Measurement of CP violation observables and parameters for the decays $B^{\pm}\to D K^{*\pm}$

We study the decay $B^-\to DK^{*-}$ using a sample of 379$\times 10^6$ $\Upsilon(4S)\to B\bar{B}$ events collected with the BABAR detector at the PEP-II $B$-factory. We perform a"GLW"analysis where the $D$ meson decays into either a CP-even ($CP+$) eigenstate ($K^+K^-$, $\pi^+\pi^-$), CP-odd ($CP-$) eigenstate ($K^0_S\pi^0$, $K^0_S\phi$, $K^0_S\omega$) or a non-CP state ($K^-\pi^+$). We also analyze $D$ meson decays into $K^+\pi^-$ from a Cabibbo-favored $\bar{D}^0$ decay or doubly suppressed $D^0$ decay ("ADS"analysis). We measure observables that are sensitive to the CKM angle $\gamma$: the partial-rate charge asymmetries ${\cal A}_{CP\pm}$, the ratios ${\cal R}_{CP\pm}$ of the B-decay branching fractions in $CP\pm$ and non-CP decay, the ratio ${\cal R}_{ADS}$ of the charge-averaged branching fractions, and the charge asymmetry ${\cal A}_{ADS}$ of the ADS decays: ${\cal A}_{CP+}= 0.09\pm0.13 \pm 0.06$, ${\cal A}_{CP-}=-0.23\pm 0.21\pm 0.07$, ${\cal R}_{CP+} =2.17 \pm 0.35 \pm 0.09$,${\cal R}_{CP-} =1.03\pm 0.27\pm 0.13$, ${\cal R}_{ADS}=0.066\pm0.031\pm0.010$, and ${\cal A}_{ADS}=-0.34\pm0.43\pm 0.16$, where the first uncertainty is statistical and the second is systematic. Combining all the measurements and using a frequentist approach yields the magnitude of the ratio between the Cabibbo-suppressed and favored amplitudes, $r_B$ = 0.31 with a one (two) sigma confidence level interval of [0.24, 0.38] ([0.17, 0.43]). The value $r_B=0$ is excluded at the 3.3 sigma level. A similar analysis excludes values of $\gamma$ in the intervals $[0, 7]^{\circ}, [55, 111]^{\circ}$, and $[175, 180]^{\circ}$ ([85, 99]$^{\circ}$) at the one (two) sigma confidence level.


I. INTRODUCTION
The Standard Model accommodates CP violation through a single phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix V [1]. The self consistency of this mechanism can be tested by overconstraining the associated unitarity triangle [2,3] using many different measurements, mostly involving decays of B mesons. In this paper we concentrate on the angle γ ≡ arg(−V ud V * ub /V cd V * cb ) by studying B meson decay channels where b → cus and b → ucs tree amplitudes interfere. We use two techniques, one suggested by Gronau and London [4] and Gronau and Wyler [5] (GLW) and the other suggested by Atwood, Dunietz and Soni [6] (ADS) to study γ. Both techniques rely on final states that can be reached from both D 0 and D 0 decays. As discussed in Ref. [7] the combination of the GLW and ADS observables can be very useful in resolving certain ambiguities inherent in each of the techniques. In this paper we use the decay B − → DK * − (892) [8] to measure the GLW and ADS observables.
In the GLW analysis the D meson [9] from B − → DK * − decays into either a CP -even (CP +) eigenstate (K + K − , π + π − ) or a CP -odd (CP −) eigenstate (K s π 0 , K s φ, K s ω). The size of the interference between the two competing amplitudes depends on the CKM angle γ as well as other parameters that are CP -conserving, discussed below. References [4,5] define several observables that depend on measurable quantities: , .
Here D 0 CP ± refers to a neutral D meson decaying into either a CP + or CP − eigenstate.
R CP ± and A CP ± depend on the physical parameters as follows: Here r B is the magnitude of the ratio of the suppressed B − → D 0 K * − and favored B − → D 0 K * − decay amplitudes, respectively, and δ B is the CP -conserving phase difference between these amplitudes. In this analysis we neglect the effects of CP violation in D meson decays, and, as justified in Ref. [10], the very small effect of D 0 D 0 mixing.
where N CP ± and N non−CP are the event yields for the CP and non-CP modes, respectively and ǫ non−CP and ǫ CP ± are correction factors that depend on branching fractions and reconstruction efficiencies. A CP ± is calculated using the event yields split by the charge of the B meson. We define two additional quantities whose experimental estimators are normally distributed even when the value of r B is comparable to its uncertainty: .
Since x ± are also directly measured in Dalitz-plot analyses [11], the different results can be compared and combined with each other. We note that an additional set of quantities measured in Dalitz-plot analyses, y ± = r B sin(δ B ± γ), are not directly accessible through the GLW analysis.
In the ADS technique, indicates that these particles are neutral D meson (D 0 or D 0 ) decay products. This final state can be reached from B → D 0 K * − and the doubly-Cabibbo-suppressed decay D 0 → K + π − or B − → D 0 K * − followed by the Cabibbo-favored decay D 0 → K + π − . In addition, the final state [K − π + ] D K * − is used for normalization. We label the decays where the K and K * have the same (opposite) charge as "right (wrong) sign" where the labels reflect that one mode occurs much more often than the other.
In analogy with the GLW method we define two measurable quantities, R ADS and A ADS , as follows: R ADS and A ADS are related to physically interesting quantities by: Here r D is the magnitude of the ratio of suppressed D 0 → K + π − and favored D 0 → K − π + decay amplitudes, respectively, while δ D is the CP -conserving strong phase difference between these two amplitudes. Both r D and δ D have been measured and we use the values given in Ref. [12]: r D = 0.0578 ± 0.0008 and δ D = 21.9 +11.3 −12.4 degrees. Estimates for r B are in the range 0.1 ≤ r B ≤ 0.3 [13,14].
It has been pointed out in Ref. [13] that complications due to possible variations in r B and/or δ B as a result of the finite width of a resonance such as the K * and its overlap with other states can be taken into account using an alternate formalism. However, in this paper we choose to follow the procedures in Refs. [14,15] and incorporate the effects of the non-K * DKπ events and finite width of the K * into the systematic uncertainties of our A and R measurements.

II. THE BABAR DETECTOR AND DATASET
The BABAR detector has been described in detail in Ref. [16] and therefore will only be briefly discussed here. The trajectories of charged tracks are measured with a five-layer double-sided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH). Both the SVT and DCH are located inside a 1.5 T magnetic field. Photons are detected by means of a CsI(Tl) crystal calorimeter also located inside the magnet. Charged particle identification is determined from information provided by a ringimaging Cherenkov device (DIRC) in combination with ionization measurements (dE/dx) from the tracking detectors. The BABAR detector's response to various physics processes as well as varying beam and environmental conditions is modeled with simulation software based on the Geant4 [17] toolkit. We use EvtGen [18] to model the kinematics of B mesons and Jetset [19] to model continuum processes (e + e − → cc, uu, dd, ss). This analysis uses data collected at and near the Υ (4S) resonance with the BABAR detector at the PEP-II storage ring. The data set consists of 345 fb −1 collected at the peak of the Υ (4S) (379 ×10 6 BB pairs) and 35 fb −1 collected 40 MeV below the resonance peak (off-peak data).
This analysis is a combined update of the previous BABAR ADS [14] and GLW [15] studies of B − → DK * − , which used 232 ×10 6 BB pairs. Other new features in this analysis include the improvement in background suppression, the refinement of various candidate selection criteria, and an update of the estimation of systematic uncertainties. The major change is the choice of neural networks in the GLW analysis over Fisher discriminants, which were used in the previous analysis. We verify the improvements on both signal efficiency and continuum background rejection in the GLW decay channels with simulated signal and continuum events. The increases in signal efficiency range from 3% to 14% for all channels except K 0 S φ, which has the same efficiency. For continuum suppression, the neural networks perform 10% to 57% better across all channels except K + K − , which displays the same performance.
We optimize our event selection criteria by maximizing the figure of merit S/ √ S + B, with S the number of signal events and B the number of background events, determined for each channel using simulated signal and background events. Kaon and pion candidates (except for the pions from K 0 S decays) are selected using a likelihoodbased particle identification algorithm which relies on dE/dx information measured in the DCH and the SVT, and Cherenkov photons in the DIRC. The efficiencies of the selectors are typically above 85% for momenta below 4 GeV while the kaon and pion misidentification rates are at the few percent level for particles in this momentum range.
The K 0 S candidates are formed from oppositely charged tracks assumed to be pions with a reconstructed invariant mass within 13 MeV/c 2 (four standard deviations) of the known K 0 S mass [3], m K 0 S . All K 0 S candidates are refitted so that their invariant mass equals m K 0 S (mass constraint). They are also constrained to emerge from a single vertex (vertex constraint). For those retained to build a K * − candidate, we further require that their flight direction and length be consistent with a K 0 S coming from the interaction point. The K 0 S candidate flight path and momentum vectors must make an acute angle and the flight length in the plane transverse to the beam direction must exceed its uncertainty by three standard deviations. K * − candidates are formed from a K 0 S and a charged particle with a vertex constraint. We select K * − candidates that have an invariant mass within 75 MeV/c 2 of the known mean value for a K * [3]. Finally, since the K * − in B − → DK * − is longitudinally polarized, we require | cos θ H | ≥ 0.35, where θ H is the angle in the K * − rest frame between the daughter pion momentum and the parent B momentum. The helicity distribution discriminates well between a B-meson decay and a false B-meson candidate from the continuum, since the former is distributed as cos 2 θ H and the latter has an approximately flat distribution.
Some decay modes of the D meson contain a neutral pion. We combine pairs of photons to form π 0 candidates with a total energy greater than 200 MeV and an invariant mass between 115 and 150 MeV/c 2 . A mass constrained fit is applied to the selected π 0 candidate momenta. Composite particles (φ and ω) included in the CP − modes are vertex-constrained. Candidate φ (ω) mesons are constructed from K + K − (π + π − π 0 ) particle combinations with an invariant mass required to be within two standard deviations, corresponding to 12 (20) MeV/c 2 , from the known peak values [3]. Two further requirements are made on the ω candidates. The magnitude of the cosine of the helicity angle θ H between the D momentum in the rest frame of the ω and the normal to the plane containing all three decay pions must be greater than 0.35 (this variable has a cos 2 θ H distribution for signal candidates and is approximately flat for background). The Dalitz angle [20] θ D is defined as the angle between the momentum of one daughter pion in the ω rest frame and the direction of one of the other two pions in the rest frame of the two pions. For signal candidates, the cosine of the Dalitz angle follows a sin 2 θ D distribution, while it is approximately flat for the background. Therefore we require the cosine of the Dalitz angle of signal candidates to have a magnitude smaller than 0.8.
All D candidates are mass constrained and, with the exception of the K 0 S π 0 final state, vertex constrained. We select D candidates with an invariant mass differing from the known mass [3] by less than 12 MeV/c 2 for all channels except K 0 S π 0 (30 MeV/c 2 ) and K 0 S ω (20 MeV/c 2 ). These limits are about twice the corresponding RMS mass resolutions.
Suppression of backgrounds from continuum events is achieved by using event-shape and angular variables. The B meson candidate is required to have | cos θ T | ≤ 0.9, where θ T is the angle between the thrust axis of the B meson and that of the rest of the event. The distribution of | cos θ T | is uniform in BB events and strongly peaked near 1 for continuum events.
A neural network (NN) is used to further reduce the e + e − → qq (q = u, d, s, c) contribution to our data sample. Seven variables are used in the NN with three being the angular moments L 0 , L 1 and L 2 . These moments are defined by L j = i p * i | cos θ * i | j where the sum is over charged and neutral particles not associated with the B-meson candidate. Here p * i (θ * i ) is the momentum (angle) of the ith particle with respect to the thrust of the candidate B meson in the center-of-mass (CM) frame. Additional details on the moments can be found in Ref. [21]. The NN also uses the ratio R 2 = H 2 /H 0 of Fox-Wolfram moments [22], the cosine of the angle between the B candidate momentum vector and the beam axis (cos θ B ), cos θ T (defined above), and the cosine of the angle between a D daughter momentum vector in the D rest frame and the direction of the D in the B meson rest frame (cos θ H (D)). The distributions of all the above variables show distinct differences between signal and continuum events and thus can be exploited by a NN to preferentially select BB events. Each decay mode has its own unique NN trained with signal and continuum Monte Carlo events. After training, the NNs are then fed with independent sets of signal and continuum Monte Carlo events to produce NN outputs for each decay mode. Finally, we verify that the NNs have consistent outputs for off-peak data (continuum data collected below the Υ (4S)) and qq Monte Carlo events. The separations between signal and continuum background are shown in Fig. 1. We select candidates with neural network output above 0.65 (K + K − ), 0.82 (π + π − ), 0.91 , and 0.73 (K − π + ). Our event selection is optimized to maximize the significance of the signal yield, determined using simulated signal and background events.
We identify B candidates using two nearly independent kinematic variables: the beam-energy-substituted mass m ES = (s/2 + p 0 · p B ) 2 /E 2 0 − p 2 B and the energy difference ∆E = E * B − √ s/2, where E and p are energy S ω, and (f) K − π + subsamples of the GLW analysis. The samples used to produce the output are shown as histograms. The signal (Monte Carlo simulation) is the shaded histogram peaking near 1; the continuum (Monte Carlo simulation) is the histogram peaking near 0. The off-peak data used to check the NN are overlaid as data points. and momentum. The subscripts 0 and B refer to the e + e − -beam system and the B candidate, respectively; s is the square of the CM energy and the asterisk labels the CM frame. The m ES distributions are all described by a Gaussian function G centered at the B mass with a resolution (sigma) of 2.50, 2.55, and 2.51 MeV/c 2 for the CP +, CP − and non-CP mode, respectively. The ∆E distributions are centered on zero for signal with a resolution of 11 to 13 MeV for all channels except K 0 S π 0 for which the resolution is asymmetric and is about 30 MeV. We define a signal region through the requirement |∆E| < 50 (25) MeV for K 0 S π 0 (all other modes). A potentially dangerous background for the B − → D(π + π − )K * − (K 0 S π − ) channel is the decay mode B − → D(K 0 S π + π − )π − which contains the same final-state particles as the signal but has a branching fraction 600 times larger. We therefore explicitly veto any selected B candidate containing a K 0 S π + π − combination within 60 MeV/c 2 of the D 0 mass.
The fraction of events with more than one acceptable B candidate depends on the D decay mode and is always less than 8%. To select the best B candidate in those events where we find more than one acceptable candidate, we choose the one with the smallest χ 2 formed from the differences of the measured and world average D 0 and K * − masses divided by the mass spread that includes the resolution and, for the K * − , the natural width: Simulations show that negligible bias is introduced by this choice and the correct candidate is picked at least 86% of the time.
From the simulation of signal events, the total reconstruction efficiencies are: 12.8% and 12.3% for the CP + modes D → K + K − and π + π − ; 5.6%, 8.9%, and 2.4% for To study BB backgrounds we look in sideband regions in ∆E and m D . We define the ∆E sideband in the interval 60 ≤ ∆E ≤ 200 MeV for all modes. This region is used to determine the combinatorial background shapes in the signal and m D sideband. We choose not to use a lower sideband because of the D * K * backgrounds in that region. The sideband region in m D is slightly mode dependent with a typical requirement that m D differs from the D 0 mass by more than four and less than 10 standard deviations. This region provides sensitivity to background sources which mimic signal both in ∆E and m ES and originate from either charmed or charmless B meson decays that do not contain a true D meson. As many of the possible contributions to this background are not well known, we measure its size by including the m D sideband in the fit described below.
An unbinned extended maximum likelihood fit to the m ES distributions of selected B candidates in the range 5.2 ≤ m ES ≤ 5.3 GeV/c 2 is used to determine signal and background yields. We use the signal yields to calculate the CP -violating quantities A CP and R CP . We use the same mean and width of the Gaussian function G to describe the signal shape for all modes considered. The combinatorial background in the m ES distribution is modeled with the so-called "ARGUS" empirical threshold function A [23]. It is defined as: where x = m ES /E max and E max is the maximum mass for pair-produced B mesons given the collider beam energies and is fixed in the fit at 5.291 GeV/c 2 . The ARGUS shape is governed by one parameter ξ that is left free in the fit. We fit simultaneously m ES distributions of nine samples: the non-CP , CP + and CP − samples for (i) the signal region, (ii) the m D sideband and (iii) the ∆E sideband. In addition the signal region is divided into two samples according to the charge of the B candidate. We fit three probability density functions (PDF) weighted by the unknown event yields. For the ∆E sideband, we use A. For the m D sideband (sb) we use a sb ·A + b sb ·G, where G accounts for fake-D candidates. For the signal region PDF, we use a · A + b · G peak + c · G signal , where b is scaled from b sb with the assumption that the number of fake D background events present in the signal region is equal to the number measured in the m D sideband scaled by the ratio of the m D signal-window to sideband widths, and c is the number of B ± → DK * ± signal events. The non-CP mode sample, with relatively high statistics, helps constrain the PDF shapes for the low statistics CP mode distributions. The ∆E sideband sample helps determine the A background shape. In total, the fit determines 19 event yields as well as the mean and width of the signal Gaussian and the ARGUS parameter ξ.
Since the values of ξ obtained for each data sample are consistent with each other, albeit with large statistical uncertainties, we have constrained ξ to have the same value for all data samples in the fit. The simulation shows that the use of the same Gaussian parameters for all signal modes introduces only negligible systematic corrections. We assume that the fake D backgrounds found in the m D sideband have the same final states as the signal and we fit these contributions with the same Gaussian parameterization.
The fake D background is assumed to not violate CP and is therefore split equally between the B − and B + sub-samples. This assumption is consistent with results from our simulations and is considered further when we discuss the systematic uncertainties. The fit results are shown graphically in Fig. 2 and numerically in Table I. Table II records the number of events measured for each individual D decay mode.   Although most systematic uncertainties cancel for A CP , a charge asymmetry inherent to the detector or data processing may exist. We quote the results from the study carried out in Ref. [24], where we used B − → D 0 π − (with D 0 decays into CP or non-CP eigenstates) events from control samples of data and simulation to measure the charge asymmetry. An average charge asymmetry of A ch = (−1.6 ± 0.6)% was measured. We add linearly the central value and one-standard deviation in the most conservative direction to assign a systematic uncertainty of 0.022. The second substantial systematic effect is a possible CP asymmetry in the fake D background that cannot be excluded due to CP violation in charmless B decays. If there is an asymmetry A fake D , then the systematic uncertainty on A CP is A fake D × b/c, where b is the contribution of the fake D background and c the signal yield. Assuming conservatively that |A fake D | ≤ 0.5, we obtain systematic uncertainties of ±0.003 and ±0.040 on A CP + and A CP − respectively. Note that since we do not observe any fake D background in CP − modes, we use the statistical uncertainty of the signal yield from the fit to estimate this systematic uncertainty.
Since R CP is a ratio of rates of processes with different final states of the D, we must consider the uncertainties affecting the selection algorithms for the different D channels. This results in small corrections which account for the difference between the actual detector response and the simulation model. The main effects stem from the approximate modeling of the tracking efficiency (a correction of 0.4% per pion track coming from a K 0 S and 0.2% per kaon and pion track coming from other candidates), the K 0 S reconstruction efficiency for CP − modes of the D 0 (1.3% per K 0 S in K 0 S φ mode and 2.0% in K 0 S π 0 and K 0 S ω), the π 0 reconstruction efficiency for the K 0 S π 0 and K 0 S [π + π − π 0 ] ω channels (3%) and the efficiency and misidentification probabilities from the particle identification (2% per track). The corrections are calculated by comparing data and Monte Carlo using high-statistics and high-purity samples. Charged kaon and pion samples obtained from D-meson decays (D * + → D 0 π + ) are used for particle identification corrections. For tracking corrections, we use τ -pair events where one τ decays to a muon and two neutrinos and the other decays to ρ 0 hν where h is a K or a π. B 0 → φK 0 S and B 0 → π + D − (D − → K 0 S π − ) decays are used for K 0 S corrections, and π 0 correction factors are calculated using τ → ρν and τ → πν samples. The total correction factors, which also include branching fractions and selection efficiencies, used in the calculation of R CP ± (Eq. 3) are given in Table II. R CP + (R CP − ) is calculated using the sum of the individual CP + (CP −) correction factors. Altogether, the systematic uncertainties due to the corrections equal ±0.078 and ±0.100 for R CP + and R CP − , respectively. The uncertainties on the measured branching fractions [3] and efficiencies for different D decay modes, are included in the calculation of the systematic errors due to these corrections.
Another systematic correction applied to the CP − measurements arises from a possible CP + background in the K 0 S φ and K 0 S ω channels. In this case, the observed quantities A obs CP − and R obs CP − are corrected: where ǫ is the ratio of CP + background to CP − signal. An investigation of the D 0 → K − K + K 0 S Dalitz plot [25] indicates that the dominant background for D 0 → K 0 S φ comes from the decay a 0 (980) → K + K − , at the level of (25 ± 1)% of the size of the φK 0 S signal. We have no information for the ωK 0 S channel and assume (30 ± 30)% of CP + background contamination. The K 0 S π 0 mode has no CP + background. The value of ǫ for the combination of CP − modes is (11 ± 7)%. The systematic uncertainty associated with this effect is ±0.02 and ±0.06 for A CP − and R CP − , respectively.
To account for the non resonant K 0 S π − pairs in the K * mass range we study a model that incorporates S-wave and P -wave pairs in both the b → cus and b → ucs amplitudes. The P -wave mass dependence is described by a single relativistic Breit-Wigner while the S-wave component is assumed to be a complex constant. It is expected that higher order partial waves will not contribute significantly and therefore they are neglected in the model. We also assume that the same relative amount of S and Pwave is present in the b → cus and b → ucs amplitudes. The amount of S-wave present in the favored b → cus amplitude is determined directly from the data by fitting the angular distribution of the K 0 S π system in the K * mass region, accounting for interference [26]. From this fit we determine that the number of non-K * K S π − events is (4 ± 1)% of the measured signal events. To estimate the systematic uncertainties due to this source we vary all the strong phases between 0 and 2π and calculate the maximum deviation between the S-wave model and the expectation if there were no non-resonant contribution for both A CP ± [Eq. (2)] and R CP ± [Eq. (1)]. This background induces systematic variations of ±0.051 for A CP ± and ±0.035 for R CP ± .
The last systematic uncertainty is due to the assumption that the parameters of the Gaussian and ARGUS functions are the same throughout the signal region, ∆E and m D sidebands. We estimate the uncertainties by varying the width and mean of the Gaussian and ξ of the ARGUS by their corresponding statistical uncertainties obtained from the fit. All the systematic uncertainties are listed in Table III. We add them in quadrature and quote the final results: These results can also be expressed in terms of x ± defined in Eq. (4): x + = 0.21 ± 0.14(stat.) ± 0.05(syst.), x − = 0.40 ± 0.14(stat.) ± 0.05(syst.), where the CP + pollution systematic effects are included. Including these effects increased x + and x − by 0.035 ± 0.024 and 0.023 ± 0.017, respectively.

IV. THE ADS ANALYSIS
In the ADS analysis we only use D decays with a charged kaon and pion in the final state and K * − decays to K 0 S π − followed by K 0 S → π + π − . The ADS event selection criteria and procedures are nearly identical to those used for the GLW analysis. However due to the small value of r D the yield of interesting ADS events (i.e. B − → [K + π − ] D K * − and B + → [K − π + ] D K * + ) is expected to be smaller than for the GLW analysis. Therefore in order to reduce the background in the ADS analysis the K 0 S invariant mass window is narrowed to 10 MeV/c 2 and the K * − invariant mass cut is reduced to 55 MeV/c 2 . A neural network using the same variables as in the GLW analysis is trained on ADS signal and continuum MC events and verified using off-peak continuum data. The separation between signal and continuum background is shown in Fig. 3. We select candidates, both right and wrong-sign, with neural network output above 0.85. All other K 0 S , K * − , and continuum suppression criteria are the same as those used in the GLW analysis.
D → K − π + and K + π − candidates are used in this analysis. Candidates that have an invariant mass within 18 MeV/c 2 (2.5 standard deviations) of the nominal D 0 mass [3] are kept for further study. We require kaon candidates to pass the same particle identification criteria as imposed in the GLW analysis.
We identify B-meson candidates using the beamenergy-substituted mass m ES and the energy difference ∆E. For this analysis signal candidates must satisfy |∆E| ≤ 25 MeV. The efficiency to detect a B − → D 0 K * − signal event where D 0 → Kπ, after all criteria are imposed, is (9.6±0.1)% and is the same for D 0 → K − π + and D 0 → K + π − . In 1.8% of the events we find more than one suitable candidate. In such cases we choose the candidate with the smallest χ 2 defined in Eq. (7). Simulations show that negligible bias is introduced by this choice and the correct candidate is picked about 88% of the time.
We study various potential sources of background using a combination of Monte Carlo simulation and data events. Two sources of background are identified in large samples of simulated BB events. One source is B − → D 0 K 0 S π − production where the K 0 S π − is nonresonant and has an invariant mass in the K * − mass window. This background is discussed later. The second background (peaking background) includes instances where a favored decay (e. g. B − → [K − π + ] D K * − ) contributes to fake candidates for the suppressed decay (i.e. B + → [K − π + ] D K * + ). The most common way for this to occur is for a π + from the rest of the event to be substituted for the π − in the K * − candidate. Other sources of peaking background include double particle-identification failure in signal events that results in D 0 → K − π + being reconstructed as D 0 → π − K + , or the kaon from the D 0 being interchanged with the charged pion from the K * . We quantify this background with the ratio of the signal efficiency of wrong-sign decay to right-sign decay multiplied by the right-sign yield from data. The total size of this right-sign pollution is estimated to be 2.4 ± 0.3 events. Another class of backgrounds is charmless decays with the same final state as the signal (e.g., B − → K * − K + π − ). Since the branching fractions for many of these charmless decays have not been measured or are poorly measured, we use the D sideband to estimate the contamination from this source. From a fit to the m ES distribution using candidates in the D sideband we find 0.0 ± 1.1 events. We take the 1.1 events as the contribution to the systematic uncertainty from this source.
Signal yields are determined from an unbinned extended maximum likelihood fit to the m ES distribution in the range 5.2 ≤ m ES ≤ 5.3 GeV/c 2 . A Gaussian function (G) is used to describe all signal shapes while the combinatorial background is modeled with an ARGUS threshold function (A) defined in Eq. (8). The mean and width of the Gaussian as well as the ξ parameter of the ARGUS function are determined by the fit. For the likelihood function we use a · A + b · G where a is the number of background events and b the number of signal events. We correct b for the right-sign peaking background previously discussed (2.4±0.3 events). It also includes the right-sign peaking background estimated from a Monte Carlo study for the wrong-sign (top) decays. The curves result from a simultaneous fit to these distributions with identical PDFs for both samples.
In Fig. 4 we show the results of a simultaneous fit to didates that satisfy all selection criteria. It is in the wrong-sign decays that the interference we study takes place. Therefore in Fig. 5 we display the same fit separately for the wrong-sign decays of the B + and the B − mesons. The results of the maximum likelihood fit are R ADS = 0.066±0.031, A ADS = −0.34±0.43, and 172.9± 14.5 B − → [K − π + ] D K * − right-sign events. Expressed in terms of the wrong-sign yield, the fit result is 11.5±5.3 wrong-sign events (3.8 ± 3.4 B − → [K + π − ] D K * − and 7.7 ± 4.2 B + → [K − π + ] D K * + events). The uncertainties are statistical only. The correlation between R ADS and A ADS is insignificant.
We summarize in Table IV the systematic uncertainties relevant to this analysis. Since both R ADS and A ADS are ratios of similar quantities, most potential sources of systematic uncertainties cancel. For the estimation of the detection-efficiency asymmetry we use the previously mentioned results from the study carried out in Ref. [24]. We add linearly the central value and one-standard deviation in the most conservative direction to assign a systematic uncertainty of δA ch = ±0.022 to the A ADS measurement. To a good approximation the systematic uncertainty in R ADS due to this source is δR ADS = R ADS · A ADS · δA ch .
To estimate the systematic uncertainty on A ADS and R ADS due to the peaking background, we use the statistical uncertainty on this quantity, ±0.3 events. With approximately 12 B − → [K + π − ] D K * − events and 173 B − → [K − π + ] D K * − events this source contributes ±0.002 and ±0.024 to the systematic uncertainties on R ADS and A ADS , respectively. Similarly, the 1.1 events uncertainty on the same-final-state background leads to systematic uncertainties of ±0.0061 and ±0.091 on R ADS and A ADS respectively.
As in Section III, we need to estimate the systematic effect due to the non-resonant K 0 S π − pairs in the K * mass range. We follow the same procedure discussed in Section III. After adding in quadrature the individual systematic uncertainty contributions, listed in Table IV, we find:

V. COMBINED RESULTS
We use the GLW and ADS results and a frequentist statistical approach [27] to extract information on r B and γ. In this technique, a χ 2 is calculated using the differences between the measured and theoretical values and the statistical and systematic errors of the six measured quantities. The values of r D and δ D are taken from Ref. [12], while we allow 0 ≤ r B ≤ 1, 0 • ≤ γ ≤ 180 • , and 0 • ≤ δ B ≤ 360 • . The minimum of the χ 2 for the r B , γ, and δ B parameter space is calculated first (χ 2 min ). We then scan the range of r B and γ minimizing the χ 2 (χ 2 m ) by varying δ B . A confidence level for each value of r B and γ is calculated using ∆χ 2 = χ 2 m − χ 2 min and one degree of freedom. We assume Gaussian measurement uncertainties and confirm this assumption using simulations. In Fig. 6 we show the 95% confidence level contours for r B versus γ as well as the 68% confidence level contours for the GLW and the combined GLW and ADS analysis (striped areas).
In order to find confidence levels for r B we use the above procedure, minimizing χ 2 with respect to γ and δ B . The results of this calculation are shown in Fig. 7. The fit which uses both the ADS and GLW results has its minimum χ 2 at r B = 0.31 with a one sigma interval of [0.24, 0.38] and a two sigma interval of [0.17, 0.43]. The value r B = 0 is excluded at the 3.3 sigma level. We find similar results for r B using the modifications to this frequentist approach discussed in Ref. [28] and using the Bayesian approach of Ref. [29].
Using the above procedure we also find confidence intervals for γ. The results of the scan in γ are shown in Fig. 8 [12] helps to resolve the ambiguities on γ and therefore explains the asymmetry in the confidence level plot shown in Fig. 8.

VI. SUMMARY
In summary, we present improved measurements of yields from B − → DK * − decays, where the neutral D-meson decays into final states of even and odd CP (GLW), and the K + π − final state (ADS). We express the results as R CP , A CP , x ± , R ADS , and A ADS . The value r B = 0 is excluded at the 3.3 sigma level. These results in combination with other GLW, ADS, and Dalitz type analyses improve our knowledge of r B and γ.

VII. ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council The GLW+ADS result (solid line and shaded area) is from a fit which uses both the GLW and ADS measurements as well as rD and δD from [12]. The horizontal lines show the exclusion limits at the 1, and 2 standard deviation levels. cia (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation.