Observation of the Leptonic Decay D + → τ + ν τ

We report the ﬁrst observation of D + → τ + ν τ with a signiﬁcance of 5 . 1 σ . We measure B ( D + → τ + ν τ ) = (1 . 20 ± 0 . 24 stat. ± 0 . 12 syst. ) × 10 − 3 . Taking the world average B ( D + → µ + ν µ ) = (3 . 74 ± 0 . 17) × 10 − 4 , we obtain R τ/µ = Γ( D + → τ + ν τ ) / Γ( D + → µ + ν µ ) = 3 . 21 ± 0 . 64 stat. ± 0 . 43 syst. , which is consistent with the standard model expectation of lepton ﬂavor universality. Using external inputs, our results give values for the D + decay constant f D + and the Cabibbo-Kobayashi-Maskawa

In the purely leptonic decay of the charmed meson D + , the c andd quarks annihilate into a pair of charged and neutral leptons via a virtual W boson. (Unless otherwise noted, charge conjugate modes are implied throughout this Letter.) To the lowest order, the decay rate for D + → + ν is given in a very simple form: where the D + mass M D + , the masses of the charged leptons m ( = e + , µ + , or τ + ), and the Fermi coupling constant G F are known to great precision [1]. Because of this, measuring B(D + → + ν ) (B ν ) allows determination of the product f 2 D + |V cd | 2 of the D + decay constant and the square of the c → d Cabibbo-Kobayashi-Maskawa (CKM) matrix element. One can then extract |V cd | by using the predicted value of f D + , e.g., from lattice quantum chromodynamics (LQCD), or obtain f D + by using the experimentally measured |V cd | to test the LQCD prediction. Such studies have been done using the muonic mode D + → µ + ν µ ( [2], [3]), which is a simple two-body decay with a clear experimental signature. The energetic track produced in this decay can be reconstructed very efficiently with minimal systematic uncertainty.
Experimental information about D + → τ + ν τ is more sparse, with only an upper limit of 1.2 × 10 −3 on B τ ν at a 90% confidence level (C.L.) [1] that was set by the CLEO Collaboration [3]. Measuring B τ ν is an important check of the standard model, which predicts the ratio of the τ + ν τ and µ + ν µ decay rates. Applying Eq. (1) to both which provides a clean test of the standard model expectation of lepton flavor universality. Deviation from the expected value of R τ /µ could signify contributions of a charged intermediate boson that couples to the leptons differently, e.g., through a leptoquark [4]. The fact that B τ ν has not been measured previously, together with the recent hints of possible violation of lepton universality in B decays [5], establishes that R τ /µ is an important quantity to determine experimentally. We note, however, that in some supersymmetric models, such as the two-Higgsdoublet model [6], the charged Higgs couples to the lepton mass leading to a mass dependence identical to that from the W boson process, including its helicity suppression. Thus, Eq. (1) is modified by a factor that does not depend on the lepton masses, leaving R τ /µ unchanged. From the standard model prediction R τ /µ = 2.67 and B µν = (3.74 ± 0.17) × 10 −4 [1], one expects B τ ν = (1.01 ± 0.05) × 10 −3 , which is very close to CLEO's upper limit based on 818 pb −1 of e + e − annihilation data. In this Letter, we report the first observation of D + → τ + ν τ and the measurement of its branching fraction with an e + e − annihilation sample produced at the Beijing Electron Positron Collider (BEPCII) [7] near the nominal mass of the ψ(3770) resonance, √ s = 3.773 GeV, with an integrated luminosity of 2931.8 pb −1 [8] collected with the BESIII detector.
BESIII is a cylindrical detector with a solid angle coverage of 93% of 4π. The detector consists of a Heliumgas-based main drift chamber (MDC), a plastic scintillator time-of-flight system, a CsI(Tl) electromagnetic calorimeter (EMC), a superconducting solenoid providing a 1.0 T magnetic field, and muon counters. The charged particle momentum resolution is 0.5% at a transverse momentum of 1 GeV/c. The photon energy resolution at 1 GeV is 2.5% in the central barrel region and 5.0% in the end cap region. More details about the design and performance of BESIII are given in Ref. [9].
Detection efficiencies and background processes are determined with a Monte Carlo (MC) simulation sample with an equivalent luminosity roughly 10 times larger than the data set. It consists of events from e + e − → ψ(3770) → DD, e + e − → qq (q = u, d, s), e + e − → γJ/ψ, e + e − → γψ(3686), and e + e − → τ + τ − . The effects of initial-and final-state radiation are simulated by the KKMC generator [10] and the PHOTOS package [11], respectively. The generated four-momenta are propagated into EvtGen [12], which simulates decays using known rates [13] and correct angular distributions. We generate charmonium decays not accounted for by exclusive measurements with Lundcharm [14]. Finally, the detector response is simulated with geant4 [15].
We measure B τ ν by reconstructing τ + via τ + → π +ν τ , which has the feature of only a single charged track from the D + decay. Because pions and muons are charged particles with similar masses, the BESIII selection of pion tracks based on specific-ionization and time-of-flight measurements also accepts muon tracks with comparable efficiency (> 90%), allowing simultaneous measurement of B τ ν and B µν . For this analysis our main result is obtained by fixing B µν to the world average of (3.74 ± 0.17) × 10 −4 [1] to maximize our statistical sensitivity for measuring B τ ν . We also perform a cross-check of our result by measuring B µν and B τ ν simultaneously.
This analysis employs a double-tag technique, pioneered by the Mark III Collaboration [16]. We obtain the branching fraction by reconstructing D + → τ + (→ π +ν τ )ν τ in events with D − decays reconstructed in one of the six tag modes listed in Table I: In Eq. (3) N τ ν is the number of events with any D − tag and a D + → τ + (→ π +ν τ )ν τ candidate, i τ ν is the signal selection efficiency including B(τ + → π +ν τ ) for an event with a D − in the ith tag mode, and N i tag and i tag are the number of tag and reconstruction efficiency for D − tags in mode i.
In selecting tags our criteria for the final-state particles are identical to those in Ref. [17]. In each event, we allow only one D candidate for a given tag mode separately for D + and D − , following the method of Ref. [18]. For each tag mode, we extract N i tag from distributions of beam-constrained mass M BC c 2 = E 2 beam − | p tag c| 2 , where p tag is the three-momentum of the tag D − candidate and E beam is the beam energy in the center-of-mass system of the ψ(3770). We fit to these M BC distributions with MC-based signal shapes that are convolved with a Gaussian to accommodate resolution differences between simulation and data. The background shape is parametrized with an ARGUS function [19]. Figure 1 shows the fits to M BC distributions. To select the tag, we require that 1863 < M BC < 1877 MeV/c 2 [20]. Table I shows N i tag , i tag , and i τ ν for all tag modes.
, and (f) K + K − π − . Red lines are the overall fits, while the yellow-dashed (blue-dotted) lines are the fitted signals (backgrounds).
797.6 ± 1.0 51.06 ± 0.03 3.6 ± 0.1 K + π − π − π 0 245. Once we select the tag, we require that there be only one additional charged track and that it have charge opposite to that of the tag. It must originate within 1 cm (10 cm) from the beam interaction point in the plane transverse to (along) the beam direction, be within the fiducial region for reliable track reconstruction (| cos θ| < 0.93, where θ is the polar angle with respect to the direction of the positron beam), and match a shower in the EMC. Furthermore, to distinguish between π-like and µ-like tracks, we rely on the minimum-ionizing character of the µ track, which has a mean energy deposit of E EMC 200 MeV, as was done in Refs. [2,3]. Thus we partition the selected events into two samples, one with µ-like tracks (E EMC ≤ 300 MeV) and the other with π-like tracks (E EMC > 300 MeV). The first portion includes 99% of the muon tracks from D + → µ + ν µ , while the second has 44% of the pion tracks from D + → τ + ν τ , τ + → π +ν τ . To suppress backgrounds further, we apply four additional requirements, which are optimized based on MC calculations. (1) E EMC /| pc| < 0.95 for the π-like sample, where p is the signal track momentum measured by the MDC. As this variable sharply peaks around 1 for an electron, this requirement suppresses events from semileptonic decays like D + → K 0 L e + ν e . (2) E max < 300 MeV for both samples, where E max is the maximum energy of all EMC showers that are not assigned to any charged track or neutral EMC shower in the reconstruction of both D + and D − . This suppresses events with extra particles, including misreconstructed neutral pions. (3) | cos θ missing | < 0.95(0.75) for the µ (π)-like sample, where θ missing is the polar angle of the missing momentum p missing = − p D − − p µ(π) , p D − =p D − (E beam /c) 2 − (M D + c) 2 , andp D − is the unit momentum vector of the D − . This ensures that p missing points to an active region of the detector. (4) α > 25 • (45 • ) for the µ (π)-like sample, where α is the opening angle between p missing and the direction of the most energetic unassigned shower. A shower from an asymmetric decay of π 0 or from K 0 L tends to deposit energy in the EMC in the p missing direction. The minimum required energy of the unassigned shower is 25 MeV for | cos θ| < 0.8 and 50 MeV for 0.86 < | cos θ| < 0.93.
We expect peaking backgrounds from D + → π 0 π + and D + → K 0 L π + . The first is relatively small, but is close to M 2 miss = 0. The latter peaks away from M 2 miss = 0 at m 2 K 0 , but is a concern because of an expected rate of 40 times the expected signal.
We use data-based control samples to construct the probability density functions (PDFs) to represent these two peaking backgrounds. The black points in Fig. 2 show M 2 miss distributions from exclusively reconstructed D + → π 0 (→ γγ)π + (left column) and D + → K 0 S (→ π + π − )π + (right column) events in which we treat the K 0 S and the π 0 as missing particles, respectively. The red-shaded histograms are from true D + → π 0 π + and D + → K 0 L π + MC events after applying all signal selection criteria, scaled to the same sizes as the data. Agreement between the shapes of the expected distributions and our control samples is excellent. We generate the corresponding PDFs by smoothing the distributions of the data points by the kernel estimation method [21]. Additional peaking backgrounds from D + → η(→ γγ)π + S (→ π + π − )π + (b), (d) events from data (black points) for the µ-like (a), (b) and π-like (c), (d) samples. The blue lines are the PDFs derived from the black points, while the redshaded histograms are true D + → π 0 π + and D + → K 0 L π + MC events with all selection criteria applied. and D + → K 0 S (→ π 0 π 0 )π + are also considered, but both are small and peak away from M 2 miss = 0. For these two small backgrounds, we use the MC events to predict the PDF.
We perform an unbinned simultaneous maximum likelihood fit to the µ-and π-like samples. The signal PDFs are based on MC events, including D + → τ + ν τ with τ + final states other than π +ν τ . This contribution is dominated by τ + → µ + ν µντ and π + π 0ν τ in the µ-like sample, while the π-like sample mostly contains τ + → e + ν eντ and π + π 0ν τ . To take into account the M 2 miss resolution difference between the data and the MC samples, the PDFs of the signal and of the backgrounds are smeared using a Gaussian. The Gaussian mean and width are free parameters of the fit. The remaining background ("smooth background") comes from other well known D decays, such as semileptonic decays, as well as continuum events. It is represented by the smoothed MC prediction. We fix the sizes of D + decays to µ + ν µ , π 0 π + , ηπ + , and K 0 S π + according to Ref. [1], while we leave the normalizations for decays to τ + ν τ and K 0 L π + , as well as the smooth background as free fit parameters. The ratio of the normalizations of the smooth background between the µ-like and π-like samples is constrained based on the MC prediction. Applying this fitting procedure to the DD MC sample, we obtain the signal selection efficiencies i τ ν for each tag mode listed in Table I. Figure 3 shows the simultaneous fit to data, which yields 137 ± 27 signal events. This corresponds to B τ ν = (1.20 ± 0.24 stat. ) × 10 −3 .
As a cross check, we treat the D + → µ + ν µ component as a free fit parameter and obtain B µν = (3.70 ± 0.20 stat. ) × 10 −4 , along with B τ ν = (1.21 ± 0.24 stat. ) × 10 −3 . The obtained B µν is consistent with both the world average of (3.74 ± 0.17) × 10 −4 [1] and the recent BESIII measurement of (3.71 ± 0.19 stat. ± 0.06 syst. ) × 10 −4 [2]. The agreement with the latter measurement provides independent confirmation, as Ref. [2] uses muon counter information and is based on simulations of the signal efficiency and the background that are different from the current work.
The total systematic uncertainty is dominated by two sources. The first is the uncertainty on B µν , which is fixed to the value from Ref. [1]. The second is the uncertainty due to the assumed shapes of the smooth background. For this we vary the shape by changing the e + e − → ψ(3770) → DD and e + e − → qq cross sections from the defaults in our MC calculations. We also consider two different values of the smoothing parameter ρ in the Gaussian kernel estimation method [21], ρ = 1 (the author's suggestion) and ρ = 2. The dependence on the choice of 300 MeV for the boundary between π-and µ-like samples, which potentially changes the shapes of the smooth backgrounds, is also assessed by varying it by ±50 MeV.
Other sources of systematic uncertainty are also considered. The uncertainty in the signal track reconstruction efficiency has been obtained from previous BESIII studies of double-tagged DD events. The uncertainty in B(τ + → π +ν τ ) is from Ref. [1]. Statistical uncertainties in the tag counts in data and MC calculations are taken directly from the respective samples. Variations in the fit ranges, selection windows, binning, and signal and background parametrizations are used to probe uncertainties in the tag-side fits. We estimate uncertainties due to the E EMC /| pc| and E max criteria with double-tagged events including D + → K 0 S π + . Uncertainties from the cuts on | cos θ missing | and α are estimated with fully reconstructed D 0 → K − e + ν e events. Possible mismodeling of efficiencies due to multiplicity differences among D decay modes is estimated based on a study of tracking and particle identification efficiencies in different event environments. The uncertainty due to the normalization of the peaking backgrounds, and the ratio of smooth background sizes between µ-and π-like samples in the M 2 miss fit are estimated by studies of the D + → K 0 S π + control sample and by varying parametrizations and branching fractions, respectively. The D + → τ + ν τ signal-shape dependence is estimated by altering the mixture of τ + decay modes. Table II summarizes the systematic uncertainty estimate.
This is consistent with both the world average |V cd | = 0.218 ± 0.004 [1] and the global fit result [1]. The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National