Measurement of $CP$ asymmetries in two-body $B_{(s)}^0$-meson decays to charged pions and kaons

The time-dependent $CP$ asymmetries in $B^0\to {\pi }^{+}{\pi }^{-}$ and $B_s^0\to K^{+}{K}^{-}$ decays are measured using a data sample of $p$ $p$ collisions corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The same data sample is used to measure the time-integrated $CP$ asymmetries in $B^0\to K^{+}{\pi }^{-}$ and $B_s^0\to {\pi }^{+}{K}^{-}$ decays. The results are $C_{{\pi }^{+}{\pi }^{-}}=-0.34\pm 0.06\pm 0.01$, $S_{{\pi }^{+}{\pi }^{-}}=-0.63\pm 0.05\pm 0.01$, $C_{K^{+}{K}^{-}}=0.20\pm 0.06\pm 0.02$, $S_{K^{+}{K}^{-}}=0.18\pm 0.06\pm 0.02$, $A_{K^{+}{K}^{-}}^{\mathrm{\Delta }\mathrm{\Gamma }}=-0.79\pm 0.07\pm 0.10$, $A_{CP}^{B^0}=-0.084\pm 0.004\pm 0.003$, and $A_{CP}^{B_s^0}=0.213\pm 0.015\pm 0.007$, where the first uncertainties are statistical and the second systematic. Evidence for $CP$ violation is found in the $B_s^0\to K^{+}{K}^{-}$ decay for the first time.

Figure 1

Efficiencies as a function of decay time for (top left) $B^0\to K^{+}{\pi }^{-}$, (top right) $B_s^0\to {\pi }^{+}{K}^{-}$, (bottom left) $B^0\to {\pi }^{+}{\pi }^{-}$ and, (bottom right) $B_s^0\to K^{+}{K}^{-}$ decays. The black line is the result of the best fit of Eq. (13) to the histograms, obtained as described in the text. The dark and bright areas correspond to the 68% and 95% confidence intervals, respectively.

Figure 2

The triangles represent the standard deviation of the difference between the reconstructed ($t$) and true decay ($t_{\mathrm{true}}$) time versus ${\delta }_t$ for simulated (left) $B_s^0\to {\pi }^{+}{K}^{-}$ and (right) $B_s^0\to D_s^{-}{\pi }^{+}$ decays. The dotted lines are the results of linear-function fits. The histograms represent the corresponding ${\delta }_t$ distributions with arbitrary normalizations.

Figure 3

Time-dependent asymmetries of (left) $B^0\to D^{-}{\pi }^{+}$ and (right) $B_s^0\to D_s^{-}{\pi }^{+}$ decays obtained from data. The results of the best fits are superimposed. The time-dependent asymmetry of the $B_s^0\to D_s^{-}{\pi }^{+}$ decays is folded into one mixing period $2\pi /\mathrm{\Delta }{m}_s$ of the $B_s^0$ meson. The parameter $t_0=0.3\mathrm{ps}$ corresponds to the minimum value allowed by the selection.

Figure 4

Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) ${\eta }_{\mathrm{OS}}$, and (bottom) ${\eta }_{\text{SSc}}$ for candidates in the $K^{\pm }$ ${\pi }^{\mp }$ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

Figure 5

Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) ${\eta }_{\mathrm{OS}}$, and (bottom) ${\eta }_{\text{SSc}}$ for candidates in the ${\pi }^{+}$ ${\pi }^{-}$ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

Figure 6

Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) ${\eta }_{\mathrm{OS}}$, and (bottom) ${\eta }_{\mathrm{SS}K}$ for candidates in the $K^{+}{K}^{-}$ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

Figure 7

Time-dependent asymmetries for $K^{\pm }$ ${\pi }^{\mp }$ candidates with invariant-mass values in the interval $5.20<m<5.32\mathrm{GeV}/c^2$: (left) using the OS-tagging decision and (right) the SS-tagging decision. The result of the simultaneous fit is overlaid.

Figure 8

Time-dependent asymmetries for (top) ${\pi }^{+}$ ${\pi }^{-}$ and (bottom) $K^{+}{K}^{-}$ candidates with mass values in the intervals $5.20<m<5.35\mathrm{GeV}/c^2$ and $5.30<m<5.44\mathrm{GeV}/c^2$, respectively: (left) using the OS-tagging decision and (right) using either the SSc-tagging decision (for the ${\pi }^{+}$ ${\pi }^{-}$ candidates) or the $\mathrm{SS}K$-tagging decision (for the $K^{+}{K}^{-}$ candidates). The result of the simultaneous fit is overlaid.

Figure 9

Relation between ${\omega }_{\mathrm{tag}}$ on ${\eta }_{\mathrm{tag}}$ for (top left) $\mathrm{SS}\pi$, (top right) $\mathrm{SS}p$, (bottom left) SSc, and (bottom right) $\mathrm{SS}K$ taggers. The black dots represent the average value of ${\omega }_{\mathrm{tag}}$ in bins of ${\eta }_{\mathrm{tag}}$, as described in the text. The black straight line represents the linear relation between ${\omega }_{\mathrm{tag}}$ and ${\eta }_{\mathrm{tag}}$ obtained from the calibration procedure. The darker and brighter areas are the corresponding 68% and 95% confidence intervals, respectively. The distributions of ${\eta }_{\mathrm{tag}}$ are also reported as histograms with arbitrary normalizations.