Results

Final results for $B_s \rightarrow \phi \phi$ optimized selection are shown in Fig. 5, 6 7, respectively for Scenario A, LOWPT and the sum of the two. We found in the search window 8 events in Scenario A and 4 events in the LOWPT, when respectively $0.75 \pm 0.41$ and $1.2 \pm 0.48$ total background events were expected.

In order to estimate the significance of the signals we evaluate the probability $P$ for the expected background to fluctuate to the observed number of events, under the hypothesis of null signal, using a poisson distribution with the expected background events as mean value. The P-values $P$ are defined as:

$$P = 1 - \Sigma_{k=0}^{N-1} \frac{\mu^{k}}{k!} \cdot e^{-\mu}$$ (1)

Where $N$ is the number of observed events and $\mu$ is the number of expected background events. The P-value evaluated from 1 is the poisson probability for the background to fluctuate to N or more events.

The P-values for Scenario A and LOWPT data, together with the corresponding significance given in terms of sigmas $N_{\sigma}$ for a one-side gaussian tail, are shown in Tab.2.

Table 2: $B_s \rightarrow \phi \phi$ signal significance. Systematic on the background estimate has been ignored

	P-value	$N_{\sigma}$
Scenario A	$1.28\cdot10^{-6}$	4.71
LOWPT	0.034	1.83

Total significance of $B_s \rightarrow \phi \phi$ signal, calculated as $\sigma_{tot} = \sigma_{ScA} \cdot \sigma_{LOW} \cdot ( 1 - ln(\sigma_{ScA} \cdot \sigma_{LOW} ))$, is then $\sigma_{tot} = 4.8 \sigma$.

Using BR( $B_s \rightarrow J/\psi \phi$) as a normalization we can extract BR( $B_s \rightarrow \phi \phi$) which is given by:

$$BR( B_s \rightarrow \phi \phi ) = \frac{N(\phi\phi)} {N^{corr}(\p... ...ghtarrow J/\psi \phi ) \cdot BR(\psi\rightarrow\mu\mu)}{BR(\phi\rightarrow KK)}$$ (2)

where $\varepsilon$ the total acceptances and N are the yields, which in the case of $\psi\phi$ is corrected for muon acceptance and reconstruction efficiency. Since the value of $BR( B_s \rightarrow J/\psi \phi )$ is from a CDF Run I measurement which was obtained using a ${f_s}/{f_d} = 0.40 \pm 0.06$, we rescaled this BR to the current PDG average ${f_s}/{f_d} = 0.26 \pm 0.04$. Relative acceptance $\frac {\varepsilon(\psi\phi)}{\varepsilon(\phi\phi)}$ of the two modes was evaluated from a detailed simulation of detector and trigger. The efficiencies were reweighted according to the luminosity integrated in different period of data taking to take in to account trigger configuration variations as well as other time dependent effect like those induced by the central drift chamber aging process that causes the relative trigger efficiency for particles of different species (i.e. muons vs Kaons) to change with time. The effects of polarization of Vector mesons in the decay and of $B_s$ mass eigenstate lifetime difference on acceptance have been studied and included in the systematic.

Table 3: Relative total efficiencies after reweighting

	Scenario A	LOWPT
$\frac{\varepsilon_{TOT}(B_{s}\rightarrow J/\psi \phi)} {\varepsilon_{TOT}(B_{s}\rightarrow \phi \phi)}$	$0.816\pm0.015$	$0.605\pm0.012$

Final result for BR is then:

$$BR ( B_s \rightarrow \phi \phi ) = (1.4 \pm 0.6(stat.) \pm 0.2(syst.) \pm 0.5(BR's) ) \cdot 10^{-5}$$ (3)