# Measurement of $CP$ asymmetry in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays

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## Abstract

We report the measurements of the $CP$-violating parameters in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays observed in $pp$ collisions, using a data set corresponding to an integrated luminosity of $3.0 \text{fb}^{-1}$ recorded with the LHCb detector. We measure $C_f = 0.73 \pm 0.14 \pm 0.05$, $A^{\Delta \Gamma}_f = 0.39 \pm 0.28 \pm 0.15$, $A^{\Delta \Gamma}_{\overline{f}} = 0.31 \pm 0.28 \pm 0.15$, $S_f = -0.52 \pm 0.20 \pm 0.07$, $S_{\overline{f}} = -0.49 \pm 0.20 \pm 0.07$, where the uncertainties are statistical and systematic, respectively. These parameters are used together with the world-average value of the $B_s^0$ mixing phase, $-2\beta_s$, to obtain a measurement of the CKM angle $\gamma$ from $B_s^0 \to D_s^{\mp} K^{\pm}$ decays, yielding $\gamma = (128 _{-22}^{+17})^\circ$ modulo $180^\circ$, where the uncertainty contains both statistical and systematic contributions. This corresponds to $3.8 \sigma$ evidence for $CP$ violation in the interference between decay and decay after mixing.

## Figures and captions

 Feynman diagrams for $\overline{ B }{} {}^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^+ K^-$ decays (left) without and (right) with $B ^0_ s$ -- $\overline{ B }{} {}^0_ s$ mixing. Fig1a.pdf [57 KiB] HiDef png [33 KiB] Thumbnail [20 KiB] *.C file Fig1b.pdf [59 KiB] HiDef png [54 KiB] Thumbnail [33 KiB] *.C file Distributions of the (upper left) $B ^0_ s$ and (upper right) $D ^-_ s$ invariant masses for $B ^0_ s \rightarrow D ^-_ s \pi ^+$ final states, and (bottom) of the logarithm of the companion track PID log-likelihood, $\ln(L(\pi/K))$. In each plot, the contributions from all $D ^-_ s$ final states are combined. The solid blue curve is the total result of the simultaneous fit. The dotted red curve shows the $B ^0_ s \rightarrow D ^-_ s \pi ^+$ signal and the fully coloured stacked histograms show the different background contributions. Normalised residuals are shown underneath all distributions. Fig2a.pdf [58 KiB] HiDef png [404 KiB] Thumbnail [332 KiB] *.C file Fig2b.pdf [56 KiB] HiDef png [357 KiB] Thumbnail [276 KiB] *.C file Fig2c.pdf [56 KiB] HiDef png [334 KiB] Thumbnail [253 KiB] *.C file Distributions of the (upper left) $B ^0_ s$ and (upper right) $D ^-_ s$ invariant masses for $B ^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^\mp K^\pm$ final states, and (bottom) of the logarithm of the companion track PID log-likelihood, $\ln(L(K/\pi))$. In each plot, the contributions from all $D ^-_ s$ final states are combined. The solid blue curve is the total result of the simultaneous fit. The dotted red curve shows the $B ^0_ s \rightarrow D ^-_ s \pi ^+$ signal and the fully coloured stacked histograms show the different background contributions. Normalised residuals are shown underneath all distributions. Fig3a.pdf [46 KiB] HiDef png [407 KiB] Thumbnail [338 KiB] *.C file Fig3b.pdf [44 KiB] HiDef png [350 KiB] Thumbnail [264 KiB] *.C file Fig3c.pdf [43 KiB] HiDef png [323 KiB] Thumbnail [268 KiB] *.C file Data points show the measured resolution $\sigma$ as a function of the per-candidate uncertainty $\sigma_t$ for prompt $D_s^{\mp}$ candidates combined with a random track. The dashed lines indicate the values used to determine the systematic uncertainties on this method. The solid line shows the linear fit to the data as discussed in the text. The histogram overlaid is the distribution of the per-candidate decay-time uncertainty for $B ^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^\mp K^\pm$ candidates. Fig4.pdf [17 KiB] HiDef png [168 KiB] Thumbnail [150 KiB] *.C file Decay time distribution of $B ^0_ s \rightarrow D ^-_ s \pi ^+$ candidates obtained by the sPlot technique. The solid blue curve is the result of the \it sFit procedure and the dashed red curve shows the measured decay-time acceptance in arbitrary units. Normalised residuals are shown underneath. Fig5.pdf [40 KiB] HiDef png [268 KiB] Thumbnail [254 KiB] *.C file The (top) decay-time distribution of $B ^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^\mp K^\pm$ candidates obtained by the sPlot technique. The solid blue curve is the result of the \it sFit procedure and the dashed red curve shows the decay-time acceptance in arbitrary units, obtained from the \it sFit procedure applied to the $B ^0_ s \rightarrow D ^-_ s \pi ^+$ candidates and corrected for the ratio of decay-time acceptances of $B ^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^\mp K^\pm$ and $B ^0_ s \rightarrow D ^-_ s \pi ^+$ from simulation. Normalised residuals are shown underneath. The $C P$ -asymmetry plots for (bottom left) the $D ^+_ s K^-$ final state and (bottom right) the $D ^-_ s K^+$ final state, folded into one mixing period $2\pi/\Delta m_s$, are also shown. Fig6a.pdf [34 KiB] HiDef png [269 KiB] Thumbnail [256 KiB] *.C file Fig6b.pdf [17 KiB] HiDef png [116 KiB] Thumbnail [105 KiB] *.C file Profile likelihood contours of (top left) $r_{ D_{\hspace{-0.0625em}s} \hspace{-0.0625em} K }$ vs. $\gamma$ , and (top right) $\delta$ vs. $\gamma$ . The markers denote the best-fit values. The contours correspond to 68.3% CL (95.5% CL). The graph on the bottom left shows $1-{\rm CL}$ for the angle $\gamma$ , together with the central value and the 68.3% CL interval as obtained from the frequentist method described in the text. The bottom right plot shows a visualisation of how each of the amplitude coefficients contributes towards the overall constraint on the weak phase, $\gamma - 2\beta_s$ . The difference between the phase of $(- {A_{ f }^{\Delta\Gamma}} , S_{ f } )$ and $(- {A_{\overline{ f } }^{\Delta\Gamma}} , S_{\overline{ f } } )$ is proportional to the strong phase $\delta$, which is close to $360^\circ$ and thus not indicated in the figure. Fig7a.pdf [14 KiB] HiDef png [387 KiB] Thumbnail [245 KiB] *.C file Fig7b.pdf [14 KiB] HiDef png [315 KiB] Thumbnail [202 KiB] *.C file Fig7c.pdf [14 KiB] HiDef png [169 KiB] Thumbnail [130 KiB] *.C file Fig7d.pdf [27 KiB] HiDef png [369 KiB] Thumbnail [221 KiB] *.C file Animated gif made out of all figures. PAPER-2017-047.gif Thumbnail

## Tables and captions

 Calibration parameters and tagging asymmetries of the OS and SS taggers obtained from $B ^0_ s \rightarrow D ^-_ s \pi ^+$ decays. The first uncertainty is statistical and the second is systematic. Table_1.pdf [36 KiB] HiDef png [56 KiB] Thumbnail [28 KiB] tex code Performances of the flavour tagging for $B ^0_ s \rightarrow D ^-_ s \pi ^+$ candidates tagged by OS only, SS only and both OS and SS algorithms. Table_2.pdf [52 KiB] HiDef png [79 KiB] Thumbnail [40 KiB] tex code Values of the $C P$ -violation parameters obtained from the fit to the decay-time distribution of $B ^0_ s \rightarrow D_{\hspace{-0.0625em}s} ^\mp K^\pm$ decays. The first uncertainty is statistical and the second is systematic. Table_3.pdf [42 KiB] HiDef png [108 KiB] Thumbnail [51 KiB] tex code Statistical correlation matrix of the $C P$ parameters. Other fit parameters have negligible correlations with the $C P$ parameters. Table_4.pdf [42 KiB] HiDef png [50 KiB] Thumbnail [24 KiB] tex code Systematic uncertainties on the $C P$ parameters, relative to the statistical uncertainties. Table_5.pdf [40 KiB] HiDef png [120 KiB] Thumbnail [57 KiB] tex code Correlation matrix of the total systematic uncertainties of the $C P$ parameters. Table_6.pdf [41 KiB] HiDef png [49 KiB] Thumbnail [24 KiB] tex code

Created on 16 August 2019.Citation count from INSPIRE on 20 August 2019.