Improved measurement of the Pseudoscalar Decay Constants fDS from D∗+ γµ+ ν data sample s → Abstract + − Determination of fDS using 14 million e e cc¯ events obtained with the CLEO → II and CLEO II.V detector is presented. New measurement of the branching ratio gives Γ (D+ µ+ν)/Γ (D+ φπ+) = 0.137 0.013 0.022. Using Γ (D+ µ+ν) = 0.036 S → S → ± ± S → 0.09, fDS was calculated and found to be (247 12 20 31) MeV. Comparison ± ± ± ± of these results with other theoretical and experimental results are also presented. 1 Introduction Purely leptonic decay modes of heavy mesons predict their decay constants, which is connected with measured quantities such as CKM matrix elements. Currently it is not possible to measure fB experimentally, but measurements of the Cabibbo-flavor pseudoscalar decay constants such as fDS is possible. This measurement provides a check of these theoretical calculations and helps to establish different theoretical models. + The decay width of Ds is given by [1] G2 m2 Γ(D+ ℓ+ν)= F f 2 m2M 1 ℓ V 2 (1) s 6π DS ℓ DS 2 cs → − MDS ! | | where MDS is the Ds mass, mℓ is the mass of the final state lepton, Vcs is a CKM matrix element equal to 0.974 [2] and GF is the Fermi coupling constant. Various theoretical predictions of fDS range from 190 MeV to 350 MeV. The relative widths of three lepton flavors are 10 : 1 : 10−5 for tau, muon and electron respectively. Helicity suppression reduces smaller width for low mass electron. Largest branching mode τν is very difficult to use for experimental measurement due to more than one missing neutrino in the final state of events. So the only choice is the µν mode. In previous publications [3, 4] CLEO reported the measurements of fDS = (280 19 ∗+ + + + ± 28 34) MeV, using the decay chain Ds γ Ds , Ds µ ν. Four other groups ± ± → → + + also published their results of fDS on the basis of their observations of Ds µ ν. + → WA75 published fDS = (232 45 20 48) MeV using muons from Ds leptonic ± ± ± +150 decay in emulsion [5], BES published a value of (430 −130 40) MeV, using fully + ± ±+ − reconstructed Ds mesons close to the production threshold in e e collisions [6], E653 measured a value of (194 35 20 14) MeV from one prong decays into muons in ± ± ± an emulsion target [7] and WA92 reported a value (323 44 12 34) MeV from ± ± ± the visible kink Ds to µ [8]. ∗+ + This paper describe an improved CLEO analysis of the decay chain Ds γ Ds , + + + − → Ds µ ν which included 15 million e e c c¯ events collected with the CLEO II → → −1 [9] and CLEO II.V [10] at CESR. The integrated luminosity is 13.7 fb of which 4.8 fb−1 was taken at CLEO II configuration and previous CLEO results based on that subsection of data sample. This analysis includes better neutrino reconstruction algorithms, more data hence improved statistics, and more precise measurement of lepton fake rates which reduces systematic error. 1 There are several sources of background for the D∗+ γµ+ ν process. The main s → physics background comes from semileptonic decay of heavy mesons. Due to lepton universality, contribution of electron and muon samples are nearly the same. Thus applying exactly same selection criteria as for electrons, one can get a qualitative estimation of background level from real leptons. D+ µ+ ν and D+ µ+ ν are the s → → only physics processes which produce significantly more muons than electrons with high momentum lepton in the continuum e+e− annihilation near Υ(4S) region. D+ µ+ ν → is highly suppressed by the CKM parameter (Eq. 1), and by the small branching fraction of D∗0 γ D0, 1.7 0.4 0.3% [11]. → ± ± Another source of background is the misidentification of hadron as a lepton. As CLEO has more fake muons than electrons, their relative contribution is taken care of from total samples. ∗+ + Besides the above two backgrounds, there are backgrounds arising from Ds γ DS , + + → Ds µ ν samples where true photon in decay chain is replaced by another photon → + + of the event and combination of spurious photons with D µ ν event samples. The s → shape of the second component of these backgrounds is determined by using the fully reconstructed D∗+ π+ D0, D0 K− π+ data samples and normalization is deter- → ∗+ + → mined from the ratio of Ds /Ds production ratio. 2 Event Selection The analysis presented here is based on previous CLEO measurements of fDS [4], i.e. ∗+ + + + ∗+ search for the decay chain Ds γ Ds , Ds µ ν. The photon from Ds and muon + → → + from Ds are directly measured, where as neutrino from Ds are measured indirectly ∗ from missing momenta of the events. Mass difference between reconstructed Ds + and + Ds are looking as a signal of the event, ∆ M = M(γµ+ ν) M(µ+ν) (2) − such that most of the relatively large error of missing momenta is canceled out. Data and MC samples of decay chains, D∗0 γ D0, D0 K− π+ and D∗+ π+ D0, D0 K− π+ → → → → are used to verify this missing momenta calculation and the shape of backgrounds. 2.1 Global event A collection of purely hadronic events is selected for further analysis by requiring at least 5 good tracks in the tracking system or at least 3 tracks with 3 isolated shower in calorimeter (definition of good tracks and isolated showers are given in Appendix A). Each event hemisphere should have more than 2 particles (tracks or shower). Visible energy of the event should be more than half of the center of mass energy (√S) and less than √S. All these criteria are used to eliminate low multiplicity source of leptons i.e. two photon processes and τ + τ − pairs. To reduce the background process where particles escaped in the beam direction, a criteria used such that the missing momentum direction should be away from the beam pipe, cos θmiss < 0.85. | | 2 2.2 Lepton identification Dominant background component of lepton from semileptonic decay mode of heavy flavor mesons is removed using the criteria that the momentum of lepton should be greater than 2.4 GeV, which is 36% efficient for signal events. Muons are required to penetrate at least 7 interaction lengths of material and have to be away from beam pipe, Cos θ < 0.85. Muon efficiency is measured with e+e− µ+µ− γ events and has | | → a flat efficiency at 85.88 0.8 % beyond a momentum of 2.4 GeV [12]. Electrons are ± also confined within Cos θ < 0.85. Energy deposit of electrons in the electromagnetic | | calorimeter should be close to the fitted track momentum, dE/dx measurement of track in the tracking system expected as an electron track and most importantly calorimeter shower profile should be matched with an electromagnetic shower. The electron iden- tification efficiency is calculated by embedding tracks from radiative Bhabha events to hadronic events. For momentum of more than 2.4 GeV, the efficiency is 80 2% [13]. ± 2.3 Photon selection Photons are selected only from showers in the barrel calorimeter with energy greater than 200 MeV (details are given in Appendix A). For D∗+ γ D+ event sample, s → s photon acceptance efficiency including this energy cut is 36%. The shower must be isolated from any charged track by more than 20◦ and have a shower shape for which the probability that the energy deposition is due to a single photon is greater than 99%. Pion veto is used to reject photons from π0 decay, which are a dominant source of electromagnetic showers. Photons combination with invariant masses within 2σ (σ = 5 MeV) of the π0 mass are rejected. 2.4 Missing momenta (ν) calculation Neutrino 4-momenta were calculated by using the near-hermetic property of the CLEO detector. An Event is divided into two hemispheres by bisecting the thrust axis of the event. Loop over all particles (here particles are the ensemble of charged tracks in the tracking system and isolated neutral shower in the calorimeter) in both hemispheres is taken to calculate the 4-momenta separately. Next we take the direction of the 3- momenta of opposite hemispheres (hemisphere opposite to lepton), divide the event into two hemispheres by bisecting that direction and loop over all particles to get a new 4-momenta for the two hemispheres. This iteration is continued until we get two stable hemispheres. Though CLEO is a near hermetic detector, a particle might be undetectable when it passes through a crack or goes in the forward direction. The average loss is calculated from MC signal events. As shown in the figure 1 the visible energy in CLEO is less than the energy of generated stable particles (except ν), similarly reconstructed 3-momenta are different from true 3-momenta. Therefore, the true 4-momenta of each hemisphere are taken as a function of visible 4-momenta. So, the missing energy and momentum are found according to Emiss = Ebeam f1(Ehem) (3) − ~pmiss = ~popp f2(~phem) (4) − − 3 Figure 1: MC generated 4-momenta in the lepton hemisphere is plotted as a function of visible 4-momenta (a) Energy (b) 3-momenta where Ebeam is the CESR beam energy, Ehem is the visible energy in lepton hemisphere, direction of ~popp is given by momentum vector of opposite hemisphere and magnitude is 2 2 given by ~popp = Ebeam mjet. mjet is the average mass of charm quark jet, measured − 2 2 to be 3.2 GeV [4].q Events with M < 2 GeV and Cos θmiss < 0.85 are processed miss | | for further analysis using event shape variables.