Optimization of analysis cuts

The $B_{d,s}\rightarrow h^{+}h^{'-}$ signal is reconstructed by applying a vertex constrained fit to each track pair of the event and confirming the trigger cuts (on transverse momenta and impact parameters of the tracks, and on transverse decay length and impact parameter of the $B$ candidate) using offline quantities. The cuts applied on certain variables (impact parameter of the two tracks and transverse decay length, impact parameter, and isolation of the $B$ candidate), particularly effective in reducing the background level, have been then optimised by maximizing $S/(S+B)^{1/2}$. The B isolation is defined as $\frac{p_T(B)}{p_T(B)+\sum p_T}$, where the sum on the transverse momentum is extended to the tracks contained in a cone with radius = 1 in the $\eta$-$\phi$ space around the $B$ meson flight direction. The final values of the cuts are summarized in Tab. , top left.

The resulting $B_{d,s}\rightarrow h^{+}h^{'-}$ invariant mass distribution, with pion mass assignment to both decay tracks, is reported in Fig. 1. A clean signal of $893 \pm 47$ events is observed.

Figure: $M_{\pi\pi}$ distribution of the $B\rightarrow h^{+}h^{'-}$ candidates selected applying the cuts reported in Tab.  and assigning the pion mass to both decay tracks. The result of the fit of the fractions is overlaid.