Measurements of branching fraction ratios and CP-asymmetries in suppressed B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^- decays

D D indicates D 0 D^{0} and D ¯ 0 \bar{D}^{0} , and the charge conjugate state is implied throughout the paper, except in formulas and sentences where both are mentioned explicitly

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r B r_{B} is defined as the magnitude of the amplitude ratio of the suppressed process b → u b\to u over the favored process b → c b\to c , r B = | ℳ ⁡ ( b → u ) ℳ ⁡ ( b → c ) | r_{B}=\left|\frac{\mathcal{M}(b\to u)}{\mathcal{M}(b\to c)}\right| . Since the suppressed transition is associated to the B − → D ¯ 0 ​ K − B^{-}\to\bar{D}^{0}K^{-} decay and the favored to B − → D 0 ​ K − B^{-}\to D^{0}K^{-} , r B r_{B} corresponds also to | ℳ ⁡ ( B − → D ¯ 0 ​ K − ) ℳ ⁡ ( B − → D 0 ​ K − ) | \left|\frac{\mathcal{M}(B^{-}\to\bar{D}^{0}K^{-})}{\mathcal{M}(B^{-}\to{D}^{0}K^{-})}\right| . In the text we will distinguish between r B r_{B} of the kaon, r B ​ ( K ) r_{B}(K) , and of the pion, r B ​ ( π ) r_{B}(\pi) . The definitions for the pion are analogous to the definitions for the kaon

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CDF II uses a cylindrical coordinate system in which ϕ \phi is the azimuthal angle, r r is the radius from the nominal beam line, and z z points in the proton-beam direction, with the origin at the center of the detector. The transverse plane is the plane perpendicular to the z z axis

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Isolation is defined as I B = p T ​ ( B ) / ( p T ​ ( B ) + ∑ i p T ​ i ) I_{B}=p_{T}(B)/(p_{T}(B)+\sum_{i}p_{Ti}) , where p T ​ ( B ) p_{T}(B) is the transverse momentum of the B B candidate, and the sum runs over all other tracks within a cone in the η − ϕ \eta-\phi space around the B B flight-direction. Its value is typically higher for bottom–flavored hadrons than for random track combinations

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The kaon probability is defined as κ = d ​ E / d ​ x 𝑚𝑒𝑎𝑠 − d ​ E / d ​ x 𝑒𝑥𝑝 ​ ( π ) d ​ E / d ​ x 𝑒𝑥𝑝 ​ ( K ) − d ​ E / d ​ x 𝑒𝑥𝑝 ​ ( π ) \kappa=\frac{dE/dx_{\it meas}-dE/dx_{\it exp}(\pi)}{dE/dx_{\it exp}(K)-dE/dx_{\it exp}(\pi)} , where d ​ E / d ​ x 𝑚𝑒𝑎𝑠 dE/dx_{\it meas} is the measured specific energy loss of the track and d ​ E / d ​ x 𝑒𝑥𝑝 dE/dx_{\it exp} is the expected energy loss; κ \kappa has an average value of 1 for kaons and 0 for pions

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