Measurements of CP-Violating Asymmetries in the Decay B0-->K+K-K0

We analyze the decay B0 -->K+ K- K0 using 383 million B-Bbar events collected by the BaBar detector at SLAC to extract CP violation parameter values over the Dalitz plot. Combining all K+ K- K0 events, we find A_CP = -0.015 +/- 0.077 +/- 0.053 and beta_eff = 0.352 +/- 0.076 +/- 0.026 rad, corresponding to a CP violation significance of 4.8 sigma. A second solution near pi/2 - beta_eff is disfavored with a significance of 4.5 sigma. We also report A_CP and beta_eff separately for decays to phi(1020) K0, f0(980) K0, and K+ K- K0 with m_{K+ K-}>1.1 GeV/c^2.

We analyze the decay B 0 → K + K − K 0 using 383 million BB events collected by the BABAR detector at SLAC to extract CP violation parameter values over the Dalitz plot. Combining all K + K − K 0 events, we find ACP = −0.015 ± 0.077 ± 0.053 and β eff = 0.352 ± 0.076 ± 0.026 rad, corresponding to a CP violation significance of 4.8σ. A second solution near π/2 − β eff is disfavored with a significance of 4.5σ. We also report ACP and β eff separately for decays to φ(1020)K 0 , f0(980)K 0 , and K + K − K 0 with m K + K − > 1.1 GeV/c 2 .
PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er In the Standard Model (SM), the phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1] is the sole source of CP violation in the quark sector. Due to interference between decays with and without mixing, this phase yields observable time-dependent CP asymmetries in B 0 meson decays. In particular, significant CP asymmetries in b → sss decays, such as B 0 → K + K − K 0 [2], are expected [3,4]. Deviations from the predicted CP asymmetry behavior for B 0 → K + K − K 0 are expected to depend weakly on Dalitz plot (DP) position [5,6]. Since the b → sss amplitude is dominated by loop contributions, heavy virtual particles beyond the SM might contribute significantly [6,7]. This sensitivity motivates measurements of CP asymmetries in multiple b → sss decays [3,8,9,10].
Previous measurements of CP asymmetries in B 0 → K + K − K 0 have been performed separately for events with K + K − invariant mass (m K + K − ) in the φ mass [11] region, and for events excluding the φ region, neglecting interference effects among intermediate states [3,8,10]. In this Letter we describe a time-dependent DP analysis of B 0 → K + K − K 0 decay from which we extract the values of the CP violation parameters A CP and β eff by taking into account the complex amplitudes describing the entire B 0 and B 0 Dalitz plots. We first extract the values of the parameters of the amplitude model, and measure the average CP asymmetry in B 0 → K + K − K 0 decay over the entire DP. Using this model, we then measure the CP asymmetries for the φK 0 and f 0 K 0 decay channels, from a "low-mass" analysis of events with m K + K − < 1.1 GeV/c 2 . Finally, we perform a "highmass" analysis to determine the average CP asymmetry for events with m K + K − > 1.1 GeV/c 2 .
The data sample for this analysis was collected with the BABAR detector [12] at the PEP-II asymmetric-energy e + e − collider at SLAC. Approximately 383 × 10 6 BB pairs recorded at the Υ (4S) resonance were used.
For each fully reconstructed B 0 meson (B CP ), we use the remaining tracks in the event to reconstruct the decay vertex of the other B meson (B tag ), and to identify its flavor q tag [4]. For each event we calculate the difference ∆t ≡ t CP − t tag between the proper decay times of the B CP and B tag mesons, and its uncertainty σ ∆t .
We characterize B 0 (+−) and B 0 (00) candidates using two kinematic variables: the beam-energy-substituted mass m ES and the energy difference ∆E [8]. The signal region (SR) is defined as m ES > 5.26 GeV/c 2 , and |∆E| < 0.06 GeV for B 0 (+−) , or −0.120 < ∆E < 0.06 GeV for B 0 (00) . For B 0 (L) the SR is defined by −0.01 < ∆E < 0.03 GeV [8], and the missing momentum for the entire event is required to be consistent with the calculated K 0 L laboratory momentum.
The main source of background is continuum e + e − → qq (q = u, d, s, c) events. We use event-shape variables to exploit the jet-like structure of these events in order to remove much of this background [8].
We perform an unbinned maximum likelihood fit to the selected K + K − K 0 events using the likelihood function defined in Ref. [8]. The probability density function (PDF), P i , is given by where i = (signal, continuum, BB background), and R is the ∆t resolution function [4]. For B 0 (L) , P(m ES ) is not used. P Low is a PDF used only in the low-mass fit, which depends on the event-shape variables and, for B 0 (L) only, the missing momentum in the event [8]. We characterize B 0 (B 0 ) events on the DP in terms of m K + K − and cos θ H , the cosine of the helicity angle between the K + (K − ) and the K 0 (K 0 ) in the rest frame of the K + K − system. The DP PDF for signal events is where dΓ is the time-and flavor-dependent decay rate over the DP, ε is the efficiency, and J is the Jacobian of the transformation to our choice of DP coordinates.
The time-and flavor-dependent decay rate is where τ and ∆m d are the lifetime and mixing frequency of the B 0 meson, respectively [14].
B 0 decay as a sum of isobar amplitudes [14], where the minus signs are associated with the A, the parameters c r and ϕ r are the magnitude and phase of the amplitude of component r, and we allow for different isobar coefficients for B 0 and B 0 decays through the asymmetry parameters b r and δ r . Our isobar model includes resonant amplitudes φ, f 0 , χ c0 (1P ), and X 0 (1550) [15,16]; non-resonant terms; and incoherent terms for B 0 decay to D − K + and D − s K + . For each resonant term, the function f r = F r × T r × Z r describes the dynamical properties, where F r is the Blatt-Weisskopf centrifugal barrier factor for the resonance decay vertex [17], T r is the resonant mass-lineshape, and Z r describes the angular distribution in the decay [18]. The barrier factor F r = 1/ 1 + (Rq) 2 [17] for the φ, where q is the K + momentum in the φ rest frame and R = 1.5 GeV −1 ; F r = 1 for the scalar resonances. For φ decay Z r ∼ q · p, where p is the momentum of the K 0 in the φ rest frame, while Z r = 1 for the scalar decays. We describe the φ, X 0 (1550), and χ c0 (1P ) with relativistic Breit-Wigner lineshapes [14]. For the φ and χ c0 (1P ) parameters we use average measurements [14]. For the X 0 (1550) resonance, we use parameters from our analysis of the B + → K + K − K + decay [15]. The f 0 resonance is described by a coupled-channel amplitude [19], with the parameter values of Ref. [20].
We include three non-resonant (NR) amplitudes parameterized as f NR,k = exp(−αm 2 k ), where the parameter α = 0.14 ± 0.01 c 4 / GeV 2 is taken from measurements of B + → K + K − K + decays with larger signal samples [15,16]. We include a complex isobar coefficient PDFs for qq background in B 0 → K + K − K 0 S are modeled using events in the region 5.2 < m ES < 5.26 GeV/c 2 . The region 0.02 < ∆E < 0.04 GeV is used for B 0 (L) . Simulated BB events are used to define BB background PDFs. We use two-dimensional histogram PDFs to model the DP distributions for qq and BB backgrounds.
We compute the CP asymmetry parameters for component r from the asymmetries in amplitude (b r ) and phase (δ r ) given in Eq. (4). The rate asymmetry is and β eff ,r = β + δ r is the phase asymmetry. The selection criteria yield 3266 B 0 (+−) , 1611 B 0 (00) , and 27513 B 0 (L) candidates which we fit to obtain the event yields, the isobar coefficients of the DP model, and the CP asymmetry parameters averaged over the DP. The parameters b r and δ r are constrained to be the same for all model components, so in this case A CP,r = A CP and β eff ,r = β eff . We find 947 ± 37 B 0 (+−) , 144 ± 17 B 0 (00) , and 770 ± 71 B 0 (L) signal events. Isobar coefficients and fractions are reported in Table I, and CP asymmetry results are summarized in Table II. The fraction F r for resonance r is computed as in Ref. [15]. Note that there is a ±π rad ambiguity in the χ c0 (1P )K 0 phase. In Fig. 1, we plot twice the change in the negative logarithm of the likelihood as a function of β eff . We find that the CP -conserving case of β eff = 0 is excluded at 4.8σ (5.1σ), including statistical and systematic errors (statistical errors only). Also, the interference between CP -even and CP -odd amplitudes leads to the exclusion of the β eff solution near π/2 − β at 4.5σ (4.6σ).  We also measure CP asymmetry parameters for events with m K + K − < 1.1 GeV/c 2 . In this region, we find 1359 B 0 (+−) , 348 B 0 (00) , and 7481 B 0 (L) candidates. The fit yields 282 ± 20, 37 ± 9 and 266 ± 36 signal events, respectively. The most significant contributions in this region are from φK 0 and f 0 K 0 decays, with a smaller contribution from the low-mass tail from non-resonant decays. In this fit we vary the amplitude asymmetries b r and δ r for the φ and f 0 , while the other components are fixed to the SM expectations of β eff = 0.370 rad and A CP = 0 [21]. We also vary the isobar coefficient for the φ, while fixing the others to the results from the whole DP fit. There are two solutions with likelihood difference of only ∆ log L = 0.1. Solution (1) is consistent with the SM, while in Solution (2) β eff for the f 0 differs significantly from the SM value (Table II). The solutions also differ significantly in the values of the φ isobar coefficient. There is also a mathematical ambiguity of ±π rad on β eff for the φ, with a corresponding change of ±π rad in the solution for ϕ φ . This ambiguity is present for both solutions. The fit correlation between the φ and f 0 in δ r is 0.71 [22].
Finally, we perform a fit to extract the average CP asymmetry parameters in the high-mass region. In the 2384 B 0 (+−) , 1406 B 0 (00) , and 20032 B 0 (L) selected events with m K + K − > 1.1 GeV/c 2 , we find signal yields of 673± 31, 87 ± 14 and 462 ± 56 events, respectively; the CP asymmetry results are shown in Table II. We find that for this fit the CP -conserving case of β eff = 0 is excluded at 5.1σ, including statistical and systematic errors. Figure 2 shows distributions of the DP variables m K + K − and cos θ H obtained using the method described in [23]. Figure 3 shows the ∆t-dependent asymmetry between B 0 -and B 0 -tagged events.  (1) φK 0 −0.08 ± 0.18 ± 0.04 0.11 ± 0.14 ± 0.06 (1) f0K 0 0.41 ± 0.23 ± 0.07 0.14 ± 0.15 ± 0.05 (2) φK 0 −0.11 ± 0.18 0.10 ± 0.13 (2) f0K 0 −0.20 ± 0.31 3.09 ± 0.19 Systematic errors on the CP -asymmetry parameters are listed in Table III. The fit bias uncertainty includes effects of detector resolution and possible correlations among the fit variables determined from full-detector simulations. We also account for uncertainties due to the isobar model: experimental precision of resonance parameter values; alternate X 0 (1550) parameter values [16]; and, in the low-and high-mass fits, the statistical uncertainties on the isobar coefficients determined in the fit to the whole DP. Other uncertainties common to many BABAR time-dependent analyses, including those due to fixed PDF parameters, and possible CP asymmetries in the BB background are also taken into account [8,24]. Uncertainties due to fixed PDF parameters are evaluated by shifting the fixed parameters and refitting the data. As a cross-check, we perform the analysis using B 0 (+−) alone and find results consistent with those in Table II. In summary, in a sample of 383 × 10 6 BB meson pairs we simultaneously analyze the DP distribution and measure the time-dependent CP asymmetries for B 0 → K + K − K 0 decays. The values of β eff and A CP are consistent with the SM expectations of β ≃ 0.370 rad, A CP ≃ 0 [21]. The signficance of CP violation is 4.8σ, and we reject the solution near π/2 − β at 4.5σ. We also measure CP asymmetries for the decays B 0 → φK 0 and B 0 → f 0 K 0 , where we find β eff lower than the SM expectation by about 2σ. The CP parameters in the high-mass region are compatible with SM expectations, and we observe CP violation at the level of 5.1σ.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality.