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Observation of the decay

###### Abstract

We measure the decay using data collected at the resonance with the Belle detector at the KEKB collider. The data sample used corresponds to an integrated luminosity of 121.4 fb. We measure a branching fraction with a significance of 5.1 standard deviations. This measurement constitutes the first observation of this decay.

###### pacs:

13.25.Hw, 14.40.NdThe Belle Collaboration

The two-body decays , where is either a pion or kaon, have now all been observed PDG (). In contrast, the neutral-daughter decays have yet to be observed. The decay charge-conjugate () is of particular interest because the branching fraction is predicted to be relatively large. In the standard model (SM), the decay proceeds mainly via a loop (or “penguin”) transition as shown in Fig. 1, and the branching fraction is predicted to be in the range SM-branching (). The presence of non-SM particles or couplings could enhance this value Chang:2013hba (). It has been pointed out that asymmetries in decays are promising observables in which to search for new physics susy ().

The current upper limit on the branching fraction, at 90% confidence level, was set by the Belle Collaboration using of data recorded at the resonance Peng:2010ze (). Here, we update this result using the full data set of recorded at the . The analysis presented here uses improved tracking, reconstruction, and continuum suppression algorithms. The data set corresponds to pairs Oswald:2015dma () produced in three decay channels: , or , and . The latter two channels dominate, with production fractions of and % Esen:2012yz ().

The Belle detector is a large-solid-angle magnetic spectrometer consisting of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters, a barrel-like arrangement of time-of-flight scintillation counters, and an electromagnetic calorimeter comprising CsI(Tl) crystals. These detector components are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside the coil is instrumented to detect mesons and to identify muons. The detector is described in detail elsewhere Belle (); svd2 (). The origin of the coordinate system is defined as the position of the nominal interaction point (IP). The axis is aligned with the direction opposite the beam and is parallel to the direction of the magnetic field within the solenoid. The axis is horizontal and points towards the outside of the storage ring; the axis points vertically upward.

Candidate mesons are reconstructed via the decay using a neural network (NN) technique Feindt:2006pm (). The NN uses the following information: the momentum in the laboratory frame; the distance along between the two track helices at their closest approach; the flight length in the - plane; the angle between the momentum and the vector joining the decay vertex to the IP; the angle between the pion momentum and the laboratory-frame direction in the rest frame; the distance-of-closest-approach in the - plane between the IP and the two pion helices; and the pion hit information in the SVD and CDC. The selection efficiency is 87% over the momentum range of interest. We also require that the invariant mass be within 12 MeV/ (about 3.5 in resolution) of the nominal mass PDG ().

To identify candidates, we define two variables: the beam-energy-constrained mass ; and the energy difference , where is the beam energy and and are the energy and momentum, respectively, of the candidate. These quantities are evaluated in the center-of-mass frame. We require that events satisfy GeV/ and .

To suppress background arising from continuum production, we use a second NN Feindt:2006pm () that distinguishes jetlike continuum events from more spherical events. This NN uses the following input variables, which characterize the event topology: the cosine of the angle between the thrust axis Brandt:1964sa () of the candidate and the thrust axis of the rest of the event; the cosine of the angle between the thrust axis and the axis; a set of 16 modified Fox-Wolfram moments SFW (); and the ratio of the second to zeroth (unmodified) Fox-Wolfram moments. All quantities are evaluated in the center-of-mass frame. The NN is trained using Monte Carlo (MC) simulated signal events and background events. The MC samples are obtained using EvtGen Lange:2001uf () for event generation and Geant3 geant3 () for modeling the detector response. The NN has a single output variable () that ranges from for backgroundlike events to for signal-like events. We require , which rejects approximately 85% of background while retaining 83% of signal decays. We subsequently translate to a new variable {linenomath}

(1) |

where and is the maximum value of obtained from a large sample of signal MC decays. The distribution of is well modeled by a Gaussian function.

After applying all selection criteria, approximately 1.0% of events have multiple candidates. For these events, we retain the candidate having the smallest value of obtained from the deviations of the reconstructed masses from their nominal values PDG (). According to MC simulation, this criterion selects the correct candidate % of the time.

We measure the signal yield by performing an unbinned extended maximum likelihood fit to the variables , , and . The likelihood function is defined as {linenomath}

(2) |

where is the yield of component ; is the probability density function (PDF) of component for event ; runs over the two event categories (signal and background); and runs over all events in the sample (). Backgrounds arising from other and non- decays were studied using MC simulation and found to be negligible. As correlations among the variables , , and are found to be small, the three-dimensional PDFs are factorized into the product of separate one-dimensional PDFs.

The signal PDF is defined as {linenomath}

where , , and are the PDFs for signal arising from , and decays. The and PDFs are modeled with Gaussian functions, and the PDFs are each modeled with a sum of two Gaussian functions having a common mean. All parameters of the signal PDF are fixed to the corresponding MC values. The peak positions for and are adjusted according to small data-MC differences observed in a control sample of decays Esen:2012yz (). As this control sample has only modest statistics, the resolutions for , , and , and the peak position for , are adjusted for data-MC differences using a high statistics sample of decays. For background, the , , and PDFs are modeled with an ARGUS function Albrecht:1990am (), a first-order Chebyshev polynomial, and a Gaussian function, respectively. All parameters of the background PDFs except for the end point of the ARGUS function are floated in the fit.

The results of the fit are signal events and continuum background events. Projections of the fit are shown in Fig. 2. The branching fraction is calculated via {linenomath}

(4) |

where is the fitted signal yield; is the number of events; is the branching fraction for PDG (); and is the signal efficiency as determined from MC simulation. The efficiency is corrected by a factor for each reconstructed , to account for a small difference in reconstruction efficiency between data and simulation. This correction is estimated from a high statistics sample of decays. The factor 0.50 accounts for the 50% probability for (since is even). Inserting these values gives , where the error is statistical.

The systematic uncertainty on arises from several sources, as listed in Table 1. The uncertainties due to the fixed parameters in the PDF shape are estimated by varying the parameters individually according to their statistical uncertainties. For each variation the branching fraction is recalculated, and the difference with the nominal branching fraction is taken as the systematic uncertainty associated with that parameter. We add together all uncertainties in quadrature to obtain the overall uncertainty due to fixed parameters. The uncertainties due to errors in the calibration factors and the fractions are evaluated in a similar manner. To test the stability of our fitting procedure, we generate and fit a large ensemble of MC pseudoexperiments. By comparing the mean of the fitted yields with the input value, a bias of is found. We attribute this bias to our neglecting small correlations among the fitted observables. An 0.9% systematic uncertainty is assigned due to the selection; this is obtained by comparing the selection efficiencies in MC simulationand data for the control sample. We assign a 2.0% systematic uncertainty for each reconstructed ; this is determined using a sample. The uncertainty on due to the MC sample size is 0.2%. The total of the above systematic uncertainties is calculated as their sum in quadrature. In addition, there is a 10.1% uncertainty due to the number of pairs. As this large uncertainty does not arise from our analysis, we quote it separately.

Source | Uncertainty (%) |
---|---|

PDF parametrization | 0.2 |

Calibration factor | |

Fit bias | |

reconstruction | 4.0 |

selection | 0.9 |

MC sample size | 0.2 |

0.1 | |

Total (without ) | |

10.1 |

The signal significance is calculated as , where is the likelihood value when the signal yield is fixed to zero, and is the likelihood value of the nominal fit. We include systematic uncertainties in the significance by convolving the likelihood function with a Gaussian function whose width is equal to that part of the systematic uncertainty that affects the signal yield. We obtain a signal significance of 5.1 standard deviations; thus, our measurement constitutes the first observation of this decay.

Figure 3 shows the background-subtracted sPlot splot () distributions of , where the selection is removed for the pair being plotted. No contribution is observed. We check this quantitatively by performing our signal fit for events in the mass sidebands of each [ and ]. The extracted signal yields, and for the higher momentum and lower momentum , respectively, are consistent with zero. We calculate the expected number of events in our signal sample using MC simulation and the measured branching fraction, Aaij:2013uta (); the result is 0.001.

In summary, we report the first observation of the decay . The branching fraction is measured to be {linenomath}

where the first uncertainty is statistical, the second is systematic, and the third reflects the uncertainty due to the total number of pairs. This value is in good agreement with the SM predictions SM-branching (), and it implies that the Belle II experiment Abe:2010gxa () will reconstruct over 1000 of these decays. Such a sample would allow for a much higher sensitivity search for new physics in this penguin-dominated decay.

ACKNOWLEDGMENTS

We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, the National Institute of Informatics, and the PNNL/EMSL computing group for valuable computing and SINET4 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council; Austrian Science Fund under Grants No. P 22742-N16 and P 26794-N20; the National Natural Science Foundation of China under Contracts No. 10575109, No. 10775142, No. 10875115, No. 11175187, and No. 11475187; the Chinese Academy of Science Center for Excellence in Particle Physics; the Ministry of Education, Youth and Sports of the Czech Republic under Contract No. LG14034; the Carl Zeiss Foundation, the Deutsche Forschungsgemeinschaft and the VolkswagenStiftung; the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; the WCU program of the Ministry of Education, National Research Foundation (NRF) of Korea Grants No. 2011-0029457, No. 2012-0008143, No. 2012R1A1A2008330, No. 2013R1A1A3007772, No. 2014R1A2A2A01005286, No. 2014R1A2A2A01002734, No. 2015R1A2A2A01003280 , No. 2015H1A2A1033649; the Basic Research Lab program under NRF Grant No. KRF-2011-0020333, Center for Korean J-PARC Users, No. NRF-2013K1A3A7A06056592; the Brain Korea 21-Plus program and Radiation Science Research Institute; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Research; the Slovenian Research Agency; the Basque Foundation for Science (IKERBASQUE) and the Euskal Herriko Unibertsitatea (UPV/EHU) under program UFI 11/55 (Spain); the Swiss National Science Foundation; the National Science Council and the Ministry of Education of Taiwan; and the U.S. Department of Energy and the National Science Foundation. This work is supported by a Grant-in-Aid from MEXT for Science Research in a Priority Area (“New Development of Flavor Physics”) and from JSPS for Creative Scientific Research (“Evolution of Tau-lepton Physics”).

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