Measurement of $CP$ violation in $B_s^0\to \varphi \varphi$ decays

A measurement of the decay time-dependent $CP$-violating asymmetry in $B_s^0\to \varphi \varphi$ decays is presented, along with measurements of the $T$-odd triple-product asymmetries. In this decay channel, the $CP$-violating weak phase arises from the interference between $B_s^0\text{−}{\overline{B}}_s^0$ mixing and the loop-induced decay amplitude. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ collected with the LHCb detector, a signal yield of approximately 4000 $B_s^0\to \varphi \varphi$ decays is obtained. The $CP$-violating phase is measured to be ${\varphi }_s=-0.17\pm 0.15(\text{stat})\pm 0.03(\text{syst})\mathrm{rad}$. The triple-product asymmetries are measured to be $A_U=-0.003\pm 0.017(\text{stat})\pm 0.006(\text{syst})$ and $A_V=-0.017\pm 0.017(\text{stat})\pm 0.006(\text{syst})$. Results are consistent with the hypothesis of $CP$ conservation.

Figure 1

Four-kaon invariant mass distributions for the (left) 2011 and (right) 2012 data sets. The data points are represented by the black markers. Superimposed are the results of the total fit (red solid line), the $B_s^0\to \varphi \varphi$ (red long dashed), the $B^0\to \varphi K^{*0}$ (blue dotted), the ${\mathrm{\Lambda }}_b^0\to \varphi p{K}^{-}$ (green short-dashed), and the combinatoric (purple dotted) fit components.

Figure 2

Decay angles for the $B_s^0\to \varphi \varphi$ decay, where the $K^{+}$ momentum in the ${\varphi }_{1,2}$ rest frame and the parent ${\varphi }_{1,2}$ momentum in the rest frame of the $B_s^0$ meson span the two $\varphi$ meson decay planes, ${\theta }_{1,2}$ is the angle between the $K^{+}$ track momentum in the ${\varphi }_{1,2}$ meson rest frame and the parent ${\varphi }_{1,2}$ momentum in the $B_s^0$ rest frame, $\mathrm{\Phi }$ is the angle between the two $\varphi$ meson decay planes, and ${\widehat{n}}_{V_{1,2}}$ is the unit vector normal to the decay plane of the ${\varphi }_{1,2}$ meson.

Figure 3

Angular acceptance found from simulated $B_s^0\to \varphi \varphi$ events (top-left) integrated over $\cos {\theta }_2$ and $\mathrm{\Phi }$ as a function of $\cos {\theta }_1$, (top-right) integrated over $\cos {\theta }_1$ and $\mathrm{\Phi }$ as a function of $\cos {\theta }_2$, and (bottom) integrated over $\cos {\theta }_1$ and $\cos {\theta }_2$ as a function of $\mathrm{\Phi }$.

Figure 4

Decay time acceptance (left) calculated using $B_s^0\to D_s^{-}{\pi }^{+}$ data events and (right) comparing $B_s^0\to \varphi \varphi$ and $B_s^0\to D_s^{-}{\pi }^{+}$ simulation, where $B_s^0\to D_s^{-}{\pi }^{+}$ events are reweighted to match the distribution of the minimum $p_{\mathrm{T}}$ of the final-state particles in $B_s^0\to \varphi \varphi$ decays.

Figure 5

One-dimensional projections of the $B_s^0\to \varphi \varphi$ fit for (top-left) decay time with binned acceptance, (top-right) helicity angle $\mathrm{\Phi }$, and (bottom-left and bottom-right) cosine of the helicity angles ${\theta }_1$ and ${\theta }_2$. The background-subtracted data are marked as black points, while the black solid lines represent the projections of the best fit. The $CP$-even $P$-wave, the $CP$-odd $P$-wave, and $S$-wave combined with double $S$-wave components are shown by the red long-dashed, green short-dashed, and blue dotted lines, respectively.

Figure 6

Profile log likelihood for the ${\varphi }_s$ parameter.

Figure 7

Background-subtracted distributions of the (left) $U$ and (right) $V$ observables for the 2011 and 2012 data sets and restricted to the mass range $5246.8<m_{K^{+}{K}^{-}{K}^{+}{K}^{-}}<5486.8\mathrm{MeV}/c^2$. The 2011 distributions are scaled to have the same area as the 2012 distributions.