Amplitude analysis and branching fraction measurement of the decay $$ {\textrm{D}}_{\textrm{s}}^{+} $$ → K+π+π−π0

Published for SISSA by Springer Received: May 30, 2022 Revised: September 1, 2022 Accepted: September 13, 2022 Published: September 29, 2022 The BESIII collaboration E-mail: Abstract: The singly Cabibbo-suppressed decay Ds+ → K + π + π − π 0 is observed by using a data set corresponding to an integrated luminosity of 6.32 fb−1 recorded by the BESIII detector at the centre-of-mass energies between 4.178 and 4.226 GeV. The first amplitude analysis of Ds+ → K + π + π − π 0 reveals the sub-structures in this decay and determines the fractions and relative phases of different intermediate processes. The dominant intermediate process is Ds+ → K ∗0 ρ+ , with a fit fraction of (40.5 ± 2.8stat. ± 1.5syst. )%. With the detection efficiency based on our amplitude analysis, the absolute branching fraction for Ds+ → K + π + π − π 0 is measured to be (9.75 ± 0.54stat. ± 0.17syst. ) × 10−3 . Keywords: Charm Physics, e+ -e− Experiments, Particle and Resonance Production ArXiv ePrint: 2205.13759 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP09(2022)242 JHEP09(2022)242 Amplitude analysis and branching fraction + + − 0 measurement of the decay D+ s → K π π π Contents 1 2 Detector and data sets 3 3 Event selection 4 4 Amplitude analysis 4.1 Further selection criteria 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 the amplitude analysis 6 6 7 9 9 12 12 15 5 Branching fraction measurement 16 6 Summary 21 A Clebsch-Gordan relation 22 B Other intermediate processes tested 22 The BESIII collaboration 28 1 Introduction The hadronic decays of charmed mesons have been studied extensively in both experiment and theory since the discovery of charmed mesons in 1976 by Mark I [1, 2]. However, a precise theoretical description for exclusive hadronic charmed meson decays is still challenging because the mass of charm quark is too light to adopt a sensible heavy quark expansion and too heavy to apply chiral perturbation theory [3]. Amplitude analyses and measurements of the branching fractions (BFs) for hadronic decays of charmed mesons provide valuable information about the underlying mechanism of the charmed meson decays. Four-body hadronic decays of Ds+ mesons can be dominated by two-body intermediate processes [4], such as Ds+ → V V and Ds+ → AP decays, where V, A, and P denote vector, axial-vector and pseudoscalar mesons, respectively. The investigations of the Ds+ → V V decays have attracted a great deal of attention [5–9], but the experimental information about the Ds+ → V V decays is sparse. And the improved knowledge of BFs of Ds+ → AP –1– JHEP09(2022)242 1 Introduction Figure 2. The T -diagrams (left) and A-diagrams (right) for the decay Ds+ → K ∗+ ρ0 . decays, such as Ds+ → K1 (1270)0 π + and Ds+ → K1 (1400)0 π + , is important to improve the understanding of the mixing of the K1 (1270)0 and K1 (1400)0 mesons [10]. The singly Cabibbo-suppressed hadronic decay of Ds+ → K + π + π − π 0 is expected to be dominated by the intermediate decays Ds+ → K ∗0 ρ+ and K10 π + (ρ denotes ρ(770), K ∗ denotes K ∗ (892) and K1 denotes K1 (1270)/K1 (1400)), since the decay width calculated by external Wemission process with final states of neutral kaonioc states (i.e. K ∗0 , K10 ) is greater than internal W-emission process with charged kaonic states (i.e. K ∗+ , K1+ ) and the difference between the annihilation amplitudes could be ignored [11]. Take Ds+ → K ∗0 ρ+ and K ∗+ ρ0 states as an example, the tree T -diagrams and annihilation A-diagrams of these two decay modes are shown in figure 1 and figure 2, respectively. More experimental information from the amplitude analysis of this decay will offer important experimental input to improve the theory predictions and explore charge-parity (CP ) violation in the charm meson decays [9, 12]. The amplitude analysis of Ds+ → K + π + π − π 0 also provides access to Ds+ → V P decays, such as Ds+ → ωK + . Evidence for Ds+ → ωK + was first reproted by BESIII experiment, and the BF was measured to be (0.87 ± 0.25stat. ± 0.07syst. ) × 10−3 [13], which was based √ on 3.19 fb−1 data samples taken at the center-of-mass energy (Ecm or s) 4.178 GeV. The predicted value of BF (2.12 × 10−3 ) [11] was too large compared to the experimental value of (0.87 × 10−3 ), but after taking into account SU(3)F breaking in internal W-emission, the predicted BF now is reduced to (0.99 × 10−3 ) [14]. Therefore, the amplitude of Ds+ → ωK + decay is important to investigate the W-annihilation contribution in Ds+ → V P decays and –2– JHEP09(2022)242 Figure 1. The T -diagrams (left) and A-diagrams (right) for the decay Ds+ → K ∗0 ρ+ . improve the understanding of SU(3)F flavor symmetry breaking effects in hadronic decays of charmed mesons [11, 14, 15]. This paper reports the first amplitude analysis and BF measurement of the decay + Ds → K + π + π − π 0 , using e+ e− collision data samples corresponding to an integrated √ luminosity of 6.32 fb−1 collected at the s between 4.178 and 4.226 GeV with the BESIII detector. Charged-conjugate modes are always implied throughout this paper except when discussing CP violation. Detector and data sets The BESIII detector is a magnetic spectrometer [16, 17] located at the Beijing Electron Positron Collider (BEPCII) [18]. 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 flux-return yoke with resistive plate counter muon identification modules interleaved with steel. The resolution of chargedparticle momentum at 1 GeV/c is 0.5%, and the resolution of specific energy loss dE/dx 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 [19–21]. About 83% of the data in this analysis benefits from the upgrade. The integrated luminosities of different centre-of-mass energies of the data samples used in this analysis are listed in table 1 [22–24]. For some aspects of the analysis, these samples are organised into three sample groups, 4.178 GeV, 4.189–4.219 GeV, and 4.226 GeV, and each of them is acquired during the same year under consistent running conditions. Since the cross section of Ds∗± Ds∓ production in e+ e− annihilation is about a factor of twenty larger than that of Ds+ Ds− [25], and the Ds∗± meson decays to γDs± have a dominant BF of (93.5 ± 0.7 (...truncated)