Measurement of Polarization and Search for $CP$ Violation in $B_s^0\to \varphi \varphi$ Decays

We present the first measurement of polarization and $CP$-violating asymmetries in a $B_s^0$ decay into two light vector mesons, $B_s^0\to \varphi \varphi$, and an improved determination of its branching ratio using 295 decays reconstructed in a data sample corresponding to $2.9{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the CDF experiment at the Fermilab Tevatron collider. The fraction of longitudinal polarization is determined to be $f_L=0.348\pm 0.041(\mathrm{stat})\pm 0.021(\mathrm{syst})$, and the branching ratio $\mathcal{B}(B_s^0\to \varphi \varphi )=[2.32\pm 0.18(\mathrm{stat})\pm 0.82(\mathrm{syst})]\times {10}^{-5}$. Asymmetries of decay angle distributions sensitive to $CP$ violation are measured to be $A_u=-0.007\pm 0.064(\mathrm{stat})\pm 0.018(\mathrm{syst})$ and $A_v=-0.120\pm 0.064(\mathrm{stat})\pm 0.016(\mathrm{syst})$.

Figure 1

The invariant mass of the four kaons (left) and of the $J/\psi$ and two kaons (right) for $B_s^0\to \varphi \varphi$ and $B_s^0\to J/\psi \varphi$ candidates, overlayed with fit projections and separate signal and background components. The narrower signal peak for the $B_s^0\to J/\psi \varphi$ is due to the $J/\psi$ mass constraint applied in the reconstruction.

Figure 2

Angular distribution for $B_s^0\to \varphi \varphi$ events with the fit projection, signal, and background component superimposed.