Introduction

This work is the first attempt to study charmless $B\rightarrow VV$ decays in CDF. In this report we measure the decay rate of $B_s \rightarrow \phi \phi$ with $\approx$ 180 $\rm pb^{-1}$ of data collected with the displaced track trigger. We have also studied two $b\rightarrow c\bar{c}s$ mediated decays: $B_d \rightarrow J/\psi K^{\ast 0}$ and $B_s \rightarrow J/\psi \phi$. The former offers a significantly high rate and allow us to check the available Monte Carlo simulation used for the determination of the acceptance corrections and in the cuts optimization procedure, the latter is instead our normalization mode, chosen to be the most topologically similar decay among those of the $B_s$ meson. This allows us to extract the BR( $B_s \rightarrow \phi \phi$) without any uncertainty due to the $B_s$ to $B_d$ production cross section.

The decay under study is mediated by the reaction $b\rightarrow s\bar{s}s$ which is involved also in two puzzling results coming from recent B factory data: namely the hint for a contribution other than the usual $B_{d}$ mixing induced phase in the time dependent CP violation of $B_d\rightarrow \phi K_s$ events, and the longitudinal polarization in $B\rightarrow \phi K^\ast$ that is less than the expected value. With CDF data we can study similar decays of $B_s$ mesons in order to further verify some of these effects.

The present analysis uses all the data taken with the displaced track trigger up to August 2003. There exist two trigger path in the present trigger menu of CDF DAQ, Scenario A and LOWPT.

The basic trigger is called, for historical reasons, Scenario A and requires the identification at all trigger levels of two oppositely charged tracks with transverse momenta $p_T\ge2\,{\rm GeV/c}$ and $p_{T1}+p_{T2}\ge5.5\,{\rm GeV/c}$. At the second and third level trigger further requirements on the two trigger tracks are imposed using the precise information on the track impact parameter available from the Silicon Vertex Tracker (SVT) at level 2, and from full offline track reconstruction at level 3. Events are selected by requiring two tracks with $120\,\mu{\rm m}\le d_0 \le1.0\rm\,mm$. Furthermore the two trigger tracks must have an opening angle in the transverse plane satisfying $2^\circ\le\vert\Delta\phi\vert\le90^\circ$ and must satisfy the requirement $L_{xy}>200\rm\,\mu m$, where the two dimensional decay length, $L_{xy}$, is calculated as the transverse distance from the beam line to the two track vertex projected along the total transverse momentum of the track pair.

At low instantaneous luminosity an additional trigger selection is introduced. This one drops the opposite charge and the $p_{T1}+p_{T2}$ requirement. In order to fully exploit the surplus bandwidth available in the data acquisition system the prescale applied to this trigger path is dynamical, i.e. it changes continuously to match the trigger rate to the available bandwidth. This trigger is called in the following LOWPT trigger. It has a lower purity compared to the Scenario A trigger but offers a significantly increased acceptance for B decay.

The integrated luminosity corresponding to the Scenario A trigger is $179 \pm 10 ~{\rm {pb}^{-1}}$. Due to the dynamic prescale applied to the LOWPT trigger its effective luminosity is reduced to $L_{LOW} = 102 \pm 6 ~{\rm pb^{-1}}$.

In the following we will analyze separately the two trigger paths. We select data for the LOWPT analysis that only fire the LOWPT trigger but do not satisfy the Scenario A trigger, thus ensuring that there is no double counting of events.

To reconstruct B candidate we search all four-prong vertexes that satisfy trigger criteria and we fit them to a common vertex. All the tracks that are used in the vertex fit are required to have both drift chamber and silicon vertex hits and a minimum transverse momentum of 400 MeV.