Fit results

The fit yields the results reported in Tab.  top right. To extract relative branching fractions from the results of the fit it is necessary to apply the corrections which account for the different relative efficiencies between each decay. These differences among the efficiencies are due to several sources: trigger, reconstruction and analysis cuts. Most effects can be simulated and estimated by Monte Carlo, except for the relative efficiency of the $B$ isolation cut, which affects only the BR measurements of $B_s$ decays relative to $B_d$ decays and has been estimated from CDF II data using fully reconstructed $B_s$ and $B_d$ samples. The complete list of correction factors is reported in Tab.  bottom. The kinematic and isolation efficiencies have to be multiplied to determine the total relative efficiency.

Table: Top left: list of cuts applied to extract the $B^0\rightarrow h^{+}h^{'-}$ signal. Top right: fit results with statistical errors. Bottom center: relative efficiency corrections used to convert the relative fractions determined by the fit to relative branching fractions.

Parameter	value
# axial COT hits	$\geq$ 20
# stereo COT hits	$\geq$ 20
# axial SVXII hits	$\geq$ 3
max( $\mid \eta (\pi_1)\mid$, $\mid \eta (\pi_2)\mid$)	$\leq$ 1
min($p_T(\pi_1)$, $p_T (\pi_2)$)	$\geq$ 2 GeV/c
$p_T(\pi_1) + p_T (\pi_2)$	$\geq$ 5.5 GeV/c
$q(\pi_1) \cdot q(\pi_2)$	$<$ 0
$\Delta\phi(\pi_1, \pi_2)$	$[20^{\circ}, 135^{\circ}]$
min( $\mid d_0(\pi_1) \mid$, $\mid d_0(\pi_2) \mid$)	$\geq$ 0.0150 cm
max( $\mid d_0(\pi_1) \mid$, $\mid d_0(\pi_2) \mid$)	$\leq$ 0.1000 cm
$d_0(\pi_1) \cdot d_0(\pi_2)$	$<$ 0
$\mid \eta(B)\mid$	$\leq$ 1
$\mid d_0(B) \mid$	$\leq$ 0.0080 cm
$L_{xy}(B)$	$\geq$ 0.0300 cm
B isolation	$\geq$ 0.5

Fit parameter	Value
$f(B_d\rightarrow\pi\pi)$	0.15$\pm$0.03
$f(B_d\rightarrow K^\pm\pi^\mp)$	0.57$\pm$0.03
$A_{\mathsf{CP}}(B_d\rightarrow K^\pm\pi^\mp)$	-0.05$\pm$0.08
$f(B_s\rightarrow K^\pm\pi^\mp)$	0.02$\pm$0.03
$f(B_s\rightarrow KK)$	0.26$\pm$0.03
$\frac{N(B_s\rightarrow KK)}{N(B_d\rightarrow K\pi)}$	0.47$\pm$0.08
$\frac{N(B_d\rightarrow \pi\pi)}{N(B_d\rightarrow K\pi)}$	0.26$\pm$0.06
$\frac{N(B_d\rightarrow \pi\pi)}{N(B_s\rightarrow KK)}$	0.55$\pm$0.14
$f_\pi$ ( $4.850< M_{\pi\pi}< 5.125$)	0.53$\pm$0.01
$f_\pi$ ( $5.125< M_{\pi\pi}< 5.400$)	0.45$\pm$0.02
$f_\pi$ ( $5.400< M_{\pi\pi}< 5.800$)	0.46$\pm$0.02
background fraction	0.82$\pm$0.01
$c_0$	14.0$\pm$6.2
$c_1$	-2.1$\pm$0.4
$c_2$	8.7$\pm$57.5

Correction factor	Kin. and Trigger	B-Isolation
$\frac{\epsilon(B_d\rightarrow K\pi)}{\epsilon(B_d\rightarrow K\pi)}$	0.93 $\pm$ 0.01	-
$\frac{\epsilon(B_d\rightarrow K\pi)}{\epsilon(B_s\rightarrow KK)}$	1.13 $\pm$ 0.01	0.935 $\pm$ 0.10
$\frac{\epsilon(B_s\rightarrow KK)}{\epsilon(B_d\rightarrow \pi\pi)}$	0.82 $\pm$ 0.01	1.07 $\pm$ 0.11
$\frac{\epsilon(B^0_d\rightarrow K^+\pi^-)}{\epsilon(\overline{B}^0_d\rightarrow K^-\pi^+)}$	1.018 $\pm$ 0.001	-