Description

We have measured the relative branching ratio of the $B^{\pm } \rightarrow \phi K^{\pm }$ decay mode to the $B^{\pm} \rightarrow J/\psi K^{\pm}$ one, detecting the $\phi$ in the decay to $KK$ and the $J/\psi$ in $\mu\mu$. We searched for both decay channels in the Two Track Trigger data sample using the CharmMods package. The topology of the two decays is very similar and they can be reconstructed with the same reconstruction code and almost identical cuts. Most of the systematic errors are the same and cancel in the ratio. The residual corrections for the combined trigger, acceptance and analysis efficiency ratios have been extensively studied with Monte Carlo simulations.

We reconstruct all the three-prong vertices, in the hypothesis of three kaons and in the hypothesis of two muons plus one kaon, with a reconstructed invariant mass in the $B$ mass range. Candidates are then selected requiring:

• track level cuts:

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  $\vert\eta\vert \le 1.4$,

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  3 silicon $R$-$\varphi$ hits,

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  25 Axial and 25 Stereo COT hits;

• $\Delta Z \le 5$ cm;
• $\vert d_0^B\vert \le 0.01$ cm;
• $P_{T}^{\:\text{\it soft}} \ge 1.3$ GeV/$c$;
• $\vert d_{0}^{\:\text{\it soft}}\vert \ge 120$ $\mu$m;
• $P_{T}^{B} \ge 4$ GeV/$c$;
• $L_{xy} \ge 350$ $\mu$m;
• $\chi^2_{xy} \le 8$;
• $Isol \ge 0.5$;
• $\vert M_{KK}-1.02\vert\le0.04$ GeV/$c^2$.

The Isolation variable ($Isol$) is defined as the ratio between the sum of the candidate track transverse momenta divided by the sum of the same quantity plus the transverse momenta of all tracks within a cone of radius 1 of the $B$ candidate flight direction. The cut values are determined by maximizing the significance $S/\sqrt{S+B}$, where $S$ is taken from the CDF detector and trigger simulation and $B$ is determined by a $\phi$ sideband sample. In the case of $B^{\pm} \rightarrow J/\psi K^{\pm}$ channel the mass window is $\vert M_{\mu\mu}-3.094\vert\le0.1$ GeV/$c^2$. Moreover, we require a positive muon identification for at least one of the $J/\psi$ legs in order to distinguish $J/\psi \to\mu\mu$ from $J/\psi \to ee$.

The $B^{\pm } \rightarrow \phi K^{\pm }$ yield and charge asymmetry are estimated by means of an extended unbinned maximum likelihood fit on the following discriminating variables:

• three-track invariant mass: $5 \le M_{KKK} \le 5.6$ GeV/$c^2$;
• two-track invariant mass: $1 \le M_{KK} \le 1.06$ GeV/$c^2$;
• $\phi$ helicity, defined in the $\phi$ mass rest frame as the cosine of the angle between the $K^{+}$ outgoing direction and the flight direction of the $B$ meson: $-1 \le \cos\vartheta_{K^+} \le 1$;
• specific ionization $dE/dx$ in the drift chamber.

$B^+$ and $B^-$ samples are fitted simultaneously. The $B^{\pm} \rightarrow J/\psi K^{\pm}$ yield is extracted from a similar fit on:

• three-track invariant mass: $4.8 \le M_{\mu\mu K} \le 5.8$ GeV/$c^2$;
• two-track invariant mass: $\vert M_{\mu\mu}-3.094\vert\le0.1$ GeV/$c^2$.