Amplitude analysis and branching-fraction measurement of D s + $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ → π+π0η′

Published for SISSA by Springer Received: February 10, 2022 Revised: March 10, 2022 Accepted: March 17, 2022 Published: April 8, 2022 The BESIII collaboration E-mail: Abstract: Using data collected with the BESIII detector in e+ e− collisions at center-ofmass energies between 4.178 and 4.226 GeV and corresponding to 6.32 fb−1 of integrated luminosity, we report the amplitude analysis and branching-fraction measurement of the Ds+ → π + π 0 η 0 decay. We find that the dominant intermediate process is Ds+ → ρ+ η 0 and the significances of other resonant and nonresonant processes are all less than 3σ. The upper limits on the branching fractions of S-wave and P -wave nonresonant components are set to 0.10% and 0.74% at the 90% confidence level, respectively. In addition, the branching fraction of the Ds+ → π + π 0 η 0 decay is measured to be (6.15 ± 0.25(stat.) ± 0.18(syst.))%, which receives significant contribution only from Ds+ → ρ+ η 0 according to the amplitude analysis. Keywords: Branching fraction, Charm Physics, e+ -e− Experiments, Particle and Resonance Production ArXiv ePrint: 2202.04232 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP04(2022)058 JHEP04(2022)058 Amplitude analysis and branching-fraction + 0 0 measurement of D+ s → π π η Contents 1 2 Detector and data sets 3 3 Event selection 4 4 Amplitude analysis 4.1 Further event selection 4.2 Fit method 4.2.1 Blatt-Weisskopf barrier factors 4.2.2 Propagator 4.2.3 Spin factors 4.3 Fit results 4.4 Systematic uncertainties for amplitude analysis 5 5 6 8 9 9 10 10 5 Branching fraction measurement 13 6 Summary 18 The BESIII collaboration 22 1 Introduction Hadronic decays of the Ds± meson probe the interplay of short-distance weak-decay matrix elements and long distance QCD interactions. Measurements of the branching fractions (BFs) of these decays provide direct knowledge of the amplitudes and phases in the decay process [1–3]. In addition, an improved understanding of Ds± decays is particularly valuable for studies of the Bs0 meson, which mainly decays to final states involving Ds± mesons [4]. There are two kinds of topological diagrams for Ds+ → ρ+ η 0 , including tree (T )- and annihilation (A)-diagrams, as shown in figure 1 [5]. Based on reference [6], the topological amplitude (A) expressions of Ds+ → ρ+ η, Ds+ → ρ+ η 0 and Ds+ → π + ω satisfy the sum rule: 1 cos φ A(Ds+ → π + ω) = A(Ds+ → ρ+ η) + A(Ds+ → ρ+ η 0 ). sin φ sin φ (1.1) Here, φ is the mixing angle between η and η 0 : η η0 !  cos φ − sin φ  sin φ cos φ  = –1– ηq ηs  , (1.2) JHEP04(2022)058 1 Introduction Figure 1. The TP -diagram (left), AV -diagram (middle) and AP -diagram (right) for Ds+ → ρ+ η 0 . The subscript P (V ) implies a pseudoscalar (vector) meson. Decay Theory Experiment B(%) Ds+ → ρ+ η 0 3.0 ± 0.5 [7] Ds+ → π + π 0 η 0 5.6 ± 0.5 ± 0.6 Ds+ → ρ+ η 0 5.8 ± 1.4 ± 0.4 Ds+ → π + π 0 η 0 < 5.1 (nonresonant) (90% confidence level) 1.7 [8] 1.6 [8] CLEO [9] BESIII [10] Table 1. B(Ds+ → ρ+ η 0 ) from theoretical approaches and previous experimental measurements. where ηq and ηs are defined by ηq = √12 (uu + dd) and ηs = ss. Considering the BFs of Ds+ → π + ω and Ds+ → ρ+ η and noting a simple triangular inequality in eq. (1.1), one obtains the bounds (2.19 ± 0.27)% < B(Ds+ → ρ+ η 0 ) < (4.51 ± 0.38)% [6]. The predictions of the BF of Ds+ → ρ+ η 0 from several theoretical approaches [7, 8] and the corresponding BFs from experimental measurements are shown in table 1. The theoretical predictions for B(Ds+ → ρ+ η 0 ) are lower than the experimental measurement by around 2σ as shown in table 1. A possible way to reconcile the predictions with the measured values would be to take account of the QCD flavor-singlet hairpin contribution shown in figure 2 [5]. A more precise measurement of the BF of Ds+ → ρ+ η 0 will be very valuable in establishing whether indeed the existing predictions are incorrect. Previously, BESIII reported the BF measurement of Ds+ → ρ+ η 0 performed through the process e+ e− → Ds+ Ds− , with a 482 pb−1 data sample collected at center-of-mass (C.M.) √ energy s = 4.009 GeV and CLEO measured the BF of Ds+ → π + π 0 η 0 using 586 pb−1 of √ e+ e− collisions recorded at C.M. energy s = 4.17 GeV. In this paper, we perform the first amplitude analysis of Ds+ → π + π 0 η 0 and improve the BF measurement of this decay via the process e+ e− → Ds∗± Ds∓ by using data samples corresponding to an integrated luminosity √ of 6.32 fb−1 collected by the BESIII detector at C.M. energies s = 4.178–4.226 GeV. Charge-conjugate states are implied throughout this paper. –2– JHEP04(2022)058 Figure 2. Hairpin-topological diagram for Ds+ → ρ+ η 0 . √ s (GeV) Lint (pb−1 ) Mrec (GeV/c2 ) 4.178 3189.0±0.2±31.9 [2.050, 2.180] 4.189 526.7±0.1±2.2 [2.048, 2.190] 4.199 526.0±0.1±2.1 [2.046, 2.200] 4.209 517.1±0.1±1.8 [2.044, 2.210] 4.219 514.6±0.1±1.8 [2.042, 2.220] 4.226 1056.4±0.1±7.0 [2.040, 2.220] 2 Detector and data sets The BESIII detector [11] records symmetric e+ e− collisions provided by the BEPCII storage ring [12], which operates in the C.M. energy range from 2.00 to 4.95 GeV. BESIII has collected large data samples in this energy region [13]. 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. The solenoid is supported by an octagonal fluxreturn yoke with resistive plate counter muon identification modules interleaved with steel. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the specific 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, while that in the end-cap region is 110 ps. The end-cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [14–16]. The data samples used in this analysis are listed in table 2 [17]. Since the cross section of Ds∗± Ds∓ production in e+ e− annihilation is about a factor of twenty larger than that of √ Ds+ Ds− [18] at C.M. energies s = 4.178–4.226 GeV, and the Ds∗± meson decays to γDs± with a dominant BF of (93.5 ± 0.7)% [4], the signal events discussed in this paper are selected from the process e+ e− → Ds∗± Ds∓ → γDs+ Ds− . Simulated data samples produced with a geant4-based [19] Monte Carlo (MC) package, which includes the geometric description of the BESIII detector and the detector response, are used to determine detection efficiencies and to estimate backgrounds. The simulation models the beam energy spread and initial-state radiation ( (...truncated)