Observation of the Rare Decay B0 -->KsK+/-pi-/+

We report an analysis of charmless hadronic decays of neutral B mesons to the final state KsK+/-pi-/+, using a data sample of (465 +/- 5) x 10^6 BB-bar events collected with the BABAR detector at the Y(4S) resonance. We observe an excess of signal events with a significance of 5.2 standard deviations including systematic uncertainties and measure the branching fraction to be BF(B0 -->KsK+/-pi-/+) = (3.2 +/- 0.5 +/- 0.3) x 10^-6, where the uncertainties are statistical and systematic, respectively.

We report an analysis of charmless hadronic decays of neutral B mesons to the final state K 0 S K ± π ∓ , using a data sample of (465 ± 5) × 10 6 BB events collected with the BABAR detector at the Υ (4S) resonance. We observe an excess of signal events with a significance of 5.2 standard deviations including systematic uncertainties and measure the branching fraction to be B B 0 → K 0 S K ± π ∓ = (3.2 ± 0.5 ± 0.3) × 10 −6 , where the uncertainties are statistical and systematic, respectively. Charmless decays of B mesons to hadronic final states containing an even number of kaons are suppressed in the standard model (SM). Decays of this type mainly proceed via the b → d "penguin" transition, involving a virtual loop, and hence are sensitive to potential new physics contributions since the presence of new particles in the loops can produce deviations from SM expecta-tions. In recent years, there has been a surge of new results on these decays: B 0 → K 0 S K 0 S and B + → K 0 S K + have been observed [1,2], and there is evidence for the related vector-vector final states [3][4][5]. Only upper limits on the corresponding pseudoscalar-vector final states exist: B(B 0 → K 0 K * 0 ) + B(B 0 → K 0 K * 0 ) < 1.9 × 10 −6 [6] and B(B + → K + K * 0 ) < 1.1×10 −6 [7], both at 90 % con-fidence level (unless explicitly stated otherwise we use the symbol K * to denote the K * (892) resonance and the inclusion of charge conjugate modes is implied). Note that decays with additional suppression in the SM, such as B 0 → K ( * )+ K ( * )− , which are expected to proceed via annihilation amplitudes, have not been observed [2, 3, [8][9][10][11][12][13].
Since the vector resonances involved have nonnegligible widths, the pseudoscalar-vector decays are best studied using Dalitz plots of the three-body KKπ final states. In the three-body channels, contributions from suppressed b → u tree amplitudes are expected to be important, in addition to the b → d penguin amplitudes. Recent investigations of three-body channels suggest that additional resonances are present. Most notably, the B + → K + K − π + channel exhibits an unexpected peak near 1.5 GeV/c 2 in the K + K − invariant-mass spectrum, which accounts for approximately half of the total event rate [14]. We call this peak, with unknown spin and isospin quantum numbers, the f X (1500). The lack of a f X (1500) signal in B + → K 0 S K 0 S π + decays implies that the f X (1500) does not have even spin if isospin is conserved in the decay [15]. A search for an isospin partner to the f X (1500) that decays to K 0 K + and which could be produced recoiling against a pion in B decay could help to clarify the nature of this resonance.
In this paper, we present the results of a search for the three-body decay B 0 → K 0 S K ± π ∓ , including intermediate two-body modes that decay to this final state but do not contain charm quarks. No decays to this final state have been observed as yet. The best available upper limit on the inclusive branching fraction is B(B 0 → K 0 K ± π ∓ ) < 18 × 10 −6 [16]. There appears to be no explicit prediction for the inclusive branching fraction of B 0 → K 0 S K ± π ∓ . Some theoretical predictions exist, however, for the relevant resonant modes. Expected branching fractions for B 0 → (K * 0 K 0 + K * 0 K 0 ) and B 0 → K * ± K ∓ are in the range (0.2-2.0) × 10 −6 and (0.2-1.0) × 10 −7 , respectively [17][18][19][20][21][22][23][24]. Extensions to the SM can yield significantly larger branching fractions. For instance, in supersymmetric models with R-parity violation, the branching fraction for B 0 → (K * 0 K 0 + K * 0 K 0 ) could be as large as 10 −5 [25].
The data used in the analysis, collected with the BABAR detector [26] at the PEP-II asymmetric energy e + e − collider at SLAC, consist of an integrated luminosity of 424 fb −1 recorded at the Υ (4S) resonance ("onpeak") and 44 fb −1 collected 40 MeV below the resonance ("off-peak"). The on-peak data sample contains (465 ± 5) × 10 6 BB events.
We reconstruct B 0 → K 0 S K ± π ∓ decay candidates by combining a K 0 S candidate with one charged kaon and one oppositely charged pion candidate. The K ± and π ± candidates are required to have a minimum transverse momentum of 50 MeV/c and to be consistent with having originated from the interaction region. Identifi-cation of charged kaons and pions is accomplished with energy-loss information from the tracking subdetectors, and the Cherenkov angle and number of photons measured by a ring-imaging Cherenkov detector. We distinguish kaons from pions by applying criteria to the product of the likelihood ratios determined from these individual measurements. The efficiency for kaon selection is approximately 80 % including geometrical acceptance, while the probability of misidentification of pions as kaons is below 5 % up to a laboratory momentum of 4 GeV/c. A K 0 S → π + π − candidate is formed from a pair of oppositely charged tracks (with the pion mass hypothesis assumed) having an invariant mass that lies within 15 MeV/c 2 of the nominal K 0 S mass [27], corresponding to 5 times the K 0 S mass resolution. We require the ratio of the measured K 0 S decay length and its uncertainty to be greater than 20, the cosine of the angle between the line connecting the B and K 0 S decay vertices and the K 0 S momentum vector to be greater than 0.999, and the K 0 S vertex fit probability to be greater than 10 −6 .
To suppress the dominant background contribution, which arises from continuum e + e − → qq (q = u, d, s, c) events, we employ a Fisher discriminant that combines four variables. These are the ratio of the second to the zeroth order momentum-weighted angular moment [28], the absolute value of the cosine of the angle between the B direction and the beam axis, the magnitude of the cosine of the angle between the B thrust axis and the beam axis, and the proper time difference between the decays of the two B mesons divided by its statistical uncertainty. The first three quantities are calculated in the center-of-mass (CM) frame.
In addition to the Fisher output (F ), we distinguish signal from background events using two kinematic variables: the difference ∆E between the CM energy of the B candidate and √ s/2, and the beam-energy-substituted where √ s is the total CM energy and p B is the momentum of the candidate B meson in the CM frame. The signal m ES distribution peaks near the B mass with a resolution of about 2.6 MeV/c 2 , while its ∆E distribution peaks at zero with a resolution of approximately 20 MeV. We select signal candidates that satisfy 5.272 < m ES < 5.286 GeV/c 2 , |∆E| < 0.075 GeV, and F > −0.145. The requirement on F removes approximately 70 % of continuum background while retaining 90 % of signal events. Another source of background arises from B decays, mostly involving intermediate charm or charmonium mesons, or charmless final states that are misreconstructed. We exclude B candidates that have two-body mass combinations in any of the following invariant-mass ranges: 1.82 < m(K 0 S K ± ) < 2.04, 1.81 < m(K 0 S π ∓ ) < 1.91, 1.83 < m(K ± π ∓ ) < 1.90, 3.06 < m(K ± π ∓ ) < 3.17, and 3.66 < m(K ± π ∓ ) < 3.73 (all in units of GeV/c 2 ). These ranges reject decays from D + and D + s , D + , D 0 , J/ψ , and ψ(2S) mesons, respectively. Charmo-nium contributions result mainly from the leptonic decays of J/ψ and ψ(2S), where one lepton is misidentified as a charged pion and the other as a kaon.
The efficiency for signal events to pass all the selection criteria is determined as a function of position in the Dalitz plot. Using a Monte Carlo (MC) simulation in which events uniformly populate the phase-space, we obtain an average efficiency of 20 %, though values as high as double (as low as half) that value are found near the center (corners) of the Dalitz plot.
An average of 1.1 B candidates is found per selected event. In events with multiple candidates we choose the one with the highest B vertex fit probability. We verify that this procedure does not bias our fit variables. In some signal events, the B candidate is misreconstructed due to one track being replaced with a track from the rest of the event. The fraction of such events is below 2 % in the phase-space MC, but is closer to 5 % in MC samples where the events populate the K * bands. Misreconstructed signal events are considered as a part of the signal component in the fit described below. We assign a systematic error to account for the uncertainty in the rate of these events, which is related to the unknown Dalitz-plot distribution of the B 0 → K 0 S K ± π ∓ decay. We study residual background contributions from BB events that survive the invariant-mass exclusion requirements described earlier, using MC simulations. It is found that these events can be combined into four categories based on their shapes in m ES and ∆E. The first category (BB 1 ) comprises B 0 → η ′ K 0 S , η ′ → ρ 0 γ and misreconstructed B 0 → D − π + , D − → K 0 S K − decays and has a broad peak in m ES and a nonpeaking ∆E shape. The second and third categories (BB 2 and BB 3 ) represent the charmless decays B 0 → K 0 S K + K − and B 0 → K 0 S π + π − , where a kaon or a pion is misidentified leading to a ∆E distribution that peaks with negative or positive mean, respectively. The MC simulations of these decays are based on our recent studies of their Dalitz plot distributions [29,30]. The fourth category (BB 4 ) contains the remainder of the BB background and is mainly combinatorial in nature. Based on the MC-derived efficiencies, total number of BB events, and known branching fractions [27,31], we expect 25, 173, 215, and 668 events from the four BB background categories, respectively.
To obtain the B 0 → K 0 S K ± π ∓ signal yield, we perform an unbinned extended maximum likelihood fit to the candidate events using three input variables: m ES , ∆E, and F . These variables are found to be largely uncorrelated -the maximum correlation is between the signal m ES and ∆E distributions and is about 13 %. For each component j (signal, qq background, and the four BB background categories), we define a probability density function (PDF) where i denotes the event index. The extended likelihood function is given as where n j(k) is the yield of the event category j(k).
For the signal component, the m ES and ∆E distributions are each parametrized by the sum of two Gaussian functions, while the F distribution is described by a bifurcated Gaussian function with a small admixture from the sum of two Gaussians. We fix the shape parameters to the values obtained from the B 0 → K 0 S K ± π ∓ phase-space MC sample, after adjusting them to account for possible differences between data and MC simulations determined with a control sample of B 0 → D − π + , D − → K 0 S π − decays. For the continuum background, we use an ARGUS function [32] to parametrize the m ES shape and a linear function for ∆E. The continuum Fisher shape is modeled with a function that is composed of a Gaussian tail with relative fraction 99.6 % (large component) and a small Gaussian with different mean and width values. This shape provides a good description of the offpeak Fisher distribution, as well as of the corresponding MC distribution. One-dimensional histograms are used as nonparametric PDFs to represent all three fit variables for the four BB background components.
The free parameters of our fit are the yields of signal, BB 2 , BB 3 , and continuum background together with the slope of the continuum ∆E PDF and the mean and width of the large Gaussian component of the continuum F PDF. The ARGUS ξ parameter and parameters of the small Gaussian component of the continuum Fisher function are fixed to values determined from candidates selected in the off-peak data sample with a looser requirement on m ES . The yields of BB 1 and BB 4 , and all shape parameters of the four BB background categories are fixed to the values determined from MC simulations.
We cross check our analysis procedure by removing the requirements that reject backgrounds from B decays involving charm mesons, instead selecting regions of the Dalitz plot dominated by intermediate charm We then apply our fit to find the yields for the B 0 → D − π + and B 0 → D − K + channels. We find values consistent with the expectations based on world-average product branching fractions [27] within statistical uncertainties.
Applying the fit method described above to the 14 276 selected candidate B 0 → K 0 S K ± π ∓ events, we find 262 ± 47 signal events. The fitted yields of the BB 2 and BB 3 categories are 199 ± 51 and 262 ± 55, respectively, consistent with the MC-based expectations. The fitted values of all other free parameters of the fit are also consistent with expectations based on studies of control samples and MC simulations. The results of the fit are shown in Fig. 1. The statistical significance of the signal yield, given by the square root of the difference between twice the value of negative log likelihood obtained assuming zero signal events to that at its minimum, is 6.0 σ. Including systematic uncertainties (discussed below), the significance is 5.2 σ.
The B 0 → K 0 S K ± π ∓ branching fraction is determined from the result of the fit by calculating signal probabilities for each candidate event with the s Plot technique [33]. These are divided by event-by-event efficiencies that take the Dalitz-plot position dependence into account, and summed to obtain an efficiency-corrected signal yield of 1326 ± 207 events. We further correct for the effect of the charm and charmonium vetoes (estimated using a range of MC samples with different Dalitz-plot distributions), and divide by the total number of BB events in the data sample assuming equal production of B 0 B 0 and B + B − at the Υ (4S). The result for the branching fraction is B B 0 → K 0 S K ± π ∓ = (3.2 ± 0.5 ± 0.3)×10 −6 , where the first error is statistical and the second is systematic.
We find the systematic error to be due to uncertainties in the signal PDFs (5.2 %), including possible data-MC differences in the signal PDF shapes evaluated using the control sample of B 0 → D − π + , D − → K 0 S π − decays; uncertainties in the background PDFs (2.5 %), including effects due to the fixed values of some of the qq PDF parameters (recall that the parametrization used is validated with off-peak and MC samples and that the most critical parameters are floated in the fit to data; the uncertainties are evaluated by varying the fixed parameters) and due to the fixed content of the histograms used to describe the BB background PDFs; potential fit biases, studied using ensembles of simulated experiments where continuum events are drawn from the PDF shapes and signal and BB background events are randomly extracted from MC samples (1.1 %); uncertainties in the efficiency due to tracking (0.8 %), K 0 S selection (0.9 %), and particle identification (2.8 %); and the error in the number of BB events (1.1 %). We assign two systematic uncertainties to account for the nonuniform Dalitz plot structure of the signal, both of which are estimated from MC simulations with different resonant contributions: uncertainty in the fraction of misreconstructed events (3.0 %) and uncertainty in the correction due to vetoes (4.1 %). Other sources of systematic uncertainty, including the fixed yields of BB 1 and BB 4 , are found to be negligible (recall that the fitted yields of BB 2 and BB 3 are consistent with expectation).
In Fig. 2 we show the efficiency-corrected Dalitz plot for signal decays, obtained using event-by-event signal probabilities. We verify that this technique correctly reconstructs the signal Dalitz plot distribution using MC simulations in which the B 0 → K 0 S K ± π ∓ events contain different structures. There appears to be some structure in the K * 0 region at low K ± π ∓ invariant mass, and an excess of events at low K 0 S K ± mass with a highly asymmetric helicity angle distribution. Quantitative statements concerning the content of the Dalitz plot require a dedicated amplitude analysis, which is beyond the scope of the present study. However it appears that there is no major contribution from an isospin partner of the f X (1500) decaying to K 0 S K + , which contrasts to the clear signal seen in B + → K + K − π + decays [14].
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. This work is supported by DOE    S K ± π ∓ decays, obtained with the sP lot technique [33]. Bins with negative content appear empty as do regions corresponding to the charm and charmonium vetoes. The area of each box is proportional to the number of weighted events in that bin; the largest bin corresponds to 12 events.