Measurement of CP Asymmetries in B 0 → K 0 S K 0 S K 0 S Decays

B. Aubert, M. Bona, D. Boutigny, Y. Karyotakis, J. P. Lees, V. Poireau, X. Prudent, V. Tisserand, A. Zghiche, J. Garra Tico, E. Grauges, L. Lopez, A. Palano, G. Eigen, I. Ofte, B. Stugu, L. Sun, G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, Y. Groysman, R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, D. Lopes Pegna, G. Lynch, L. M. Mir, T. J. Orimoto, M. Pripstein, N. A. Roe, M. T. Ronan, ∗ K. Tackmann, W. A. Wenzel, P. del Amo Sanchez, C. M. Hawkes, A. T. Watson, T. Held, H. Koch, B. Lewandowski, M. Pelizaeus, T. Schroeder, M. Steinke, J. T. Boyd, J. P. Burke, W. N. Cottingham, D. Walker, D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom, C. Hearty, N. S. Knecht, T. S. Mattison, J. A. McKenna, A. Khan, M. Saleem, L. Teodorescu, V. E. Blinov, A. D. Bukin, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu Todyshev, M. Bondioli, M. Bruinsma, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, D. P. Stoker, S. Abachi, C. Buchanan, S. D. Foulkes, J. W. Gary, F. Liu, O. Long, B. C. Shen, L. Zhang, H. P. Paar, S. Rahatlou, V. Sharma, J. W. Berryhill, C. Campagnari, A. Cunha, B. Dahmes, T. M. Hong, D. Kovalskyi, J. D. Richman, T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, T. Schalk, B. A. Schumm, A. Seiden, D. C. Williams, M. G. Wilson, L. O. Winstrom, E. Chen, C. H. Cheng, A. Dvoretskii, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter, G. Mancinelli, B. T. Meadows, K. Mishra, M. D. Sokoloff, F. Blanc, P. C. Bloom, S. Chen, W. T. Ford, J. F. Hirschauer, A. Kreisel, M. Nagel, U. Nauenberg, A. Olivas, J. G. Smith, K. A. Ulmer, S. R. Wagner, J. Zhang, A. Chen, E. A. Eckhart, A. Soffer, W. H. Toki, R. J. Wilson, F. Winklmeier, Q. Zeng, D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, J. Merkel, A. Petzold, B. Spaan, K. Wacker, T. Brandt, V. Klose, H. M. Lacker, W. F. Mader, R. Nogowski, J. Schubert, K. R. Schubert, R. Schwierz, J. E. Sundermann, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, Ch. Thiebaux, M. Verderi, P. J. Clark, W. Gradl, F. Muheim, S. Playfer, A. I. Robertson, Y. Xie, M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, A. Cecchi, G. Cibinetto, P. Franchini, E. Luppi, M. Negrini, A. Petrella, L. Piemontese, E. Prencipe, V. Santoro, F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Pacetti, P. Patteri, I. M. Peruzzi, † M. Piccolo, M. Rama, A. Zallo, A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge, S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, S. Tosi, K. S. Chaisanguanthum, M. Morii, J. Wu, R. S. Dubitzky, J. Marks, S. Schenk, U. Uwer, D. J. Bard, P. D. Dauncey, R. L. Flack, J. A. Nash, M. B. Nikolich, W. Panduro Vazquez, P. K. Behera, X. Chai, M. J. Charles, U. Mallik, N. T. Meyer, V. Ziegler, J. Cochran, H. B. Crawley, L. Dong, V. Eyges, W. T. Meyer, S. Prell, E. I. Rosenberg, A. E. Rubin, A. V. Gritsan, C. K. Lae, A. G. Denig, M. Fritsch, G. Schott, N. Arnaud, J. Béquilleux, M. Davier, G. Grosdidier, A. Höcker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot, S. Rodier, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, A. Stocchi, W. F. Wang, G. Wormser, D. J. Lange, D. M. Wright, C. A. Chavez, I. J. Forster, J. R. Fry, E. Gabathuler, R. Gamet, D. E. Hutchcroft, D. J. Payne, K. C. Schofield, C. Touramanis, A. J. Bevan, K. A. George, F. Di Lodovico, W. Menges, R. Sacco, G. Cowan, H. U. Flaecher, D. A. Hopkins, P. S. Jackson, T. R. McMahon, F. Salvatore, A. C. Wren, D. N. Brown, C. L. Davis, J. Allison, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, J. I. Yi, J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, J. M. Tuggle, G. Blaylock, C. Dallapiccola, S. S. Hertzbach, X. Li, T. B. Moore, E. Salvati, S. Saremi, R. Cowan, P. H. Fisher, G. Sciolla, S. J. Sekula, M. Spitznagel, F. Taylor, R. K. Yamamoto, H. Kim, S. E. Mclachlin, P. M. Patel, S. H. Robertson, A. Lazzaro, V. Lombardo, F. Palombo, J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, D. A. Sanders, D. J. Summers, H. W. Zhao, S. Brunet, D. Côté, M. Simard, P. Taras, F. B. Viaud, H. Nicholson, G. De Nardo, F. Fabozzi, ‡ L. Lista, D. Monorchio, C. Sciacca, M. A. Baak, G. Raven, H. L. Snoek, C. P. Jessop, J. M. LoSecco, G. Benelli, L. A. Corwin, Revised November 2007

We present measurements of the time-dependent CP -violating asymmetries in B 0 → K 0 S K 0 S K 0 S decays based on 384 million Υ (4S) → BB decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC.We obtain the CP asymmetry parameters C = 0.02 ± 0.21 ± 0.05 and S = −0.71± 0.24 ± 0.04, where the first uncertainties are statistical and the second systematic.These results are consistent with standard model expectations.
PACS numbers: 13.25.Hw, 13.25.-k,14.40.Nd In the standard model (SM) of particle physics, the decays B 0 → K 0 S K 0 S K 0 S are dominated by the b → sss gluonic penguin amplitude.A large violation of CP symmetry is predicted by the SM in the proper-time dependence of b → ccs decays of neutral B mesons.Recent measurements of CP violation in b → ccs decays [1] are in good agreement with the SM prediction [2].The predicted amplitude of this CP violation (CPV) is sin 2β, where is defined in terms of the elements V ij of the Cabibbo-Kobayashi-Maskawa (CKM) [3] quark mixing matrix.The SM also predicts that the amplitude of time-dependent CPV in b → sqq (q = d, s) decays, defined as sin 2β eff , is approximately equal to sin 2β.Contributions from loops involving non-SM particles can give large corrections to the time-dependent CPV amplitudes for these decays.The theoretical uncertainty in the SM prediction of sin 2β eff is particularly small, less than 4%, for the decay B 0 → K 0 S K 0 S K 0 S , which is a pure CP -even eigenstate [4].A violation of sin 2β eff sin 2β would be a clear sign of physics beyond the SM [5].In this paper we present a measurement of the time-dependent CP -violating asymmetries in the decay The results presented here are based on 383.6 ± 4.2 million Υ (4S) → BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e + e − collider, located at the Stanford Linear Accelerator Center.The BABAR detector [7] measures the trajectories of charged particles with a five-layer double-sided silicon microstrip detector (SVT) and a 40-layer central drift chamber (DCH), both operating in a uniform 1.5 T magnetic field.Charged kaons and pions are identified using measurements of particle energy-loss in the SVT and DCH, and of the Cherenkov cone angle in a detector of internally reflected Cherenkov light.A segmented CsI(Tl) electromagnetic calorimeter (EMC) provides photon detection and electron identification.Finally, the instrumented flux return of the magnet allows discrimination of muons from pions.
The time-dependent CP asymmetries are functions of the proper-time difference Δt ≡ t CP −t tag between a fully reconstructed B 0 → K 0 S K 0 S K 0 S decay (B CP ) and the other B meson decay in the event (B tag ), which is partially reconstructed.The decay rate f + (f − ) when the tagging meson is a B 0 (B 0 ) is given as where τ B 0 is the B 0 lifetime and Δm d is the B 0 -B 0 mixing frequency.The parameters C and S describe the amount of CP violation in decay and in the interference between decays with and without mixing, respectively.Neglecting CKM-suppressed decay amplitudes, we expect S = − sin 2β and C = 0 in the SM.
The data are divided into two subsamples, one where all three K 0 S mesons decay into the π + π − channel (B CP (+−) ) and another where one of the K 0 S mesons decays into the π 0 π 0 channel, while the other two decay into the π + π − channel (B CP (00) ).
We form π 0 → γγ candidates from pairs of photon candidates in the EMC.An energy deposit in the EMC is determined to be a photon candidate if no track intersects any of its crystals, it has a minimum energy of 50 MeV, and it has the expected lateral shower shape in the EMC.We reconstruct K 0 S → π 0 π 0 candidates from π 0 pairs with an invariant mass in the range 480 < m π 0 π 0 < 520 MeV/c 2 .We reconstruct K 0 S → π + π − candidates from pairs of oppositely charged tracks, originating from a common vertex, with an invariant mass within 12 MeV/c 2 (about 4 standard deviations) of the nominal K 0 S mass [2].We also require the decay vertex to be along the expected flight path and the significance of the reconstructed flight distance τ K 0 S /σ τ K 0 S to be larger than 5.
For each B CP (+−) candidate two nearly independent kinematic variables are computed; the beam-energysubstituted mass Here, (E i , p i ) ≡ q e + e − is the four-momentum of the initial e + e − system in the laboratory frame and √ s is the center-of-mass energy, while p B is the reconstructed momentum of the B 0 candidate in the laboratory frame and E * B is its energy calculated in the e + e − rest frame.For each B CP (00) candidate we use two different kinematic variables.They are the reconstructed B 0 mass m B and the missing mass m miss = (q e + e − − qB ) 2 , where qB is the four-momentum of the B CP (00) candidate after a mass constraint on the B 0 meson has been applied.Due to leakage effects in the EMC, which affect the photon energy measurement and therefore the π 0 reconstruction, the shape of the m B distribution is asymmetric around the mean value.This results in this combination of variables being less correlated than ΔE and m ES , with better background suppression [8].
For B CP signal decays, the m ES , m miss and m B distributions peak near the B 0 mass, while the ΔE distribution peaks near zero.For B CP (+−) candidates, we require 5.22 < m ES < 5.30 GeV/c 2 and |ΔE| < 120 MeV.For B CP (00) candidates, we require 5.11 < m miss < 5.31 GeV/c 2 and |m B − m P DG B | < 150 MeV/c 2 , where m P DG B represents the world-average B 0 mass [2].These selection windows include the signal peak and a "sideband" region which is used for characterization of the background.
The sample of B CP candidates is dominated by random d, s, c) fragmentation (the q q continuum).We use topological observables to discriminate jet-like e + e − → qq events from the more spherical BB events.In the e + e − rest frame we compute the angle θ * T between the thrust axis of the B CP (+−) (B CP (00) ) candidate's decay products and that of the remaining particles in the event.We require | cos θ * T | < 0.90(0.95),which reduces the number of background events by one order of magnitude.We also use the Legendre monomials L 0 and L 2 , for the characterization of the event shape [8].The monomials are combined in a Fisher discriminant F [8] (ratio ) candidates, and it is used in the maximum-likelihood fit described below.
The average B CP candidate multiplicity in the B CP (00) sample is approximately 1.7, coming from multiple K 0 S → π 0 π 0 combinations.In these events, we select the combination with the smallest , where m i (m K 0 S ) is the measured (world-average) K 0 S mass [2] and σ mi is its estimated uncertainty.We use the same method in the B CP (+−) sample, where only 1.4 % of events have more than one B CP (+−) candidate.Since B 0 → χ c0,2 K 0 S decays proceed through a b → ccs transition, we remove all B CP (+−) (B CP (00) ) candidates with a K 0 S K 0 S mass combination within 3σ (2σ) of the χ c0 or χ c2 mass.After these vetoes, the total reconstruction efficiency, including K 0 S branching fractions, is about 6% (3%) for B CP (+−) (B CP (00) ) candidates, assuming a uniform Dalitz distribution.
The remaining background from BB events is estimated to be negligible for the B CP (+−) sample and is absorbed into the q q continuum component.For the B CP (00) sample, we extract the yield of BB background events simultaneously with the signal and qq event yields.
A multivariate tagging algorithm determines the flavor of the B tag meson and classifies it in one of seven mutually exclusive tagging categories [1,9].They rely upon the presence of prompt leptons, or one or more charged kaons and pions in the event, and have different purities.We measure the performance of this algorithm with a data sample (B flav ) of fully reconstructed 0.304 ± 0.003, where ε c (w c ) is the efficiency (mistag probability) for events tagged in category c.
We compute the proper-time difference Δt = Δz/γβc using the known boost of the e + e − system and the measured separation between the B CP and B tag decay vertices along the boost direction (Δz = z CP − z tag ) [9].For the B CP decay, where no charged particles are produced at the decay vertex, we determine the decay point by constraining the B production vertex to the interaction point (IP) in the plane orthogonal to the beam axis using only the K 0 S → π + π − trajectories.The IP position is determined on a run-by-run basis from two-track events.We compute Δt and its uncertainty σ Δt from a geometric fit to the Υ (4S) → B 0 B 0 system that takes into account this IP constraint and a Gaussian constraint on the sum of the two B decay times (t CP + t tag ) to be equal to 2 τ B 0 with an uncertainty of √ 2 τ B 0 [8,10].In order to ensure a well-determined vertex separation between B rec and B tag , we exclude events that have the error on Δt, determined from the vertex fit, σ Δt > 2.5 ps and events with |Δt| > 20 ps.The mean uncertainty in z CP , a convolution of the uncertainty in the interaction region position and the z tag resolution, is 75μm.The mean uncertainty on z tag is about 200μm, which dominates the Δz uncertainty.The resulting Δz resolution is comparable to that in B 0 → J/ψ K 0 S decays [8].Simulation studies and a B 0 → J/ψ K 0 S data control sample show that the procedure we use to determine the vertex for a B CP decay provides an unbiased estimate of z CP [8].
Most events have at least one K 0 S candidate for which both tracks have at least one hit in the inner three SVT layers.We have verified on simulation and on data control samples that the parameters of the signal Δt resolution function for these B CP signal decays are similar to those obtained from the B flav sample [9].When at least one K 0 S has tracks with hits in the outer two SVT layers but not in the inner three layers, the resolution is nearly two times worse and the Δt information is not used.
We extract the event yields and CP parameters with an unbinned extended maximum-likelihood fit to the kinematic, event shape, and Δt variables.For each of the sub-samples k = 1, 2 (B CP (+−) , B CP (00) ) we use: where P j is the probability density function (PDF) for the j th fit component.N j is the event yield of each of the n components: N S signal events, N qq continuum qq events and, for B CP (00) only, N B B B B background events; N T is the total number of events selected.For B CP (+−) (B CP (00) ) candidates, the PDF P j is given by the product of P j (m ES )P j (ΔE)P j (F ) (P j (m miss )P j (m B )P j (l 2 )) × P c j (Δt, σ Δt )ε c , summed over the tagging categories c.The product L 1 L 2 is maximized to determine the common CP asymmetry parameters S and C and the values of N j , which are specific to each sub-sample.Along with S and C, the fit extracts ε c and parameters describing the background.A fit to 857 B CP (+−) and 4992 B CP (00) candidates returns the event yields reported in Table I. Figure 1 shows the m ES and ΔE (m miss and m B ) distributions for signal and background B CP (+−) (B CP (00) ) candidates.The extracted CP parameters for the two separate sub-samples and the combined ones are shown in Table I.Using a Monte Carlo technique, in which we assume that the measured values for the CP parameters on the combined data sample are the true values, we find that the two subsamples agree within 1.6σ.The statistical significance of the CP violation is evaluated as 2 • Δ ln(L 1 L 2 ), where Δ ln(L 1 L 2 ) is the change in the natural log of the combined likelihood for the no CP -violation hypothesis with respect to the maximum value.We estimate it to be 2.9 standard deviations.Figure 2 shows distributions for B CP (00) candidates.The signal and background distributions have been separated using the technique described in [11].The curves represent the PDF projections.The background distributions are shown in the insets.
of Δt for B 0 and B 0 -tagged events, and the asymmetry Systematic uncertainties on the CP parameters are given in Table II.The systematic errors are evaluated using large samples of simulated B CP decays and the B flav data sample.We perform fits to the simulated B CP signal with parameters obtained either from signal or B flav events to account for possible differences in the Δt reso-  lution function.We use the differences in the resolution function and tagging parameters extracted from these samples to vary the signal parameters.We account for possible biases due to the vertexing technique by comparing fits to a large simulated sample of IP-constrained (neglecting the J/ψ contribution to the vertex and using the K 0 S trajectory only) and nominal B 0 → J/ψ K 0 S events.Several SVT misalignment scenarios are applied to the simulated B CP events to estimate detector effects.We consider variations of 20μm in the direction orthogonal to the beam axis for the IP position and resolution and find they have a negligible impact.The systematic error due to correlations between the variables used in the fit is determined from a fit to a sample of randomly selected signal Monte Carlo (MC) events added to background events generated from the background PDFs used in the fit.The values of the effective CP parameters for the B B background, which are fixed to zero in the nominal fit, are varied over the whole physically allowed range.The largest deviations in S and C resulting from this variation are used as systematic uncertainties.The world-average values of Δm d and of the B 0 mean lifetime, τ B 0 , held fixed in the fit, are varied by their uncertainties [2].We account for the possible interference between the suppressed b → ucd and the favored b → cud amplitudes for some B tag decays [12].Finally, we include a systematic uncertainty to account for imperfect knowledge of the PDFs used in the fit.Most of this uncertainty is due to MC statistics, the rest to differences between data control samples and MC simulation.In summary, we measured the B 0 → K 0 S K 0 S K 0 S timedependent CP asymmetries, S = −0.71± 0.24 ± 0.04 and C = 0.02 ± 0.21 ± 0.05, where the first errors are statistical and the second systematic.The statistical correlation between S and C is −14.1%.These results agree well with the SM expectation.This measurement, which is limited by the small statistics of the sample, constrains, but does not exclude contributions from physics beyond the SM, such as the low-energy supersymmetry [5].These results supersede our previously published CP asymmetry results for B 0 → K 0 S K 0 S K 0 S [13] and are consistent with the measurements performed by the Belle collaboration reported in [1].
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 and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom).Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

FIG. 1 :
FIG.1: Signal and background distributions of (a) mES and (b) ΔE for B CP (+−) candidates and of (c) mmiss and (d) mB for B CP (00) candidates.The signal and background distributions have been separated using the technique described in[11].The curves represent the PDF projections.The background distributions are shown in the insets.

FIG. 2 :
FIG.2: Distributions of Δt for events weighted using the technique described in[11] for Btag tagged as (a) B 0 or (b) B 0 , and (c) the asymmetry A(Δt).The points are the weighted data and the curves are PDF projections.

TABLE I :
Event yields and CP asymmetry parameters obtained in the fit.The errors are statistical only.

TABLE II :
Systematic uncertainties on S and C.