Search for B Meson Decays to eta' eta' K

We describe searches for decays of B mesons to the charmless final states eta' eta' K. The data consist of 228 million B Bbar pairs produced in e+ e- annihilation, collected with the BaBar detector at the Stanford Linear Accelerator Center. The 90% confidence level upper limits for the branching fractions are Br(B0->eta' eta' K0)<31 10^{-6} and Br(B+->eta' eta' K+)<25 10^{-6}.

We describe searches for decays of B mesons to the charmless final states η ′ η ′ K. The data consist of 228 million BB pairs produced in e + e − annihilation, collected with the BABAR detector at the Stanford Linear Accelerator Center. The 90% confidence level upper limits for the branching fractions are B(B 0 → η ′ η ′ K 0 ) < 31 × 10 −6 and B(B + → η ′ η ′ K + ) < 25 × 10 −6 .
PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er The phenomenon of CP violation has been extensively studied in recent years at the B factories. The observations of mixing-induced CP violation in B 0 → J/ψK 0 S decays [1] and of direct CP violation both in the neutral kaon system [2] and in B 0 → K + π − decays [3] are in agreement with expectations in the Standard Model (SM) of electroweak interactions [4]. Some possible evidence of disagreement between experimental results and SM expectations is found in B decay modes dominated by penguin amplitudes, for example in the decay B 0 → η ′ K 0 S [5]. Further important information about CP violation and hadronic B decays can be provided by the measurements of branching fractions and time-dependent CP asymmetries in B decays to three-body final states containing two identical neutral particles of spin zero and another spin zero neutral particle [6]. An example of such a decay is B 0 → K 0 S K 0 S K 0 S , which has already been observed [7]. Since the branching fractions for the decays B → η ′ K are large [5], another example which might be particularly interesting for time-dependent CP violation analysis is the mode B 0 → η ′ η ′ K 0 .
We present the results of searches for the exclusive decay modes B + → η ′ η ′ K + [8] and B 0 → η ′ η ′ K 0 , which are studied for the first time. The results are based on data collected with the BABAR detector [9] at the PEP-II asymmetric-energy e + e − collider [10] located at the Stanford Linear Accelerator Center. The analyses use an integrated luminosity of 207 fb −1 , corresponding to 228 million BB pairs, recorded at the Υ (4S) resonance (center-of-mass energy √ s = 10.58 GeV). Charged particles from the e + e − interactions are detected, and their momenta measured, by a combination of five layers of double-sided silicon microstrip detectors and a 40-layer drift chamber, both operating in the 1.5 -T magnetic field of a superconducting solenoid. Photons and electrons are identified with a CsI(Tl) crystal electromagnetic calorimeter (EMC). Further charged particle identification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting, ring-imaging Cherenkov detector (DIRC) covering the central region. A K/π separation of better than four standard deviations (σ) is achieved for momenta below 3 GeV/c, decreasing to 2.5 σ at the highest momenta in the B decay final states.
The B daughter candidates are reconstructed through their decays η ′ → ηπ + π − (η ′ ηππ ), where η → γγ, and We require the laboratory energy of the photons to be greater than 30 MeV for η ′ ηππ and 200 MeV for η ′ ργ . We impose the following requirements on the invariant mass (in MeV/c 2 ) of the candidate final states: 490 < m(γγ) < 600 for η, 930 < m(π + π − η) < 990 for η ′ ηππ , 930 < m(π + π − γ) < 990 for η ′ ργ , and 510 < m(π + π − ) < 1000 for ρ 0 . Secondary tracks in η ′ candidates are rejected if their PID signatures from the DIRC and dE/dx are consistent with those for protons, kaons, or electrons. Charged K candidates are selected if their PID signatures from the DIRC and dE/dx are consistent with that for kaons. Candidate K 0 S decays are formed from pairs of oppositely charged tracks with 486 < m(π + π − ) < 510 MeV/c 2 , a decay vertex χ 2 probability larger than 0.001, and a reconstructed decay length greater than three times its uncertainty.
We reconstruct the B meson candidate by combining two η ′ candidates and a charged or neutral kaon. We consider only cases with two η ′ ηππ candidates or a η ′ ηππ and a η ′ ργ . We do not consider the case with two η ′ Backgrounds arise primarily from random combinations of particles in continuum e + e − → qq events (q = u, d, s, c). We reduce these with requirements on the angle θ T between the thrust axis of the B candidate in the Υ (4S) frame and that of the rest of the charged tracks and neutral calorimeter clusters in the event. The distribution is sharply peaked near | cos θ T | = 1 for qq jet pairs, and nearly uniform for B meson decays. The requirement is | cos θ T | < 0.9 (| cos θ T | < 0.7 for the charged mode with η ′ ργ ). We define the decay angle θ ρ dec for the ρ meson as the angle between the momenta of a daughter particle and the η ′ , measured in the ρ meson rest frame. We require for the η ′ ργ decay | cos θ ρ dec | < 0.9. Events are retained only if they contain one or more charged tracks that are not used in the candidate decay.
We obtain the signal event yields from unbinned extended maximum likelihood fits. The input observables I: Fitted signal yield, fit bias, detection efficiency ǫ (%), daughter branching fraction product Bi, significance S (σ) , measured branching fraction B with statistical error for each decay mode. For the combined measurements we give the significance (with systematic uncertainties included) and the branching fraction with statistical and systematic uncertainty (in parentheses the 90% CL upper limit).

Mode
Yield are ∆E, m ES , the invariant masses of the two η ′ ηππ , a Fisher discriminant F [11], and the variable | cos θ ρ dec |. The Fisher discriminant F combines four variables: the angles, with respect to the beam axis, of the B momentum and the B thrust axis (in the Υ (4S) frame), and the zeroth and second angular moments L 0,2 of the energy flow about the B thrust axis. The moments are defined by L j = i p i × |cos θ i | j , where θ i is the angle, with respect to the B thrust axis, of track or neutral cluster i, and p i is its momentum. The sum excludes the B candidate daughters.
The average number of candidates found per selected event is in the range 1.5 to 1.8, depending on the final state. We choose the candidate with the highest B vertex χ 2 probability. From simulated events we find that this algorithm selects the correct candidate in about 82% of the events containing multiple candidates, and introduces negligible bias.
We use Monte Carlo (MC) simulation to estimate backgrounds from other B decays, including final states with and without charm. These contributions are negligible for the η ′ ηππ modes. For η ′ ργ we include a BB component in the fit. We consider four categories in the likelihood fit: signal, self-cross feed (SCF) signal, defined as a signal candidate where one B candidate daughter has been exchanged with a particle from the rest of the event, and continuum and BB backgrounds.
For each event i and category j, the likelihood function is where N is the number of candidates, n j is the number of events in category j, and P j (x i ) is the corresponding probability density function (PDF), evaluated with the observables x i of the ith event. Since correlations among the observables are small, we take each P as the product of the PDFs for the separate variables. We determine the PDF parameters from Monte Carlo simulation [12] of the signal, SCF, and BB background, while using m ES and ∆E sideband data (5.25 < m ES < 5.27 GeV/c 2 , 0.1 < |∆E| < 0.2 GeV) to model the PDFs of continuum background.
We parameterize each of the functions P(m ES ), P(∆E), P(m η ′ ), and P(m η ) for signal and SCF with two Gaussian distributions. The m ES distribution for BB and continuum background is described by a threshold function [13]. The ∆E distribution for BB and continuum background and the | cos θ ρ dec | distributions are represented by linear or quadratic functions. The distributions of m η ′ and m η in BB and continuum background are described by a Gaussian plus linear function. The distribution of F is described with an asymmetric Gaussian function with a different width below and above the peak. We allow the continuum background PDF parameters to vary in the fit. Large control samples of B → D(Kππ)π decays are used to verify the simulated ∆E and m ES resolution.
In Table I we show the fitted signal yield, the fit bias in events, the detection efficiency, the product of daughter branching fractions for each decay mode, the significance S (σ), and the measured branching fraction. We compute the branching fractions from the fitted signal event yields, detection efficiencies, daughter branching fractions, and number of produced B mesons, assuming equal production rates of charged and neutral B meson pairs. We correct the yield for a fit bias estimated with the simulations. We combine results from different sub-decay modes by adding the values of −2 ln L , taking proper account of the correlated and uncorrelated systematic uncertainties. We report the statistical significance and branching fraction for the individual decay channels. For the combined measurements we also report the 90% confidence level (CL) upper limit. The statistical error on the signal yield is the change in the central value when the quantity −2 ln L increases by one unit from its minimum value. The significance is the square root of the difference between the value of −2 ln L (with systematic uncertainties included) for zero signal and the value at its minimum. The 90% CL upper limit is taken to be the branching fraction below which lies 90% of the total likelihood integral in the positive branching fraction region. Figure 1 shows projections of charged and neutral η ′ η ′ K candidates onto m ES and ∆E for the subset of candidates for which the signal likelihood (computed without the variable plotted) exceeds a mode-dependent threshold that optimizes the sensitivity. The goodness-of-fit is further demonstrated by the distribution of the likelihood ratio between the likelihood L(Sg) for the signal category and the sum of the likelihoods for signal and all background categories L(Bg) for data and for simulation generated from the PDF model, shown in Figure 2. We see good agreement between the model and the data. The background is concentrated near zero, while any signal would appear in a peak near one.
The main sources of systematic errors include uncertainties in the PDF parameters and the maximum likelihood fit bias. For the signal, the uncertainties in the PDF parameters are estimated by comparing MC and data in control samples. Varying the signal PDF parameters within these uncertainties, we estimate yield uncertainties up to 1 event, depending on the mode. The uncertainty from the fit bias is taken as half the correction itself (up to 4 events). Uncertainties in our knowledge of the efficiency, found from auxiliary studies, include 0.8% × N t and 1.5% × N γ , where N t and N γ are the numbers of tracks and photons, respectively, in the B candidate. A systematic uncertainty of 1.8% is assigned to single photon reconstruction efficiency. There is a systematic error of 2.1% in the efficiency of K 0 S reconstruction and 3.0% per η in the efficiency of η reconstruction. The uncertainty in the total number of BB pairs in the data sample is 1.1%. Published data [14] provide the uncertainties in the B daughter product branching fractions (3.5-4.9%).
In conclusion, we have measured 90% CL upper limits for the branching fractions: The on-resonance data are shown as points with error bars; the sum of all simulated background samples is shown by the shaded (dashed-line) histograms; and the sum of these backgrounds plus the signal from the PDF model are given by the open (solid-line) histograms. and B(B + → η ′ η ′ K + ) < 25×10 −6 . From these results we conclude that no CP study is feasible in these B decays with the currently available data samples.
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