Optimization procedure

We have performed an optimization procedure to define cuts in an unbiased way both for the normalization mode $B_s \rightarrow J/\psi \phi$ and for $B_s \rightarrow \phi \phi$ signal separately. We have in fact blinded the signal region for the $B_s \rightarrow \phi \phi$ signal to minimize possible experimenter bias in the analysis. For the search mode, we derive a set of optimized cuts by maximizing the score function $\frac{S}{1.5+\sqrt{B}}$, where S is the number of signal Monte Carlo events and B is taken from the sidebands. This function is particularly suitable for a first observation of a decay mode since the signal S does not appear in the denominator a normalization factor is not needed. The optimization for the normalization mode is based on the usual significance $\frac{S}{\sqrt{S+B}}$, in this case the signal S, coming from Monte Carlo, needs to be rescaled to represent the number of signal events in our data sample. Sidebands choice for the $B_s \rightarrow J/\psi \phi$ mode is illustrated in Fig. 1 and 2. The optimization is performed separately for both channels and for the two trigger paths Scenario A and LOWPT.

The variables entering the optimization are chosen with standard criteria: low correlation, agreement of sidebands subtracted distribution with MC, effectiveness in discriminating signal from background. In particular the variables that we optimize in the $B_s \rightarrow J/\psi \phi$ mode are:

• $L_{xy}$ : transverse decay length of the reconstructed B vertex projected along the B transverse momentum
• $I_{p}^{B_{s}}$ : impact parameter of the reconstructed B meson momentum with respect to the beam line center
• $\chi^{2}_{xy}$ : $\chi^2$ of the common vertex fit
• $p_{T}^{J/\psi}$ : transverse momentum of the $J/\psi$ candidate
• $P_{t}^{\Phi}$ : transverse momentum of the $\phi$ candidate
• $d0_{min}^{J/\psi}$ : minimum value of the absolute value of the impact parameter of the two track from the $J/\psi \rightarrow l^+l^-$ decay
• $d0_{min}^{\phi}$ : minimum value of the absolute value of the impact parameter of the two track from the $\phi \rightarrow K^+K^-$ decay

In the $B_s \rightarrow \phi \phi$ case the same variables are used, the $J/\psi$ role being taken by the lower momentum between the two $\phi$ meson candidates.