Measurement of the branching fraction of $$ {\textrm{D}}_{\textrm{s}}^{+} $$ → τ+ντ via τ+ → μ+νμ $$ \overline{\nu} $$ τ

Published for SISSA by Springer Received: March 23, 2023 Revised: August 30, 2023 Accepted: September 11, 2023 Published: September 19, 2023 The BESIII collaboration E-mail: Abstract: Utilizing 7.33 fb−1 of e+ e− collision data taken at the center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and 4.226 GeV with the BESIII detector, the branching fraction of the leptonic decay Ds+ → τ + ντ via τ + → µ+ νµ ν̄τ is measured to be BDs+ →τ + ντ = (5.37 ± 0.17stat ± 0.15syst )%. Combining this branching fraction with the world averages of the measurements of the masses of τ + and Ds+ as well as the lifetime of Ds+ , we extract the product of the decay constant of Ds+ and the c → s Cabibbo-KobayashiMaskawa matrix element to be fDs+ |Vcs | = (246.7±3.9stat ±3.6syst ) MeV. Taking |Vcs | from a global fit in the standard model we obtain fDs+ = (253.4±4.0stat ±3.7syst ) MeV. Conversely, taking fDs+ from lattice quantum chromodynamics calculations, we obtain |Vcs | = 0.987 ± 0.016stat ± 0.014syst . Keywords: e+ -e− Experiments ArXiv ePrint: 2303.12468 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP09(2023)124 JHEP09(2023)124 Measurement of the branching fraction of + + D+ → µ+νµν̄τ s → τ ντ via τ Contents 1 2 BESIII detector and Monte Carlo simulation 2 3 Analysis method 3 4 Single-tag candidates 3 5 Double-tag candidates 6 6 Branching fraction determination 8 7 Systematic uncertainties 7.1 Tag-mode dependent systematic uncertainties 7.2 Tag-mode independent systematic uncertainties 7.3 Total systematic uncertainties 11 11 13 14 8 Results 14 9 Summary 15 The BESIII collaboration 21 1 Introduction Leptonic decays offer an ideal laboratory for studying strong and weak interaction effects in the charmed meson system. In the standard model (SM) of particle physics, the Ds+ meson decays into `+ ν` (` = e, µ or τ ) via annihilation mediated by a virtual W + boson. Throughout this paper, the inclusion of charge conjugate channels is always implied. The partial width of Ds+ → `+ ν` at lowest order can be related to the Ds+ decay constant fDs+ via [1] 2 2 m`  2 2 1 − ΓDs+ →`+ ν` = |Vcs |2 fD , + m` mD + s s 8π m2D+ s  G2F (1.1) where GF is the Fermi coupling constant, |Vcs | is the c → s Cabibbo-Kobayashi-Maskawa (CKM) matrix element, m` is the mass of the lepton, and mDs+ is the mass of the Ds+ meson. Extraction of fDs+ in experiments is important for testing various theoretical calculations based on different approaches [2–10]. In recent years, the precision of calculations of fDs+ based on Lattice Quantum Chromodynamics (LQCD) has reached a level of 0.2% [7], and much progress has been achieved in the experimental studies of Ds+ → `+ ν` decays by the –1– JHEP09(2023)124 1 Introduction CLEO [11–13], BaBar [14], Belle [15], and BESIII [16, 17, 19–22] collaborations. Based on the average of the branching fractions (BFs) reported by these experiments, one can derive fDs+ with a precision of 1.0%. Precise and intensive estimations of fDs+ are still desirable to test theoretical calculations with higher precision. Improved measurements of fDs × |Vcs | are therefore important for testing the unitarity of the CKM matrix [23] with higher sensitivity. In the SM, the ratio of the BFs of Ds+ → τ + ντ and Ds+ → µ+ νµ can be written as BDs+ →µ+ νµ = m2 + !2 1 − m2τ + Ds m2 + !2 , (1.2) m2µ+ 1 − m2µ + Ds which only depends on the charged lepton and Ds+ meson masses. Inserting the world averages of mτ , mµ , and mDs [24] in the above equation gives Rτ /µ = 9.75 ± 0.01. Measurements of the BFs of Ds+ → `+ ν` allow this ratio to be determined experimentally and provide an important test of τ − µ lepton flavor universality. In this paper, we present a measurement of the BF of Ds+ → τ + ντ via the decay of τ + → µ+ νµ ν̄τ , by analyzing 7.33 fb−1 of e+ e− collision data taken at the center-of-mass energies √ s = 4.128 GeV, 4.157 GeV, 4.178 GeV, 4.189 GeV, 4.199 GeV, 4.209 GeV, 4.219 GeV, and 4.226 GeV [25–27] with the BESIII detector [28]. Following previous measurements, we have not corrected the BF of Ds+ → τ + ντ by the effect of radiative photons since their uncertainties can be considered individually later, details of which are reviewed in “Leptonic Decays of Charged Pseudoscalar Mesons” by the Particle Data Group (PDG) [24]. Based on this measurement, we determine fDs+ × |Vcs | with an improved accuracy, and test τ − µ lepton flavor universality with Ds+ → `+ ν` decays. 2 BESIII detector and Monte Carlo simulation The BESIII detector [28] records symmetric e+ e− collisions provided by the BEPCII storage ring [29] in the center-of-mass energy range from 2.00 to 4.95 GeV, with a peak luminosity of √ 1×1033 cm−2 s−1 achieved at s = 3.77 GeV. BESIII has collected large data samples in this energy region [30]. The cylindrical core of the BESIII detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field [31]. The solenoid is supported by an octagonal flux-return yoke with modules of resistive plate muon counters (MUC) interleaved with steel. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and specific ionization energy loss dE/dx resolution is 6% for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end-cap) region. The time resolution in the TOF barrel region is 68 ps. The end-cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [32–34]. Approximately 83% of the data used here was collected after this upgrade. –2– JHEP09(2023)124 Rτ /µ = BDs+ →τ + ντ m2τ + 3 Analysis method In e+ e− collisions with data taken at the center-of-mass energies between 4.128 and 4.226 GeV, the Ds± mesons are produced mainly via the e+ e− → Ds∗± Ds∓ → γ(π 0 )Ds+ Ds− process. For our analysis we adopt the double-tag (DT) method pioneered by the MARK III collaboration [44]. The Ds− meson, when fully reconstructed via any hadronic decay mode, is referred to as the single-tag (ST) Ds− meson. Events in which the transition γ(π 0 ) from the Ds∗+ meson and the leptonic decay of Ds+ → τ + ντ are reconstructed, in addition to the ST Ds− meson, are denoted as DT events. The BF of Ds+ → τ + ντ is determined by j = BD + →τ + ν s τ j NDT /jDT j Bτ + →µ+ νµ ν̄τ · NST /jST , (3.1) j j where NDT and NST are the yields of the DT events and ST Ds− mesons in data, respecj j tively; and DT and ST are the efficiencies of the DT events and ST Ds− mesons estimated with MC simulation, respectively. Here, jDT , which includes the efficiency of simultaneously finding the tag side, the transition γ(π 0 ) and Ds+ → τ + ντ as we (...truncated)