Prospects of CKM elements $$|V_{cs}|$$ | V cs | and decay constant $$f_{D_{s}^+}$$ f D s + in $$D_s^+\rightarrow \mu ^+\nu _\mu $$ D s + → μ + ν μ decay at STCF

Eur. Phys. J. C (2022) 82:337 https://doi.org/10.1140/epjc/s10052-022-10260-w Regular Article - Experimental Physics Prospects of CKM elements |Vcs | and decay constant f Ds+ in Ds+ → μ+ νμ decay at STCF Jia-Jun Liu1, Xiao-Dong Shi2,3 , Hui-Jing Li4,5 , Xiao-Rong Zhou2,3,a , Bo Zheng1,b 1 University of South China, Hengyang 421000, People’s Republic of China 2 State Key Laboratory of Particle Detection and Electronics, Hefei 230026, People’s Republic of China 3 School of Physical Sciences, University of Science and Technology of China, Hefei 230026, People’s Republic of China 4 Henan Normal University, Xinxiang 453007, People’s Republic of China 5 National Demonstration Center for Experimental Physics Education, Henan Normal University, Xinxiang 453007, China Received: 1 October 2021 / Accepted: 25 March 2022 © The Author(s) 2022 Abstract We report a feasibility study of pure leptonic decay Ds+ → μ+ νμ by using a fast simulation software package at STCF. With an expected luminosity of 1 ab−1 collected at STCF at a center-of-mass energy of 4.009 GeV, the statistical sensitivity of the branching fraction is determined to be 0.3%. Combining this result with the c → s quark mixing matrix element |Vcs | determined from the current global Standard Model fit, the statistical sensitivity of Ds+ decay constant, f Ds+ , is estimated to be 0.2%. Alternatively, combining the current results of f Ds+ calculated by lattice QCD, the statistical sensitivity of |Vcs | is determined to be 0.2%, which helps probe possible new physics beyond Standard Model. The unprecedented precision to be achieved at STCF will provide a precise calibration of QCD and rigorous test of Standard Model. 1 Introduction The proposed Super Tau-Charm Facility (STCF) [1] in China is a symmetric electron-positron collider that will provide √ e+ e− annihilation at center-of-mass (c.m.) energies s ranging from 2.0 to 7.0 GeV. The peak luminosity is expected to √ be 0.5×1035 cm−2 s−1 or higher at s = 4.0 GeV and it will accumulate an integrated luminosity (L) of more than 1 ab−1 √ per year. By operating at s = 4.009 GeV, the STCF will produce 2.0 × 108 Ds+ Ds− with one-year’s data collection, enabling researchers to study the purely leptonic, semileptonic and hadronic decays of Ds+ with unprecedented precision. a e-mail: (corresponding author) Among these, the purely leptonic decay Ds+ → + ν ( = e, μ or τ ) provides a unique window into both strong and weak effects in the charm sector. In the Standard Model (SM), the partial width of the decay Ds+ → + ν can be written as [2] ⎛ ⎞2 2 m G 2F |Vcs |2 f D2 + m 2 m Ds+ ⎝1 − 2 ⎠ ,  Ds+ →+ ν = s 8π m + (1) Ds where G F is the Fermi coupling constant, |Vcs | is the c → s Cabibbo-Kobayashi-Maskawa (CKM) matrix element, f Ds+ is the Ds+ decay constant that parameterises the effect of the strong interaction, m  and m Ds+ are the masses of lepton and Ds+ , respectively. The determination of  Ds+ →+ ν can directly measure the product value of f Ds+ |Vcs | because all other variables are known with high precision [3]. One can either extract |Vcs | by using the predicted value of f Ds+ from lattice QCD (LQCD), or obtain f Ds+ by using the averaged experimental value of |Vcs |. Precise measurements of f Ds+ [4–6] and |Vcs | are required to investigate new physics beyond the SM. Currently, the averaged f Ds+ from various experiments indicates a 1.5σ [7] difference from LQCD calculation [4], the latter providing a negligible uncertainty when compared to the former. Furthermore, there are 2 σ deviations for the |Vcs | extracted in Ds+ → l + νl [7] and D → K lνl [7], which challenges the universality for the CKM elements. The most recent |Vcs | and f Ds+ results are still limited by the statistical uncertainty in the measurement of Ds+ → + ν [8]. More precise measurements of Ds+ → μ+ νμ are required to calibrate various theoretical calculations of f Ds+ and test the unitarity of the CKM matrix. b e-mail: (corresponding author) 0123456789().: V,-vol 123 337 Page 2 of 10 The SM predicts that the ratio of decay widths for Ds+ → τ + ντ and Ds+ → μ+ νμ will be 9.75, with negligible uncertainty. Lepton flavour universality (LFU) could be violated with some new physics mechanisms, such as a two-Higgs-doublet model with the mediation of charged Higgs bosons [9,10] or a Seesaw mechanism due to lepton mixing with Majorana neutrinos [11]. Based on the most recent experimental results, the ratio  Ds+ →τ + ντ /  Ds+ →μ+ νμ is obtained to be 9.98 ± 0.52 [3], which is consistent with the SM prediction within uncertainty. However, more precise measurements of Ds+ → + ν decays are required to test LFU and other physics mechanisms beyond the SM. In this research, we present a feasibility study of Ds+ → μ+ νμ decay and estimate the sensitivity of various parameters at STCF [1], where Ds+ is from e+ e− → Ds+ Ds− at √ s = 4.009 GeV with a production cross-section around 0.2 nb. Though the production cross-section of e+ e− → √ Ds+ Ds∗− + c.c is higher at s = 4.18 GeV, to be around 0.9 nb, the pair production of Ds+ Ds− without additional particles at 4.009 GeV laids into reconstruction of signals with greater purity and free of additional systematic uncertainties caused by γ or π 0 reconstruction in Ds∗− decays. This paper is organized as follows. In Sect. 2, the detector concept for STCF has been introduced as well as the Monte Carlo (MC) samples used for this study. Section 3 is the analysis of Ds+ → μ+ νμ . Section 4 is about optimizing of detector response, and Sect. 5 is the results and discussion. 2 STCF detector and MC simulation The STCF detector under development is a general purpose detector for e+ e− collider. It consists of a tracking system composed of inner and outer trackers, a particle identification (PID) system with excellent K /π identification, an electromagnetic calorimeter (EMC) with an excellent energy resolution and a good position resolution for photons or electrons, a superconducting solenoid and a muon detector (MUD) that provides good μ/π separation. The preliminary conceptual design for each sub-detector can be found in Ref. [12]. Currently, the STCF detector and the corresponding offline software system are in the research and development [13]. STCF has thus developed fast simulation software to access the physics reaches [12], which takes the most common event generator as input to perform a realistic simulation. It takes into account the effects of charged particle tracking efficiency and momentum resolution, PID efficiency, photon detection efficiency and energy/position resolution, and kinematic fits. The fast simulation also includes a pliable interface for adjusting the performance of each subsystem, which can be used to optimize the detector design based on physical constraints. The process Ds+ → μ+ νμ 123 Eur. Phys. J. C (2022) 82:337 analysed here also serves as a benchmark process for the optimization of detector response, e. (...truncated)