Measurement of the CKM angle $\gamma$ in $B^\pm\to D K^\pm$ and $B^\pm \to D \pi^\pm$ decays with $D \to K_\mathrm S^0 h^\pm h^\mp$

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Abstract

A measurement of $C P$ -violating observables is performed using the decays $B ^\pm \rightarrow D K ^\pm$ and $B ^\pm \rightarrow D \pi ^\pm$ , where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K ^0_{\mathrm{S}} \pi ^+ \pi ^-$ and $K ^0_{\mathrm{S}} K ^+ K ^-$ ($h^\pm h^\mp = \pi ^\pm \pi ^\mp , K ^\pm K ^\mp$). The decays are analysed in bins of the $D$ -decay phase space, leading to a measurement that is independent of the modelling of the $D$ -decay amplitude. Using the full Run 1 and 2 LHCb data sample, the observables of interest are measured to be \begin{align*} x_-^{ D K } & = (\phantom{-}5.6 \pm 1.0 \pm 0.2\pm 0.3) \times 10^{-2}, \\ y_-^{ D K } & = (\phantom{-}6.5\pm 1.1 \pm 0.3\pm 0.4) \times 10^{-2}, \\ x_+^{ D K } & = ( - 9.2 \pm 1.0 \pm 0.2\pm 0.2) \times 10^{-2}, \\ y_+^{ D K } & = ( - 1.2 \pm 1.2 \pm 0.3\pm 0.3) \times 10^{-2}, \\ x_\xi^{ D \pi} & = ( - 5.3 \pm 2.0 \pm 0.3\pm 0.2) \times 10^{-2}, \\ y_\xi^{ D \pi} & = (\phantom{-}1.0 \pm 2.3 \pm 0.5\pm 0.3) \times 10^{-2}, \end{align*} where the first uncertainty is statistical, the second arises from systematic effects in the method or other experimental effects, and the third from external inputs of strong-phase measurements from CLEO and BESIII . The measurements can be interpreted in terms of the CKM angle $\gamma$, leading to $\gamma =(69 \pm 5)^\circ$. Measurements of the hadronic parameters $r_ B ^{ D K }$ , $r_ B ^{ D \pi}$ , $\delta_ B ^{ D K }$ , and $\delta_ B ^{ D \pi}$ are also reported.

Figures and captions

 Binning schemes for (left) $D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^-$ decays and (right) $D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^-$ decays. The diagonal line separates the positive and negative bins, where the positive bins are in the region in which $m^2_- > m^2_+$ is satisfied. KsPiPi[..].png [74 KiB] HiDef png [153 KiB] Thumbnail [78 KiB] *.C file KsKK_2bins.png [64 KiB] HiDef png [117 KiB] Thumbnail [56 KiB] *.C file Dalitz plot for $D$ decays of (left) $B ^+ \rightarrow D K ^+$ and (right) $B ^- \rightarrow D K ^-$ candidates in the signal region, in the (top) $D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^-$ and (bottom) $D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^-$ channels. single[..].png [91 KiB] HiDef png [351 KiB] Thumbnail [178 KiB] *.C file single[..].png [90 KiB] HiDef png [359 KiB] Thumbnail [183 KiB] *.C file single[..].png [74 KiB] HiDef png [231 KiB] Thumbnail [106 KiB] *.C file single[..].png [77 KiB] HiDef png [243 KiB] Thumbnail [112 KiB] *.C file Invariant mass distributions for the (left) $B ^\pm \rightarrow D K ^\pm$ channel and (right) $B ^\pm \rightarrow D \pi ^\pm$ channel with $D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^-$ . The top (bottom) plots show data where the $K ^0_{\mathrm{S}}$ type is long (downstream). The particle within square brackets in the legend denotes the particle that has not been reconstructed. pretty[..].pdf [298 KiB] HiDef png [281 KiB] Thumbnail [174 KiB] *.C file pretty[..].pdf [299 KiB] HiDef png [284 KiB] Thumbnail [167 KiB] *.C file Invariant mass distributions for the (left) $B ^\pm \rightarrow D K ^\pm$ channel and (right) $B ^\pm \rightarrow D \pi ^\pm$ channel with $D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^-$ . The top (bottom) plots show data where the $K ^0_{\mathrm{S}}$ type is long (downstream). The particle within square brackets in the legend denotes the particle that has not been reconstructed. pretty[..].pdf [295 KiB] HiDef png [287 KiB] Thumbnail [181 KiB] *.C file pretty[..].pdf [297 KiB] HiDef png [282 KiB] Thumbnail [175 KiB] *.C file Confidence levels at 68.2 % and 95.5 % probability for (left, blue) $( x_+ ^{ D K ^\pm }, y_+ ^{ D K ^\pm })$, (left, red) $( x_- ^{ D K ^\pm }, y_- ^{ D K ^\pm })$, and (right, green) $(x_\xi^{ D \pi ^\pm },y_\xi^{ D \pi ^\pm })$ as measured in $B ^\pm \rightarrow D K ^\pm$ and $B ^\pm \rightarrow D \pi ^\pm$ decays with a profile likelihood scan. The black dots show the central values likeli[..].pdf [211 KiB] HiDef png [202 KiB] Thumbnail [157 KiB] *.C file The bin-by-bin asymmetries $(N^-_{-i}-N^+_{+i})/(N^-_{-i}+N^+_{+i})$ for each Dalitz-plot bin number for (left) $B ^\pm \rightarrow D K ^\pm$ decays and (right) $B ^\pm \rightarrow D \pi ^\pm$ decays. The prediction from the central values of the $C P$ -violation observables is shown with a solid line and the asymmetries obtained in fits with independent bin yields are shown with the error bars. The predicted asymmetries in a fit that does not allow for $C P$ violation are shown with a dotted line. paper_[..].pdf [370 KiB] HiDef png [125 KiB] Thumbnail [99 KiB] *.C file paper_[..].pdf [370 KiB] HiDef png [130 KiB] Thumbnail [104 KiB] *.C file The 68 % and 95 % confidence regions for combinations of the physics parameters $(\gamma , r_ B ^{ D K } , \delta_ B ^{ D K } , r_ B ^{ D \pi} , \delta_ B ^{ D \pi} )$ obtained using the methods described in Ref. [44]. 2d_g_r[..].pdf [14 KiB] HiDef png [331 KiB] Thumbnail [204 KiB] *.C file 2d_d_d[..].pdf [14 KiB] HiDef png [317 KiB] Thumbnail [198 KiB] *.C file 2d_g_r[..].pdf [14 KiB] HiDef png [311 KiB] Thumbnail [187 KiB] *.C file 2d_d_d[..].pdf [14 KiB] HiDef png [351 KiB] Thumbnail [214 KiB] *.C file Animated gif made out of all figures. CONF-2020-001.gif Thumbnail

Tables and captions

 The signal and background yields in the signal region $m_B\in[5249, 5309]\text{ Me V /}c^2$. In the $B ^\pm \rightarrow D K ^\pm$ channels, the yield of the partially reconstructed background includes contributions from the $B ^0_ s$ background and partially reconstructed decays where a pion is misidentified as a kaon. Table_1.pdf [70 KiB] HiDef png [67 KiB] Thumbnail [31 KiB] tex code Overview of all sources of uncertainty on the measurement. Table_2.pdf [74 KiB] HiDef png [132 KiB] Thumbnail [57 KiB] tex code

Created on 06 March 2021.