fig1_gamma_deltaB.pdf
Fig1_g[..].pdf [217 KiB]
HiDef png [1 MiB]
Thumbnail [192 KiB]
*C file
Fig1_gamma_rB.pdf

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.