Measurement of branching fraction and search for $CP$ violation in $B\to \varphi \varphi K$

We report the measurement of branching fractions and $CP$-violation asymmetries in $B\to \varphi \varphi K$ decays based on a $711{\mathrm{fb}}^{-1}$ data sample containing $772\times {10}^{6}B\overline{B}$ events. The data were recorded at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. For $B^{+}\to \varphi \varphi K^{+}$, the branching fraction and $CP$-violation asymmetry measured below the ${\eta }_c$ threshold ($m_{\varphi \varphi }<2.85\mathrm{GeV}/c^2$) are $[3.43_{-0.46}^{+0.48}(\mathrm{stat})\pm 0.22(\mathrm{syst})]\times {10}^{-6}$ and $-0.02\pm 0.11(\mathrm{stat})\pm 0.01(\mathrm{syst})$, respectively. Similarly, the branching fraction obtained for $B^0\to \varphi \varphi K^0$ below the ${\eta }_c$ threshold is $[3.02_{-0.66}^{+0.75}(\mathrm{stat})\pm 0.20(\mathrm{syst})]\times {10}^{-6}$. We also measure the $CP$-violation asymmetry for $B^{+}\to \varphi \varphi K^{+}$ within the ${\eta }_c$ region ($m_{\varphi \varphi }\in [2.94,3.02]\mathrm{GeV}/c^2$) to be $+0.12\pm 0.12(\mathrm{stat})\pm 0.01(\mathrm{syst})$.

Figure 1

Dominant Feynman diagrams that contribute to the decays (left) $B^{+}\to \varphi \varphi K^{+}$ and (right) $B^{+}\to {\eta }_c{K}^{+}$. Replacement of the spectator $u$ quark with a $d$ quark will lead to the corresponding diagrams for $B^0\to \varphi \varphi K^0$ and $B^0\to {\eta }_c{K}^0$.

Figure 2

Projections of $B^{\pm }\to \varphi \varphi K^{\pm }$ candidate events onto (top) $M_{\mathrm{bc}}$, (middle) $\mathrm{\Delta }E$, and (bottom) $O_{\mathrm{NN}}^{\prime }$. Black points with error bars are the data, solid blue curves are the total PDF, dashed green curves are the signal component, and dotted red curves are the combined $q\overline{q}$ and $B\overline{B}$ background components.

Figure 3

Projections of $B^0\to \varphi \varphi K^0$ candidate events onto (top left) $M_{\mathrm{bc}}$, (top right) $\mathrm{\Delta }E$, and (bottom) $O_{\mathrm{NN}}^{\prime }$. The legends of the plots are defined in the same manner as in Fig. 2.

Figure 4

Projections of $B^{\pm }\to \varphi \varphi K^{\pm }$ candidate events within the ${\eta }_c$ region onto (top) $M_{\mathrm{bc}}$ and (bottom) $\mathrm{\Delta }E$. The legends of the plots are defined in the same manner as in Fig. 2.

Figure 5

Distribution of data events in the $M_{K_1{K}_2}$ vs $M_{K_3{K}_4}$ plane which shows the $M_{KK}$ signal region (region 1) and two sidebands SB1 (region 2 and 3) and SB2 (region 4).

Figure 6

Background-subtracted signal yield as a function of $m_{\varphi \varphi }$ (left) and $m_{{\varphi }_{1}K}$ (right) for $B^{\pm }\to \varphi \varphi K^{\pm }$. Black points with error bars are data and solid blue histograms denote the expectation from a phase-space MC sample.