Observation of and Search for Decays at Belle
We search for the radiative penguin decays and in a 23.6 data sample collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider. We observe for the first time a radiative penguin decay of the meson in the mode and we measure . No significant signal is observed and we set a 90% confidence level upper limit of .
pacs:13.25.Gv, 13.25.Hw, 14.40.Gx, 14.40.Nd
The Belle Collaboration
Radiative penguin decays, which produce a photon via a one-loop Feynman diagram, are a good tool to search for physics beyond the Standard Model (SM) because particles not yet produced in the laboratory can make large contributions to such loop effects. The chargeconj () mode is a radiative process described within the SM by a penguin diagram (Fig. 1 left); it is the strange counterpart of the decay, whose observation by CLEO in 1993 b2kstg-cleo () unambiguously demonstrated the existence of penguin processes. In the SM, the branching fraction has been computed with uncertainty to be about bs2phigam-sm1 (); bs2phigam-sm2 (). The mode is usually described by a penguin annihiliation diagram (Fig. 1 right), and its branching fraction has been calculated in the SM to be in the range bs2gamgam-sm1 (); bs2gamgam-sm2 (); bs2gamgam-sm3 (). Neither nor has yet been observed, and the upper limits at the 90% confidence level (CL) on their branching fractions are, respectively, bs2phigam-cdf () and u5s-excl ().
A strong theoretical constraint on the branching fraction is generally assumed due to good agreement between SM expectations and experimental results for rates, such as in and decays bs2phigam-sm1 (); bs2phigam-sm2 (); b2kstg-th (); PDG2007 () or inclusive decays b2xsg-th (); PDG2007 (). The decay rate is constrained in a similar way bs2gamgam-xsg (), though various New Physics (NP) scenarios such as supersymmetry with broken -parity bs2gamgam-supersym (), a fourth quark generation bs2gamgam-4thquark () or a two Higgs doublet model with flavor changing neutral currents bs2gamgam-2higgsdoublet (), can increase the branching fraction by up to an order of magnitude without violating constraints on the branching fraction.
In this study, we use a data sample with an integrated luminosity () of 23.6 that was collected with the Belle detector at the KEKB asymmetric-energy (3.6 on 8.2 GeV) collider KEKB () operating at the resonance (10.87 GeV).
The Belle detector is a large-solid-angle magnetic spectrometer that consists of a 4-layer silicon detector (SVD SVD2 ()), a central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) 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 ().
The variety of hadronic events at the resonance is richer than at the . , and mesons are all produced in decay. mesons are produced mainly via decays, with subsequent low energy photon de-excitation. The production cross section at the , the fraction of events in the events, and the fraction of events among events have been measured to be, respectively, nb u5s-incl (), PDG2007 () and u5s-excl (). The and decay fractions are small and not yet measured.
Charged tracks are reconstructed using the SVD and CDC detectors and are required to originate from the interaction point. Kaon candidates are selected from charged tracks with the requirement , where () is the likelihood for a track to be a kaon (pion) based on the response of the ACC and on measurements from the CDC and TOF. For the selected kaons, the identification efficiency is about 85% with about 9% of pions misidentified as kaons.
We reconstruct mesons in the decay mode by combining oppositely charged kaons having an invariant mass within () of the nominal mass PDG2007 ().
We reject photons from and decays to two photons using a likelihood based on the energy and polar angles of the photons in the laboratory frame and the invariant mass of the photon pair. To reject merged photons from decays and neutral hadrons such as neutrons and , we require an ECL shower shape consistent with that of a single photon: for each cluster, the ratio of the energy deposited in the central calorimeter cells to that of the larger array of cells has to be greater than 0.95. Candidate photons are required to have a signal timing consistent with originating from the same event. For the mode, photons are selected in the barrel part of the ECL () and we require that the total energy of the event be less than 12 GeV.
meson candidates are selected using the beam-energy-constrained mass and the energy difference . In these definitions, is the beam energy and and are the momentum and the energy of the meson, with all variables being evaluated in the center-of-mass (CM) frame. We select meson candidates with for both modes, and for the mode and for the mode. No events with multiple candidates are observed in either data or Monte Carlo (MC) simulation. mesons are not fully reconstructed due to the low energy of the photon from the decay. Signal candidates coming from , and are well-separated in , but they overlap in u5s-excl ().
The main background in both search modes is due to continuum events coming from light-quark pair production (, , and ). Rejection of this background is studied and optimized using large signal MC samples and a continuum MC sample having about three times the size of the data sample. A Fisher discriminant based on modified Fox-Wolfram moments ( SFW ()) is used to separate signal from continuum background. The process is a source of high-energy photons with low polar angles and can thus be a background for radiative decays. Therefore, for the mode, we apply a more restrictive requirement when the candidate photon is recontructed outside the barrel part of the ECL. This procedure is not used for the mode where photons are selected only in the barrel. For the mode, the requirement is chosen in order to maximize a figure of merit defined as , where and are the expected number of signal events coming from events and continuum events, respectively. and are computed in the signal window (, and ) and are normalized to an integrated luminosity of 23.6 assuming . The helicity angle is the angle between the and the in the rest frame. For signal events should follow a distribution, while for continuum events the distribution is found to be flat. For the mode, we optimize the requirement to minimize the 90% CL upper limit on the branching fraction computed by the Feldman-Cousins method feldmancousins (). The upper limit calculation requires two inputs: the number of observed events () and the expected number of background events (). We assume and . and are computed in the signal window ( and ) assuming that .
Inclusive backgrounds from decays are studied using MC samples having about the same size as the data sample. Backgrounds coming from or decays are found to lie outside of the fit region. For decays, no event is reconstructed in the mode. The decay is a potential background for the mode and is studied using a dedicated MC sample. Assuming that its branching fraction is the same as its counterpart PDG2007 (), we expect to reconstruct one background event. Considering the large branching fraction uncertainty, this background is treated as a source of systematic error.
For the () mode, we perform a three-dimensional (two-dimensional) unbinned extended maximum likelihood fit to , and ( and ) using the probability density functions (PDF) described below.
The signal PDFs for and are modeled separately for events coming from , and with smoothed two-dimensional histograms built from signal MC events. The () mean for the signal is adjusted to the mass (the - mass difference) obtained from events reconstructed in the same data sample. The and resolutions for the () signal are corrected using a control sample of events ( events) recorded on the resonance. Statistical uncertainties contained in these corrections are included in the systematic uncertainty. Continuum background is modeled with an ARGUS function argus () for and a first-order polynomial function for . For the mode, the signal (continuum) PDF for is modeled with a (constant) function. The background PDF is modeled using MC events as the product of a two-dimensional PDF for and and a one-dimensional histogram for . The likelihood is defined as
where runs over all events, runs over the possible event categories (signals or backgrounds), is the number of events in each category and is the corresponding PDF.
Both fits have six free fit variables: the yields for the , and signals (, and ), the continuum background normalization and PDF parameters, except the ARGUS endpoint which is fixed to . The branching fractions ( and ) are determined from the signal yields with the relations
where ’s are the MC signal efficiencies listed in Table 1 and is the number of mesons evaluated as .
In the mode we observe signal events in the region and no significant signals in the two other regions. These signal yields are compatible with u5s-excl (). We measure and with a significance of , where the first uncertainty is statistical and the second is systematic. Systematic uncertainties and computation of the significance are detailed below. The measured branching fraction is in agreement with SM expectations bs2phigam-sm1 (); bs2phigam-sm2 () and with the measurements and PDG2007 (). We observe no significant signal and, including systematic uncertainties, determine a 90% CL upper limit of . This limit is about six times more restrictive than the previous one u5s-excl (), though still about one order of magnitude larger than SM expectations bs2gamgam-sm1 (); bs2gamgam-sm2 (); bs2gamgam-sm3 () and still above the predictions of NP models bs2gamgam-supersym (); bs2gamgam-4thquark (); bs2gamgam-2higgsdoublet (). The results are summarized in Table 1 and fit projections in the signal windows are shown in Figs. 2 and 3.
Systematic uncertainties are listed in Table 2. The error on the signal reconstruction efficiency is dominated by uncertainty on the efficiency of the requirement. This uncertainty is evaluated by comparing efficiencies in data and MC using the control sample. For the mode, we take as systematic uncertainty the difference between the results of the nominal fit and the results of a fit where the continuum is parametrized with a second-order polynomial function for . For the mode, the limit obtained with the nominal continuum parametrization is found to be conservative. For the mode, systematic uncertainties on are evaluated by repeating the fit with each parameter successively varied by plus or minus one standard deviation around its central value. The positive and negative uncertainty in are obtained from the quadratic sum of the corresponding deviations from the value returned by the nominal fit. The significance of the branching fraction measurement is defined as , where is the likelihood returned by the nominal fit and is the likelihood returned by the fit with set to zero. Systematic uncertainties are included by choosing the lowest significance value returned by the fits used to evaluate the systematic uncertainty. The background is the only source of systematic uncertainty having a non-negligible effect on the significance. For the mode, the 90% CL limit, , is computed by likelihood integration, according to . Systematic uncertainties are included by convolving the likelihood function with Gaussian distributions for the parameters giving rise to systematic uncertainty.
|Photon reconstruction efficiency|
|Kaon identification efficiency||–|
|Total (quadratic sum)|
In summary, we observe for the first time a radiative penguin decay of the meson in the mode. We measure , which is in agreement with both the SM predictions and with extrapolations from measured and decay branching fractions. No significant signal is observed in the mode and we set an upper limit at the 90% CL of . This limit significantly improves on the previously reported one and is only an order of magnitude larger than the SM prediction, providing the possibility of observing this decay at a future Super -factory superbelle (); superb ().
We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenics group for efficient solenoid operations, and the KEK computer group and the NII for valuable computing and Super-SINET network support. We acknowledge support from MEXT and JSPS (Japan); ARC and DEST (Australia); NSFC (China); DST (India); MOEHRD, KOSEF and KRF (Korea); KBN (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE (USA).
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