In the ADS method (I. Dunietz, Phys. Rev. Lett. B 270 (1991) 75; Phys. Rev. Lett. D 52 (1995) 3048; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997)),
is measured from the study of
decays, where
mesons decay into non
eigenstate final states. The suppression of
transition with respect to the
one is partly overcome by the study of decays of the
meson in final states which can proceed in two ways: either through a favored
decay followed by a doubly-Cabibbo-suppressed
decay, or through a suppressed
decay followed by a Cabibbo-favored
decay.
Neglecting
-mixing effects, which in the SM give very small corrections to \g\ and do not affect the
measurement, the measured ratios
and
are related to the
and
mesons' decay parameters through the following relations:
$%A_{ADS}=\frac{\Gamma(B^{-}\rightarrow [f]_{D^{0}}K^{-})}{\Gamma(\Bp\to [\bar f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),
with
\begin{equation}\begin{split}
\rD^2 \equiv\frac{\Gamma(\Dz\to f)}{\Gamma(\Dz\to \bar f)}=
\frac{\int dm\, A_{\rm DCS}(m)}{\int dm\, A_{\rm CA}(m)},\\kD e^{i\deltaD}\equiv \frac{\int dm\, A_{\rm DCS}(m)A_{\rm CA}
e^{i\delta(m)}}{\sqrt{\int dp\, A_{\rm DCS}^2(p)\int dp\, A_{\rm
CA}^2(p)}},
\end{split}\end{equation}
$%A_{ADS}=\frac{\Gamma(\Bm\to [f]_{\Dz}\Km)}{\Gamma(\Bp\to [\bar
f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),
The used observables are connected to the ``classical'' $\rads$ and $\aads$ set by simple relations:
$\rads=\frac{\rplus+\rminus}{2}$ and $\aads=\frac{\rminus-\rplus}{\rminus+\rplus}$.
Since $\rplus$ and $\rminus$ are two independent observables, while
$\rads$ and $\aads$ are correlated we prefer to extract the physical
parameters from $(\rplus,\rminus)$ rather than $(\rads,\aads)$.
The values of \kD\ and \deltaD\ measured by the CLEO-c
collaboration~\cite{cite:CLEO}, are used in the
signal yield estimation and
\rB\ extraction. The ratio \rD\ has been
measured in different experiments and we take the average value~\cite{cite:PDG}.