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Lepton flavour violation in D and B decays at Belle
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Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61 www.elsevier.com/locate/npbps
Lepton flavour violation in D and B decays at Belle M. Petriˇca a
Joˇzef Stefan Institure, Jamova cesta 39, 1000 Ljubljana, Slovenia We search for the flavour-changing neutral current decays D0 → μ+ μ− and D0 → e+ e− , and for the leptonflavour violating decays D0 → e± μ∓ using 660 fb−1 of data. We also search for lepton-number violating decays B + → D− e+ e+ , B + → D− μ+ μ+ and B + → D− μ+ e+ using 710 fb−1 of data. All the data is collected with the Belle detector at the KEKB asymmetric-energy e+ e− collider. We find no evidence for any of these decays. We obtain significantly improved upper limits on the branching fractions: B D0 → μ+ μ− < 1.4 × 10−7 , B D0 → e+ e− < 7.9 × 10−8 , B D0 → e+ μ− + B D0 → μ+ e− < 2.6 × 10−7 , B(B + → D− e+ e+ ) < 2.6 × 10−6 , B(B + → D− e+ μ+ ) < 1.6 × 10−6 and B(B + → D− μ+ μ+ ) < 0.9 × 10−6 at 90% confidence level.
1. SEARCH FOR D0 → + − DECAYS In the standard model (SM) the flavourchanging neutral current (FCNC) decays D0 → e+ e− and D0 → μ+ μ− [1] are highly suppressed by the Glashow-Iliopoulos-Maiani mechanism [2]. Considering long distance contributions the branching fractions in the SM are around 10−13 [3]. The lepton-flavour violating (LFV) decays D0 → e± μ∓ are forbidden in the SM, but are possible in extensions of the SM with massive neutrinos and the branching fractions are expected to be of the order of 10−14 in such cases [3]. All these predictions are orders of magnitude below the current experimental sensitivity. Branching fractions of FCNC decays can be enhanced by many orders of magnitude in some new physics (NP) scenarios. The branching fractions of D0 → e+ e− and D0 → μ+ μ− can be, for example, increased by R-parity violating supersymmetry up to 10−12 and 10−8 , respectively [4]. The latter prediction is close to the current experimental sensitivity. It was suggested that so far unobserved leptoquarks could explain the small discrepancy between the measured value of the Ds meson decay constant and the prediction of lattice QCD [5]. In order to explain the discrepancy with a leptoquark contribution, and comply with other constraints, B D0 → μ+ μ− should 0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2011.06.011
be enhanced to 8 × 10−7 [6]. Using 660 fb−1 of data recorded by the Belle detector at the KEKB collider, we searched for the decays D0 → μ+ μ− , D0 → e+ e− and D0 → e± μ∓ . In this measurement only D0 mesons coming from c - quark production in the continuum e+ e− → cc process are considered, since the inclusion of D0 mesons from B decays would result in a higher combinatorial background. To cancel various systematic uncertainties we normalise the sensitivity of our search to topologically similar D0 → π + π − decays . Firstly, a loose event selection is performed that is the same for all data samples apart from the particle identification criteria. Secondly, tighter optimised specific criteria are used for each decay mode. To improve the purity of the D0 → + − and π + π − samples, we use D0 mesons from the decay D∗+ → D0 πs+ with a characteristic low momentum pion. To reject D-mesons produced in B-meson decays and to suppress combinatorial background, a D∗+ momentum greater than 2.5 GeV/c in the centre-of-mass (CM) frame of the collisions is required. Candidate D0 mesons are selected using two kinematic observables: the invariant mass of the D0 decay products, M , and the energy released in the D∗+ decay, q = (MD∗+ − M − mπ )c2 , where MD∗+ is the invari-
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
ant mass of the D0 πs combination and mπ is the π + mass [7]. We require 1.81 GeV/c2 < M < 1.91 GeV/c2 and q < 20 MeV. The background in D0 → + − decays originates predominantly from semileptonic B decays (80%) and from D0 decays (10%), according to Monte Carlo (MC) simulation based on EvtGen [8] and GEANT3 [9]. The background events can be grouped into two categories based on their distribution in M : (1) a smooth combinatorial background, and (2) a peaking background from the misidentification of D0 → π + π − decays. When both pions from a D0 → π + π − decay are misidentified as muons or as a muonelectron combination, this produces a signal-like background. Using signal MC simulation, which additionally includes final-state radiative effects (FSR) simulated by PHOTOS [10], the signal efficiencies and ππ are evaluated. A blind analysis technique has been adopted in order to avoid biases. Until the final event selection criteria were established, all events inside the D0 signal region of |ΔM | < 20 MeV/c2 and |Δq| < 1 MeV were blinded. We optimise the selection criteria to obtain the best upper limits, since D0 → + − decays are not expected to be observed at the current sensitivity; we maximise the figure of merit, F = /NUL , where is the efficiency for detecting D0 → + − decays obtained from the signal MC simulation and NUL is the Poisson average of Feldman-Cousins 90% confidence level upper limits on the number of observed signal events that would be obtained with the expected background and no signal [11]. The average upper limits NUL are calculated from the number of generic MC background events, surviving the selection criteria and scaled to the data size. The sample corresponds to 6-times the statistics of the data. For the optimisation we select the following variables: signal region size (ΔM, Δq), maximal missing energy Emiss . We construct Emiss from the difference between the beam energy and the sum of the energies of all four-vectors of photons and charged tracks, which are assumed to be pions. We measure quantities ΔM and Δq relative to the nominal D0 mass and nominal energy released in the D∗+ decay, respectively. An
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asymmetric signal region in M is allowed with respect to the nominal D0 mass; in the case of the μμ decay mode this is used to suppress background from misidentification D0 → π + π − decays, since their invariant mass distribution peaks about 2 standard deviations below the D0 mass; the asymmetric requirement accounts for the low mass tail due to electron bremsstrahlung for the ee and eμ modes. To suppress background from semileptonic B decays, a requirement on the maximal allowed missing energy in the event is chosen since such decays have larger missing energy due to undetected neutrinos. We use the sideband region |Δq| > 1 MeV to estimate the number of combinatorial background events in the signal region. To reduce the statistical error and to exclude possible signal events and misidentification from D0 → π + π − decays, such a region has been chosen. Good agreement in the combinatorial background distribution in this region can be seen between MC and data. We parametrise the sideband as f (M, q) = √ A(1−BM ) q, where A and B represent parameters determined from a fit to the generic MC sample. By means of integration of f (M, q) the number of combinatorial background events in the sigcomb nal region is calculated as Nbkg = p × Nside , where Nside is the number of events found in the sideband region and p is the expected ratio of events in the signal and sideband region. We estimate the peaking background in the signal region due to misidentification of D0 → π + π − decays in two steps. Firstly, D0 → π + π − decays found in data are reconstructed so that the pion mass is replaced with the lepton mass. Secondly, we weight each event with the pion-lepton misidentification probability and pion identification efficiency. The misidentification probabilities and efficiencies are measured in data using D∗+ → D0 πs+ , D0 → K − π + decays, binned in particle momentum p and cosine of polar angle. The misidentification of D0 → π + π − contributes significantly only to the D0 → μ+ μ− decay channel (1.8 events). In Figure 1 the invariant mass distributions after applying the optimised event selection criteria are shown. In the signal region we find two candidates in the D0 → μ+ μ− , zero candidates
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in the D0 → e+ e− , and three candidates in the D0 → e± μ∓ decay mode; the number of events in the signal window is consistent with the estimated background.
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Figure 1. The invariant mass distributions for (a) D0 → μ+ μ− , (b) D0 → e+ e− , and (c) D0 → e± μ∓ . Superimposed on the data (open histograms) are the estimated distribution for combinatorial background (filled histogram), the misidentification of D0 → π + π − (cross-hatched histogram), and the signal if the branching fractions were equal to the 90% confidence level upper limit (single hatched histogram). The dashed vertical lines indicate the optimised signal window [13].
To determine the yield of D0 → π + π − candidates for the normalisation, a binned maximum likelihood fit is used. The invariant mass distribution using the same kinematic selections as for individual leptonic modes, except for the criteria
on M is fitted. A sum of two Gaussian distributions with the same mean and an FSR tail for the signal, and a linear function for the background is used as the fit function. Using selection criteria for the μμ, ee, and eμ modes the number of reconstructed D0 mesons in the π + π − mode is found to be 51.2 × 103 , 44.1 × 103 , and 46.0 × 103 , respectively. The relative uncertainties on Nππ are around 0.5%. We use the signal MC to determine the efficiencies. To compensate for small differences in lepton and pion identification efficiencies between data and MC simulation, event weighting is applied. Decays γγ → + − and B → XJ/ψ(→ + − ) are used to determine the correction factors for lepton identification. The signal efficiencies are found to be 11% for π + π − decays and between 5% and 7% for + − decays. The uncertainties in are estimated to be 0.3% and include contributions from MC statistics (0.2%) and lepton identification efficiency corrections (0.2%). Because of a larger MC sample and better known pion efficiency corrections, the uncertainty in ππ is small (0.1%). We calculate the branching fraction upper limits (UL) using the programme pole.f [12], which extends the Feldman-Cousins method [11] by the inclusion of systematic uncertainties. It has been noted that the inclusion of systematic uncertainties with pole produces nearly the same result as the standard Feldman-Cousins 0 ± ∓ → e μ method. Note that B D denotes the 0 sum B D → e+ μ− + B D0 → μ+ e− . In summary, we have searched for the FCNC decays D0 → μ+ μ− and D0 → e+ e− , and the LFV decays D0 → e± μ∓ using the Belle detector and have found no evidence of these decays. The upper limits on the branching 0 fractions at + − the 90% confidence level are B D < → μ μ 1.4 × 10−7 , B D0 → e+ e− < 7.9 × 10−8 and B D0 → e± μ∓ < 2.6 × 10−7 [13]. These results improve the current limits by a factor of 9 for D0 → μ+ μ− decay, by a factor of 15 for D0 → e+ e− decay and by a factor of 3 for D0 → e± μ∓ decay [7]. The CDF collaboration recently reported a result on the UL for the D0 → μ+ μ− branching fraction [14]; but our re-
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
sult is still lower and can further constrain the parameters of NP scenarios. The result brings some tension into the explanation of the anomaly + in the measured D+ s → μ ν width with a leptoquark contribution [6]. 2. SEARCH FOR B + → D− + + DECAYS The SM defines neutrinos as left-handed massless particles that do not violate lepton number. It has been discovered through neutrino oscillation experiments that neutrinos do have mass. However, experiments were still unable determine what type of particle neutrinos are, Dirac or Majorana. If a neutrino cannot be distinguished from its own antiparticle, then it is a Majoranatype particle. This has the consequence that lepton-number-violaing (LNV) processes can occur. In the field of B meson decays the only existing experimental result for ΔL = 2 processes is from the CLEO collaboration which searched for B + → h− + + [1] (with h = π, K, ρ and K ∗ ) decays and set upper limits on the corresponding branching fractions of the order of (1.0 − 8.3) × 10−6 [15]. However, no search has been performed for B + → D− + + decays. In comparison to charmless b decays b → c decays are in general favoured, thus it is interesting to extend the search to B + → D− + + decays. Theoretical calculations, based on a heavy Majorana neutrino of mass within the range of (2 − 4) GeV/c2 , placed the branching fraction of B + → D− + + around 10−7 [16,17]. Using 772 × 106 BB pairs collected with the Belle detector we search for the B + → D− e+ e+ , D− e+ μ+ and D− μ+ μ+ decays. We use standard particle identification criteria to reconstruct B + → D− 1 2 (1 2 = e+ e+ , e+ μ+ or μ+ μ+ , where 1 (2 ) denotes the higher(lower)- momentum lepton in the pair) decays including the intermediate state D− → K + π − π − . The D− meson candidates are required to have the K + π − π − invariant mass within 3 standard distributions of its nominal mass [7]. We select the one with the K + π − π − invariant mass being closest to the nominal D− mass in case of multiple D− candidates in an event.
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Electrons are identified with an efficiency and fake rates of approximately 90% and 0.1%, respectively, whereas muons have an efficiency and fake rates of muon of around 90% and 1%, respectively. We require that electron candidates have momentum bigger than 0.5 GeV/c and 0.8 GeV/c for muons, because the lepton identification for low-momentum tracks are in general of lower efficiency and higher fake rates. A duplicated track appearing from a single vertex may contaminate the signal, since same-charge lepton pairs (e+ e+ or μ+ μ+ ) exist in the final state. We require that the invariant mass of the same-charged lepton pair be greater than the sum of its individual masses by 0.5 MeV/c2 or more, to remove duplicated tracks. Duplicate track rejection is also applied to the pion pair from the D− decay. We choose the one with the largest momenta of 1 and 2 , with the priority given to 2 , if there is more than one same-charged lepton pair in an event. By combining the D− and the + + pair the + B meson candidates are reconstructed. For this we use two kinematic variables defined in the CM frame of Υ(4S): the beam-energy-constrained B 2 = Ebeam − p2cand and energy meson mass Mbc difference ΔE = Ecand − Ebeam , where Ebeam is the beam energy and Ecand and pcand are the energy and momentum, respectively, of a B meson candidate. A dominant contribution to the background come from the continuum production of quark pairs e+ e− → qq (q = u, d, s and c). The continuum background events can be distinguished from the signal events by the different event shape. We use a Fisher discriminant (F) made out of modified Fox-Wolfram moments [18], which present topological characteristics of an event shape to distinguish continuum events from signal. We also use cos θB where θB is the polar angle of the B flight direction in the CMS frame. The cos θB distribution of a B decay event should fol2 low |Y11 | = 1 − cos2 θ due to the vector nature of the parent Υ(4S) decaying to a pair of spinless B mesons, while a random combination from continuum events should be nearly flat in cos θB . Another important source of background comes from semileptonic B decays. In such cases, the
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neutrino which is produced along each lepton has as a consequence larger missing energy Emiss , while the signal events have smaller Emiss because of no neutrinos in the final state. The pair of leptons in these events originates from different B mesons unlike in the signal events. This has the consequence that the vertex displacement δz between the two leptons tends to be larger than that of signals. Consequently, we use the variables Emiss and δz to suppress these and other b → c background events. We construct the probability density functions (PDFs), for each of the four variables explained above, for the signal and background samples, where the background sample consists of continuum and generic b → c Monte-Carlo (MC) simulation events. These are combined into the likelihood ratio R. A blind analysis technique was used to perform this search. We choose the cut value √ of R which maximises the figure of merit Ns / Nb , where Ns(b) is the number of expected signal (background) events in the signal region, to optimise the signal selection criteria. We use the signal MC to determine Ns while Nb is determined by scaling the number of on-resonance data events in the background region of the Mbc − ΔE plane. An ARGUS function [19] is being used to fit the background distribution for Mbc and 1storder Chebyshev polynomial for ΔE to model the PDFs. We also checked in addition to the above two major background sources, the possible backgrounds from semileptonic B → Xu ν decays using a dedicated high-statistics simulation sample as well as charmless hadronic B meson decays. Their contribution in the signal region was estimated to be negligible. The signal efficiencies are determined by using a MC sample in which B + → D− + + decays are generated according to 3-body phase space (3BPS) distribution and using optimised selection criteria. We take into account the data vs. MC difference by correcting the MC-determined efficiency for the following parts: tracking, pion and kaon identification, and lepton identification, in each case the correction is approximately 2% or smaller. The uncertainties in the corrections are considered as systematic errors. The Mbc distribution of events passing all se-
Figure 2. Mbc distributions of on-resonance data in the D− e+ e+ (top), D− e+ μ+ (middle) and D− μ+ μ+ (bottom) modes. In each plot, the open histogram is for the analysis region in ΔE, and the hatched histogram is for the ΔE signal region (preliminary). The vertical arrow indicates the lower bound of the Mbc signal region (5.27 GeV/c2 ).
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
lection requirements except for those on ΔE and Mbc for each mode are shown in Figure 2. The hatched histograms are for events with tighter ΔE requirements corresponding to the signal region while the open histograms are for events in the signal region of Mbc − ΔE. The vertical arrow indicates the lower bound of the Mbc signal region. No events are observed in the signal region in any mode. We calculate the upper limits on the corresponding branching fractions, using the programme pole [12], since no events were observed in the signal region. The programme pole handles the systematic uncertainty in the background estimation and that of efficiency. The estimated background uncertainties are in the range of 0.13%-0.43% and dominated by the statistical error of the onresonance event sample in the background region. The important sources of systematic uncertainties are lepton identification (3.0% - 3.5%), tracking (5.2%), and the requirements on the R (3.8% 4.9%), and Mbc −ΔE signal region (1.2% - 2.0%). A calibration sample of B 0 → J/φK ∗0 decays with J/ψ → + − and K ∗0 → K + π − is used to determine the uncertainty from the difference in Mbc and ΔE shapes between data and MC. To evaluate the uncertainty from the R requirement the B 0 → J/ψK ∗0 mode is used. We also include in the multiplicative systematic uncertainty the number of BB events (NBB ), which is not a part of the efficiency uncertainty. The combined multiplicative systematic uncertainty (8.6% for the D− e+ e+ , and 10.1% for the D− e+ μ+ and 8.8% for the D− μ+ μ+ modes) is used to calculate the upper limit. In summary, we have searched for leptonnumber- violating decays of B + mesons, B + → D− + + . We find no signal events. The preliminary upper limits on the branching fractions at the 90% confidence level are B(B + → D− e+ e+ ) < 2.7 × 10−6 , B(B + → D− e+ μ+ ) < 1.9 × 10−6 and B(B + → D− μ+ μ+ ) < 1.1 × 10−6 , based on the assumption for the 3BPS distribution for the signal decays. These upper limits represent the first experimental results for the corresponding decay modes.
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REFERENCES 1. Throughout this paper charge-conjugate decay modes are included. 2. S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D 2 (1970) 1285. 3. G. Burdman, E. Golowich, J. L. Hewett and S. Pakvasa, Phys. Rev. D 66 (2002) 014009. 4. E. Golowich, J. Hewett, S. Pakvasa and A. A. Petrov, Phys. Rev. D 79 (2009) 114030. 5. B. A. Dobrescu and A. S. Kronfeld, Phys. Rev. Lett. 100 (2008) 241802. 6. I. Dorˇsner, S. Fajfer, J. F. Kamenik and N. Koˇsnik, Phys. Lett. B 682 (2009) 67. 7. C. Amsler et al. (Particle Data Group), Phys. Lett. B 667 (2008) 1. 8. D. J. Lange, Nucl. Instrum. Meth. A 462, (2001) 152. 9. R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini, (1987), CERNDD/EE/84-1. 10. E. Barberio and Z. Was, Comput. Phys. Commun. 79 (1994) 291. 11. G. J. Feldman and R. D. Cousins, Phys. Rev. D 57 (1998) 3873. 12. J. Conrad, O. Botner, A. Hallgren and C. Perez de los Heros, Phys. Rev. D 67 (2003) 012002. 13. M. Petriˇc et al. (Belle Collaboration), Phys. Rev. D 81 (2010) 091102. 14. T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 82 (2010) 091105. 15. K. W. Edwards et al. (CLEO collaboration), Phys. Rev. D 65 (2002) 111102. 16. J.-M. Zhang and G.-L. Wang, (2010) arXiv:1003.5570 [hep-ph]. 17. G. Cvetic et al., Phys. Rev. D 82 (2010) 053010. 18. G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41 (1978) 1581. 19. H. Albrecht et al. (ARGUS Collaboration), Phys. Lett. B 241 (1990) 278.
Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61 www.elsevier.com/locate/npbps
Lepton flavour violation in D and B decays at Belle M. Petriˇca a
Joˇzef Stefan Institure, Jamova cesta 39, 1000 Ljubljana, Slovenia We search for the flavour-changing neutral current decays D0 → μ+ μ− and D0 → e+ e− , and for the leptonflavour violating decays D0 → e± μ∓ using 660 fb−1 of data. We also search for lepton-number violating decays B + → D− e+ e+ , B + → D− μ+ μ+ and B + → D− μ+ e+ using 710 fb−1 of data. All the data is collected with the Belle detector at the KEKB asymmetric-energy e+ e− collider. We find no evidence for any of these decays. We obtain significantly improved upper limits on the branching fractions: B D0 → μ+ μ− < 1.4 × 10−7 , B D0 → e+ e− < 7.9 × 10−8 , B D0 → e+ μ− + B D0 → μ+ e− < 2.6 × 10−7 , B(B + → D− e+ e+ ) < 2.6 × 10−6 , B(B + → D− e+ μ+ ) < 1.6 × 10−6 and B(B + → D− μ+ μ+ ) < 0.9 × 10−6 at 90% confidence level.
1. SEARCH FOR D0 → + − DECAYS In the standard model (SM) the flavourchanging neutral current (FCNC) decays D0 → e+ e− and D0 → μ+ μ− [1] are highly suppressed by the Glashow-Iliopoulos-Maiani mechanism [2]. Considering long distance contributions the branching fractions in the SM are around 10−13 [3]. The lepton-flavour violating (LFV) decays D0 → e± μ∓ are forbidden in the SM, but are possible in extensions of the SM with massive neutrinos and the branching fractions are expected to be of the order of 10−14 in such cases [3]. All these predictions are orders of magnitude below the current experimental sensitivity. Branching fractions of FCNC decays can be enhanced by many orders of magnitude in some new physics (NP) scenarios. The branching fractions of D0 → e+ e− and D0 → μ+ μ− can be, for example, increased by R-parity violating supersymmetry up to 10−12 and 10−8 , respectively [4]. The latter prediction is close to the current experimental sensitivity. It was suggested that so far unobserved leptoquarks could explain the small discrepancy between the measured value of the Ds meson decay constant and the prediction of lattice QCD [5]. In order to explain the discrepancy with a leptoquark contribution, and comply with other constraints, B D0 → μ+ μ− should 0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2011.06.011
be enhanced to 8 × 10−7 [6]. Using 660 fb−1 of data recorded by the Belle detector at the KEKB collider, we searched for the decays D0 → μ+ μ− , D0 → e+ e− and D0 → e± μ∓ . In this measurement only D0 mesons coming from c - quark production in the continuum e+ e− → cc process are considered, since the inclusion of D0 mesons from B decays would result in a higher combinatorial background. To cancel various systematic uncertainties we normalise the sensitivity of our search to topologically similar D0 → π + π − decays . Firstly, a loose event selection is performed that is the same for all data samples apart from the particle identification criteria. Secondly, tighter optimised specific criteria are used for each decay mode. To improve the purity of the D0 → + − and π + π − samples, we use D0 mesons from the decay D∗+ → D0 πs+ with a characteristic low momentum pion. To reject D-mesons produced in B-meson decays and to suppress combinatorial background, a D∗+ momentum greater than 2.5 GeV/c in the centre-of-mass (CM) frame of the collisions is required. Candidate D0 mesons are selected using two kinematic observables: the invariant mass of the D0 decay products, M , and the energy released in the D∗+ decay, q = (MD∗+ − M − mπ )c2 , where MD∗+ is the invari-
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
ant mass of the D0 πs combination and mπ is the π + mass [7]. We require 1.81 GeV/c2 < M < 1.91 GeV/c2 and q < 20 MeV. The background in D0 → + − decays originates predominantly from semileptonic B decays (80%) and from D0 decays (10%), according to Monte Carlo (MC) simulation based on EvtGen [8] and GEANT3 [9]. The background events can be grouped into two categories based on their distribution in M : (1) a smooth combinatorial background, and (2) a peaking background from the misidentification of D0 → π + π − decays. When both pions from a D0 → π + π − decay are misidentified as muons or as a muonelectron combination, this produces a signal-like background. Using signal MC simulation, which additionally includes final-state radiative effects (FSR) simulated by PHOTOS [10], the signal efficiencies and ππ are evaluated. A blind analysis technique has been adopted in order to avoid biases. Until the final event selection criteria were established, all events inside the D0 signal region of |ΔM | < 20 MeV/c2 and |Δq| < 1 MeV were blinded. We optimise the selection criteria to obtain the best upper limits, since D0 → + − decays are not expected to be observed at the current sensitivity; we maximise the figure of merit, F = /NUL , where is the efficiency for detecting D0 → + − decays obtained from the signal MC simulation and NUL is the Poisson average of Feldman-Cousins 90% confidence level upper limits on the number of observed signal events that would be obtained with the expected background and no signal [11]. The average upper limits NUL are calculated from the number of generic MC background events, surviving the selection criteria and scaled to the data size. The sample corresponds to 6-times the statistics of the data. For the optimisation we select the following variables: signal region size (ΔM, Δq), maximal missing energy Emiss . We construct Emiss from the difference between the beam energy and the sum of the energies of all four-vectors of photons and charged tracks, which are assumed to be pions. We measure quantities ΔM and Δq relative to the nominal D0 mass and nominal energy released in the D∗+ decay, respectively. An
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asymmetric signal region in M is allowed with respect to the nominal D0 mass; in the case of the μμ decay mode this is used to suppress background from misidentification D0 → π + π − decays, since their invariant mass distribution peaks about 2 standard deviations below the D0 mass; the asymmetric requirement accounts for the low mass tail due to electron bremsstrahlung for the ee and eμ modes. To suppress background from semileptonic B decays, a requirement on the maximal allowed missing energy in the event is chosen since such decays have larger missing energy due to undetected neutrinos. We use the sideband region |Δq| > 1 MeV to estimate the number of combinatorial background events in the signal region. To reduce the statistical error and to exclude possible signal events and misidentification from D0 → π + π − decays, such a region has been chosen. Good agreement in the combinatorial background distribution in this region can be seen between MC and data. We parametrise the sideband as f (M, q) = √ A(1−BM ) q, where A and B represent parameters determined from a fit to the generic MC sample. By means of integration of f (M, q) the number of combinatorial background events in the sigcomb nal region is calculated as Nbkg = p × Nside , where Nside is the number of events found in the sideband region and p is the expected ratio of events in the signal and sideband region. We estimate the peaking background in the signal region due to misidentification of D0 → π + π − decays in two steps. Firstly, D0 → π + π − decays found in data are reconstructed so that the pion mass is replaced with the lepton mass. Secondly, we weight each event with the pion-lepton misidentification probability and pion identification efficiency. The misidentification probabilities and efficiencies are measured in data using D∗+ → D0 πs+ , D0 → K − π + decays, binned in particle momentum p and cosine of polar angle. The misidentification of D0 → π + π − contributes significantly only to the D0 → μ+ μ− decay channel (1.8 events). In Figure 1 the invariant mass distributions after applying the optimised event selection criteria are shown. In the signal region we find two candidates in the D0 → μ+ μ− , zero candidates
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
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in the D0 → e+ e− , and three candidates in the D0 → e± μ∓ decay mode; the number of events in the signal window is consistent with the estimated background.
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Figure 1. The invariant mass distributions for (a) D0 → μ+ μ− , (b) D0 → e+ e− , and (c) D0 → e± μ∓ . Superimposed on the data (open histograms) are the estimated distribution for combinatorial background (filled histogram), the misidentification of D0 → π + π − (cross-hatched histogram), and the signal if the branching fractions were equal to the 90% confidence level upper limit (single hatched histogram). The dashed vertical lines indicate the optimised signal window [13].
To determine the yield of D0 → π + π − candidates for the normalisation, a binned maximum likelihood fit is used. The invariant mass distribution using the same kinematic selections as for individual leptonic modes, except for the criteria
on M is fitted. A sum of two Gaussian distributions with the same mean and an FSR tail for the signal, and a linear function for the background is used as the fit function. Using selection criteria for the μμ, ee, and eμ modes the number of reconstructed D0 mesons in the π + π − mode is found to be 51.2 × 103 , 44.1 × 103 , and 46.0 × 103 , respectively. The relative uncertainties on Nππ are around 0.5%. We use the signal MC to determine the efficiencies. To compensate for small differences in lepton and pion identification efficiencies between data and MC simulation, event weighting is applied. Decays γγ → + − and B → XJ/ψ(→ + − ) are used to determine the correction factors for lepton identification. The signal efficiencies are found to be 11% for π + π − decays and between 5% and 7% for + − decays. The uncertainties in are estimated to be 0.3% and include contributions from MC statistics (0.2%) and lepton identification efficiency corrections (0.2%). Because of a larger MC sample and better known pion efficiency corrections, the uncertainty in ππ is small (0.1%). We calculate the branching fraction upper limits (UL) using the programme pole.f [12], which extends the Feldman-Cousins method [11] by the inclusion of systematic uncertainties. It has been noted that the inclusion of systematic uncertainties with pole produces nearly the same result as the standard Feldman-Cousins 0 ± ∓ → e μ method. Note that B D denotes the 0 sum B D → e+ μ− + B D0 → μ+ e− . In summary, we have searched for the FCNC decays D0 → μ+ μ− and D0 → e+ e− , and the LFV decays D0 → e± μ∓ using the Belle detector and have found no evidence of these decays. The upper limits on the branching 0 fractions at + − the 90% confidence level are B D < → μ μ 1.4 × 10−7 , B D0 → e+ e− < 7.9 × 10−8 and B D0 → e± μ∓ < 2.6 × 10−7 [13]. These results improve the current limits by a factor of 9 for D0 → μ+ μ− decay, by a factor of 15 for D0 → e+ e− decay and by a factor of 3 for D0 → e± μ∓ decay [7]. The CDF collaboration recently reported a result on the UL for the D0 → μ+ μ− branching fraction [14]; but our re-
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sult is still lower and can further constrain the parameters of NP scenarios. The result brings some tension into the explanation of the anomaly + in the measured D+ s → μ ν width with a leptoquark contribution [6]. 2. SEARCH FOR B + → D− + + DECAYS The SM defines neutrinos as left-handed massless particles that do not violate lepton number. It has been discovered through neutrino oscillation experiments that neutrinos do have mass. However, experiments were still unable determine what type of particle neutrinos are, Dirac or Majorana. If a neutrino cannot be distinguished from its own antiparticle, then it is a Majoranatype particle. This has the consequence that lepton-number-violaing (LNV) processes can occur. In the field of B meson decays the only existing experimental result for ΔL = 2 processes is from the CLEO collaboration which searched for B + → h− + + [1] (with h = π, K, ρ and K ∗ ) decays and set upper limits on the corresponding branching fractions of the order of (1.0 − 8.3) × 10−6 [15]. However, no search has been performed for B + → D− + + decays. In comparison to charmless b decays b → c decays are in general favoured, thus it is interesting to extend the search to B + → D− + + decays. Theoretical calculations, based on a heavy Majorana neutrino of mass within the range of (2 − 4) GeV/c2 , placed the branching fraction of B + → D− + + around 10−7 [16,17]. Using 772 × 106 BB pairs collected with the Belle detector we search for the B + → D− e+ e+ , D− e+ μ+ and D− μ+ μ+ decays. We use standard particle identification criteria to reconstruct B + → D− 1 2 (1 2 = e+ e+ , e+ μ+ or μ+ μ+ , where 1 (2 ) denotes the higher(lower)- momentum lepton in the pair) decays including the intermediate state D− → K + π − π − . The D− meson candidates are required to have the K + π − π − invariant mass within 3 standard distributions of its nominal mass [7]. We select the one with the K + π − π − invariant mass being closest to the nominal D− mass in case of multiple D− candidates in an event.
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Electrons are identified with an efficiency and fake rates of approximately 90% and 0.1%, respectively, whereas muons have an efficiency and fake rates of muon of around 90% and 1%, respectively. We require that electron candidates have momentum bigger than 0.5 GeV/c and 0.8 GeV/c for muons, because the lepton identification for low-momentum tracks are in general of lower efficiency and higher fake rates. A duplicated track appearing from a single vertex may contaminate the signal, since same-charge lepton pairs (e+ e+ or μ+ μ+ ) exist in the final state. We require that the invariant mass of the same-charged lepton pair be greater than the sum of its individual masses by 0.5 MeV/c2 or more, to remove duplicated tracks. Duplicate track rejection is also applied to the pion pair from the D− decay. We choose the one with the largest momenta of 1 and 2 , with the priority given to 2 , if there is more than one same-charged lepton pair in an event. By combining the D− and the + + pair the + B meson candidates are reconstructed. For this we use two kinematic variables defined in the CM frame of Υ(4S): the beam-energy-constrained B 2 = Ebeam − p2cand and energy meson mass Mbc difference ΔE = Ecand − Ebeam , where Ebeam is the beam energy and Ecand and pcand are the energy and momentum, respectively, of a B meson candidate. A dominant contribution to the background come from the continuum production of quark pairs e+ e− → qq (q = u, d, s and c). The continuum background events can be distinguished from the signal events by the different event shape. We use a Fisher discriminant (F) made out of modified Fox-Wolfram moments [18], which present topological characteristics of an event shape to distinguish continuum events from signal. We also use cos θB where θB is the polar angle of the B flight direction in the CMS frame. The cos θB distribution of a B decay event should fol2 low |Y11 | = 1 − cos2 θ due to the vector nature of the parent Υ(4S) decaying to a pair of spinless B mesons, while a random combination from continuum events should be nearly flat in cos θB . Another important source of background comes from semileptonic B decays. In such cases, the
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neutrino which is produced along each lepton has as a consequence larger missing energy Emiss , while the signal events have smaller Emiss because of no neutrinos in the final state. The pair of leptons in these events originates from different B mesons unlike in the signal events. This has the consequence that the vertex displacement δz between the two leptons tends to be larger than that of signals. Consequently, we use the variables Emiss and δz to suppress these and other b → c background events. We construct the probability density functions (PDFs), for each of the four variables explained above, for the signal and background samples, where the background sample consists of continuum and generic b → c Monte-Carlo (MC) simulation events. These are combined into the likelihood ratio R. A blind analysis technique was used to perform this search. We choose the cut value √ of R which maximises the figure of merit Ns / Nb , where Ns(b) is the number of expected signal (background) events in the signal region, to optimise the signal selection criteria. We use the signal MC to determine Ns while Nb is determined by scaling the number of on-resonance data events in the background region of the Mbc − ΔE plane. An ARGUS function [19] is being used to fit the background distribution for Mbc and 1storder Chebyshev polynomial for ΔE to model the PDFs. We also checked in addition to the above two major background sources, the possible backgrounds from semileptonic B → Xu ν decays using a dedicated high-statistics simulation sample as well as charmless hadronic B meson decays. Their contribution in the signal region was estimated to be negligible. The signal efficiencies are determined by using a MC sample in which B + → D− + + decays are generated according to 3-body phase space (3BPS) distribution and using optimised selection criteria. We take into account the data vs. MC difference by correcting the MC-determined efficiency for the following parts: tracking, pion and kaon identification, and lepton identification, in each case the correction is approximately 2% or smaller. The uncertainties in the corrections are considered as systematic errors. The Mbc distribution of events passing all se-
Figure 2. Mbc distributions of on-resonance data in the D− e+ e+ (top), D− e+ μ+ (middle) and D− μ+ μ+ (bottom) modes. In each plot, the open histogram is for the analysis region in ΔE, and the hatched histogram is for the ΔE signal region (preliminary). The vertical arrow indicates the lower bound of the Mbc signal region (5.27 GeV/c2 ).
M. Petriˇc / Nuclear Physics B (Proc. Suppl.) 218 (2011) 56–61
lection requirements except for those on ΔE and Mbc for each mode are shown in Figure 2. The hatched histograms are for events with tighter ΔE requirements corresponding to the signal region while the open histograms are for events in the signal region of Mbc − ΔE. The vertical arrow indicates the lower bound of the Mbc signal region. No events are observed in the signal region in any mode. We calculate the upper limits on the corresponding branching fractions, using the programme pole [12], since no events were observed in the signal region. The programme pole handles the systematic uncertainty in the background estimation and that of efficiency. The estimated background uncertainties are in the range of 0.13%-0.43% and dominated by the statistical error of the onresonance event sample in the background region. The important sources of systematic uncertainties are lepton identification (3.0% - 3.5%), tracking (5.2%), and the requirements on the R (3.8% 4.9%), and Mbc −ΔE signal region (1.2% - 2.0%). A calibration sample of B 0 → J/φK ∗0 decays with J/ψ → + − and K ∗0 → K + π − is used to determine the uncertainty from the difference in Mbc and ΔE shapes between data and MC. To evaluate the uncertainty from the R requirement the B 0 → J/ψK ∗0 mode is used. We also include in the multiplicative systematic uncertainty the number of BB events (NBB ), which is not a part of the efficiency uncertainty. The combined multiplicative systematic uncertainty (8.6% for the D− e+ e+ , and 10.1% for the D− e+ μ+ and 8.8% for the D− μ+ μ+ modes) is used to calculate the upper limit. In summary, we have searched for leptonnumber- violating decays of B + mesons, B + → D− + + . We find no signal events. The preliminary upper limits on the branching fractions at the 90% confidence level are B(B + → D− e+ e+ ) < 2.7 × 10−6 , B(B + → D− e+ μ+ ) < 1.9 × 10−6 and B(B + → D− μ+ μ+ ) < 1.1 × 10−6 , based on the assumption for the 3BPS distribution for the signal decays. These upper limits represent the first experimental results for the corresponding decay modes.
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