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Manqi Ruan

Publications and source records attributed to Manqi Ruan.

At least 19 recordsLinked to original sources

Measurement of $\Xi^-/\bar{\Xi}^{+}$ production in jets from $Z$ boson decays with the DELPHI open data

The production rates of $\Xi^{-}/\bar{\Xi}^{+}$ baryons in energy-ranked jets produced in $Z\to\text{hadrons}$ decays are measured using $3.2$ million hadronic $Z$ events recorded by the DELPHI experiment. Jets are reconstructed using the Durham algorithm with $y_{\text{cut}}=0.005$. Quark- and gluon-enriched jet samples are obtained by ranking the jet energies in three-jet events. The softest jet are found to produce fewer $\Xi^{-}/\bar{\Xi}^{+}$ and less energetic baryons than the other jets. The ratio of $\Xi^{-}/\bar{\Xi}^{+}$ production rates in gluon and quark jets, each normalized to the corresponding mean charged-particle multiplicity, is measured to be $1.21 \pm 0.18~\mathrm{(stat.)} \pm 0.26~\mathrm{(syst.)}$. The result is consistent with the JETSET expectation and the OPAL measurements of $K_S^0$ and $\Lambda$ productions in $Z$ decays. This study presents the first measurement of the gluon-to-quark production ratio for baryons containing two $s$ quarks, providing new insights into strange-quark production and hadronization. Future $e^{+}e^{-}$ colliders such as CEPC and FCCee will provide much larger $Z$-boson samples and will allow far more precise studies of the subject.

hep-ex

Hadronic decay branching ratio measurements of the Higgs boson at future colliders using the Holistic Approach

Accurately measuring the properties of the Higgs boson is one of the primary physics objectives of the high-energy frontier. By incorporating the inclusive information of all reconstructed particles to identify the signal events, referred to as the holistic approach, we estimate the relative statistical uncertainty for the Higgs hadronic decay modes $H \to b\bar{b}$, $c\bar{c}$, $gg$, $WW^{*} \to 4q$, and $ZZ^{*} \to 4q$ at the Circular Electron--Positron Collider (CEPC) operating as a Higgs factory with an integrated luminosity of 21.6~ab$^{-1}$. In the $Z(\mu^{+}\mu^{-})H$ and $Z(\nu\bar{\nu})H$ channels, the relative statistical uncertainties for these decay modes are projected to range from 0.36\% to 5.21\% and 0.16\% to 2.52\%, respectively. Compared to the CEPC Snowmass results, the holistic approach boosts the measurement precision by a factor of two to four. The scaling behavior, specifically the dependence of the anticipated accuracy on the training dataset size, is observed and analyzed. The precision of these leading Higgs decay modes, especially the $H \to b\bar{b}$ mode, is asymptotically approaching the statistical limit. The scaling behavior could also be applied to monitor the robustness and to quantify the uncertainties of the holistic approach.

hep-ex

Conceptual Design of a Novel Highly Granular Crystal Electromagnetic Calorimeter for Future Higgs Factories

Next-generation high-energy electron-positron colliders, operating as Higgs factories, require an unprecedented jet energy resolution for precision measurements of Higgs and Z/W bosons. To address this challenge, a conceptual design is presented for a novel high-granularity crystal electromagnetic calorimeter that combines the superior intrinsic energy resolution of a homogeneous calorimeter with the fine segmentation required for particle-flow reconstruction. The crystal electromagnetic calorimeter design is based on orthogonally arranged long scintillating crystal bars read out by silicon photomultipliers (SiPMs) at both ends. Key design specifications were established through comprehensive simulation studies. Critical technical considerations, including crystal choices, photosensors, electronics, mechanical support, and radiation damage, are discussed. A dedicated digitisation framework was developed to realistically model effects from the crystal, SiPMs, and readout electronics. The performance of a single calorimeter module was evaluated using simulated electron showers. Simulation results for a single module demonstrate an excellent electromagnetic energy resolution of $1.12\%/\sqrt{E(\mathrm{GeV})}\oplus0.22\%$ and an energy linearity within $\pm0.5\%$ for electrons from 3 GeV to 100 GeV. The performance significantly exceeds the design requirement of $\leq 3\%/\sqrt{E(\mathrm{GeV})}\oplus1\%$. The results establish the feasibility of the proposed high-granularity crystal calorimeter concept and point to a promising pathway toward the precision calorimetry required for future high-energy electron-positron collider experiments.

physics.ins-det

Prospect for measurement of CP-violating parameters of $B_s^0 \to \phi\gamma$ at the Tera Z factory

$b \to s\gamma$ transition is a critical flavor-changing neutral current (FCNC) process that could be used to probe CP violation (CPV) and new physics (NP). We quantify the anticipated precision for measuring $B_s^0 \to \phi\gamma$ at the CEPC Z pole operation, showing that the relative statistical uncertainty could be as low as 0.16\%, improved by approximately two orders of magnitude compared to existing measurements. Additionally, we perform a time-dependent analysis of the $B_s^0 \to \phi\gamma$ decay, accounting for $B_s^0/\bar{B}_s^0$ mixing extract the mixing-induced and CP-violating parameters $\boldsymbol{\mathcal{A}_{\phi\gamma}^\Delta}$, $\boldsymbol{C_{\phi\gamma}}$ and $\boldsymbol{S_{\phi\gamma}}$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are $\sigma_{A_{\phi\gamma}^{\Delta}{}^{\text{stat}}} = 0.021$, $\sigma_C^{\text{stat}} = 0.0092$ and $\sigma_S^{\text{stat}} = 0.0096$, and the systematic uncertainties are $\sigma_{A_{\phi\gamma}^{\Delta}{}^{\text{syst}}} = 0.035$, $\sigma_C^{\text{syst}} = 0.0027$ and $\sigma_S^{\text{syst}} = 0.0064$. Furthermore, the 1$\sigma$ sensitivity boundaries for NP in this study are found to be $\mathcal{A}_{\phi\gamma}^\Delta < -0.05$ or $\mathcal{A}_{\phi\gamma}^\Delta > 0.15$, $\mathcal{C}_{\phi\gamma} < -0.02$ or $\mathcal{C}_{\phi\gamma} > 0.04$, and $\mathcal{S}_{\phi\gamma} < -0.04$ or $\mathcal{S}_{\phi\gamma} > 0.04$. We also conduct a relevant detector optimization study by establishing the correlation between the anticipated precision and the intrinsic resolution of the ECAL, as well as the performance of the PID system.

hep-ex

Deep-learning jet flavor tagging for precision hadronic Higgs measurements at future $e^+e^-$ Higgs factories

Precise measurements of Higgs decays into quarks and gluons are essential for probing the Yukawa couplings of the Higgs boson and testing the flavor structure of the Standard Model. We investigate the process $e^+e^- \to ZH$ at $\sqrt{s}=240~\mathrm{GeV}$ at a future $e^+e^-$ Higgs factory, taking the CEPC design as a benchmark. The analysis focuses on events with $Z\to\nu\bar{\nu}$ and hadronic Higgs decays $H\to b\bar{b}$, $c\bar{c}$, $s\bar{s}$ and $gg$. Jet flavor is identified using state-of-the-art particle-level deep neural network taggers (ParticleNet, Particle Transformer and More-Interaction Particle Transformer), whose per-jet outputs are combined with global event observables in a two-stage analysis employing XGBoost classifiers to separate the four Higgs decay modes from the dominant two- and four-fermion Standard Model backgrounds. Assuming an integrated luminosity of $20~\mathrm{ab}^{-1}$, we obtain projected relative precision on $\sigma(ZH)\times\mathrm{Br}(H\to X)$ of 0.17% for $X=b\bar{b}$, 1.06% for $c\bar{c}$, 0.50% for $gg$ and 68% for $s\bar{s}$. Compared with the CEPC published results, the precisions for $H\to c\bar{c}$ and $H\to gg$ are improved by about 43% and 29%, respectively. For $H\to s\bar{s}$ we present a quantitative sensitivity estimation corresponding to a statistical significance of about $1.5\sigma$. These results highlight the potential of deep-learning-based jet flavor tagging for precision studies of Higgs decays at future $e^+e^-$ Higgs factories.

hep-ph

Particle-level transformers for 95 GeV Higgs boson searches at future $e^+e^-$ Higgs factories

Motivated by several mild excesses around 95~GeV, we investigate the prospects for a light scalar $S$ produced via Higgsstrahlung, $e^+e^- \to Z(\mu^+\mu^-)S$, at future $e^+e^-$ Higgs factories. We take the CEPC as a benchmark, with a center-of-mass energy of $\sqrt{s}=240$ GeV and an integrated luminosity of $L=20~\mathrm{ab}^{-1}$. We focus on the decay modes $S\to\tau^+\tau^-$ and $S\to b\bar b$. To maximize sensitivity, we employ the particle-level transformer networks Particle Transformer (ParT) and its more-interactive variant MIParT, which exploit the features of all reconstructed objects and their correlations. For a representative signal benchmark, this approach improves the expected statistical precision on the signal strength by factors of 2.3 in the $\tau^+\tau^-$ channel and 1.4 in the $b\bar b$ channel compared to a cut-based analysis. Within the flipped Next-to-Two-Higgs-Doublet Model (N2HDM-F), the CEPC can measure the signal strength with a statistical precision down to 1.0% in the $\tau^+\tau^-$ channel and 0.69% in the $b\bar b$ channel using MIParT. It can achieve a $5\sigma$ discovery for $\mu_{\tau\tau}^{ZS}>1.6\times10^{-2}$ or $\mu_{bb}^{ZS}>5.0\times10^{-3}$, and reach 1% precision for $\mu_{\tau\tau}^{ZS}>0.93$ or $\mu_{bb}^{ZS}>0.14$. These gains are expected to qualitatively carry over to other future lepton colliders such as FCC-ee and the ILC. Our results demonstrate the potential of particle-level machine-learning techniques to strengthen light Higgs searches at future $e^+e^-$ Higgs factories.

hep-ph

BigBang-Proton Technical Report: Next-Word-Prediction is Scientific Multitask Learner

We introduce BigBang-Proton, a unified sequence-based architecture for auto-regressive language modeling pretrained on cross-scale, cross-structure, cross-discipline real-world scientific tasks to construct a scientific multi-task learner. BigBang-Proton incorporates three fundamental innovations compared to mainstream general-purpose LLMs: Theory-Experiment Learning paradigm aligns large-scale numerical experimental data with theoretical text corpora; Binary Patch Encoding replaces byte pair encoding(BPE) tokenization; Monte Carlo Attention substitutes traditional transformer architectures. Through next-word-prediction pretraining on cross-discipline scientific datasets of real-world problems mixed with general textual corpus, followed by fine-tuning and inference on downstream tasks, BigBang-Proton demonstrates 100\% accuracy in up to 50-digit arithmetic addition operations, performance on par with leading specialized models in particle physics jet tagging, matching MAE of specialized models in inter-atomic potential simulation, performance comparable to traditional spatiotemporal models in water quality prediction, and benchmark-exceeding performance in genome modeling. These results prove that language-guided scientific computing can match or exceed the performance of task-specific scientific models while maintaining multitask learning capabilities. We further hypothesize to scale the pretraining to the universe scale as a fundamental step toward developing material world foundational model.

cs.LG

Optimisation of the vertex detector and measurement of Higgs decays to second-generation quarks at the CEPC

The vertex detector is crucial for precision measurements of the Higgs boson at the electron-positron Higgs factory. Benchmarked with $H \to c\bar{c}$ and $H \to s\bar{s}$ measurements in the $\nu\bar{\nu}H$ channel, we perform an optimisation study on the inner radius and spatial resolution of the vertex detector using the Jet Origin Identification (JOI) framework, which determines the parton flavor of jets using advanced Artificial Intelligence (AI) algorithm. We observe that, compared to the reference detector configuration, halving the inner radius and spatial resolution improves the transverse and longitudinal impact parameter resolution approximately by a factor of two, while increasing the accuracy and significance of the $H \to c\bar{c}/s\bar{s}$ measurement by 4\% and 8\%, respectively. Conversely, doubling these parameters results in comparable degradation, with variations in the inner radius being the dominant factor. Our results provide guidance for detector design and highlight promising prospects for identifying the $H \to s\bar{s}$ decay mode at future Higgs factories.

hep-ex

Testing a 95 GeV Scalar at the CEPC with Machine Learning

Several possible excesses around 95 GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the CEPC to test this hypothesis in the Higgsstrahlung channel $e^{+}e^{-} \to ZS$ with $Z \to\mu^{+}\mu^{-}$ and $S\to\tau^{+}\tau^{-}$. Full detector simulation shows that the optimal center-of-mass energy to study the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $L = 20~\mathrm{ab}^{-1}$, the CEPC's $5\sigma$ sensitivity to the signal strength $\mu_{\tau\tau}^{ZS}$ reaches 0.016 and 0.020 for $\sqrt{s} =$ 210 GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $\mu_{\tau\tau}^{ZS} > 0.10$ and $>0.12$. At $\sqrt{s}=$ 210 GeV (240 GeV), $5\sigma$ coverage of all N2HDM-Flipped samples with $\chi^2_{h_{95}}<7.82$ requires $L=800\ \mathrm{fb}^{-1}$ (1.22 $\mathrm{ab}^{-1}$). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

hep-ph

Learning from all particles in high-energy collisions

Particle colliders stand as an irreplaceable pillar of inquiry for exploring the fundamental building blocks of matter and forces of the Universe, yet fully decoding complex collision event information remains a significant challenge. Recent advances in artificial intelligence (AI) have revolutionized complex data analysis across scientific disciplines, inspiring novel strategies to extract the rich information embedded in collider events. Here we introduce two complementary concepts -- the holistic approach and Advanced Color Singlet Identification -- to enhance signal-background separation, which is a critical prerequisite for precise physics measurements. By leveraging all reconstructed particles and inferring their parentage via deep learning, these methods improve the precision of key Higgs physics benchmark measurements by up to sixfold and enable realistic prospects for observing rare Higgs decays previously deemed inaccessible. Our results demonstrate how integrating particle-level information with modern AI technologies can substantially boost the discovery potential of high-energy colliders, paving a new path to unravel the fundamental physical laws underlying particle physics experiments.

hep-ex

Prospect for measurement of $C\!P$-violating observables in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays at a future ${Z}$ factory

A precise determination of the CKM angle $\gamma$ from $B_s^0$ oscillations in $B_s^0 \to D_s^\mp K^\pm$ decays offers a critical test of the Standard Model and probes for new physics. We present a comprehensive study on the prospects of measuring $\gamma$ at a future Tera-$Z$ factory, utilizing the baseline detector concept of the Circular Electron Positron Collider (CEPC). A two-dimensional simultaneous fit framework, incorporating flavor tagging, decay time resolution modeling, and acceptance corrections, is developed using full Monte Carlo simulations of $B_s^0 \to D_s^\mp \left(\to K^\mp K^\pm \pi^\mp\right) K^\pm$ decays and inclusive background processes. The effective flavor tagging power reaches $23.6\%$, while the decay time resolution is determined to be $26\mathrm{\,fs}$. Projecting to full statistics of signal events across three dominant $D_s^-$ decay channels, we estimate a statistical precision of $\sigma(\gamma) = 0.69^\circ$, which corresponds to $4.1$ Tera-$Z$ boson equivalent data. This study establishes the feasibility of sub-degree level $\gamma$ measurements at a $Z$-factory, highlighting its unique advantages in time-dependent $C\!P$ violation studies through ultra-precise vertexing and background suppression capabilities.

hep-ex

Flavor Physics at the CEPC: a General Perspective

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $Z$ pole, the expected production of 4 Tera $Z$ bosons will provide unique and highly precise measurements of $Z$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $Z$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\tau$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $WW$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals.

hep-ex

Determination of the Strong Coupling Constant $\alpha_s$ from Inclusive Semi-leptonic $B$ Meson Decays

We demonstrate the feasibility of determining the strong coupling constant, $\alpha_s$, from the inclusive semileptonic decay width of $B$ mesons. We express the semileptonic $B$ decay width as a function of $\alpha_s(5\mathrm{\,GeV})$, the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$, $b$- and $c$-quark masses in the $\overline{\mathrm{MS}}$ scheme. We fit $\alpha_s(5\mathrm{\,GeV})$ to current world averages of the $B^{\pm}$ and $B^{0}$ semileptonic decay widths. This yields $\alpha_s(5\mathrm{\,GeV}) = 0.245 \pm 0.009$, corresponding to a 5-flavor extrapolation of $\alpha_s(m_{Z}) = 0.1266 \pm 0.0023$. The primary uncertainty contributions arise from the uncertainty on the perturbative expansion and the value of $|V_{cb}|$. Future advancements including higher-order perturbative calculations, and precise measurements of $|V_{cb}|$ and $B$ decay widths from upcoming $B$ and $Z$ factories, could enable this method to determine $\alpha_s(m_{Z})$ with a competitive precision of $\Delta\alpha_s(m_{Z}) \sim 0.0018$. This precision is comparable to the current accuracy of $\alpha_s(m_{Z})$ measurements from $\tau$-lepton decays, which is regarded as the most precise experimental approach.

hep-ph

Scaling Particle Collision Data Analysis

For decades, researchers have developed task-specific models to address scientific challenges across diverse disciplines. Recently, large language models (LLMs) have shown enormous capabilities in handling general tasks; however, these models encounter difficulties in addressing real-world scientific problems, particularly in domains involving large-scale numerical data analysis, such as experimental high energy physics. This limitation is primarily due to BPE tokenization's inefficacy with numerical data. In this paper, we propose a task-agnostic architecture, BBT-Neutron, which employs a binary tokenization method to facilitate pretraining on a mixture of textual and large-scale numerical experimental data. We demonstrate the application of BBT-Neutron to Jet Origin Identification (JoI), a critical categorization challenge in high-energy physics that distinguishes jets originating from various quarks or gluons. Our results indicate that BBT-Neutron achieves comparable performance to state-of-the-art task-specific JoI models. Furthermore, we examine the scaling behavior of BBT-Neutron's performance with increasing data volume, suggesting the potential for BBT-Neutron to serve as a foundational model for particle physics data analysis, with possible extensions to a broad spectrum of scientific computing applications for Big Science experiments, industrial manufacturing and spacial computing. The project code is available at https://github.com/supersymmetry-technologies/bbt-neutron.

cs.LG

One-to-one correspondence reconstruction at the electron-positron Higgs factory

We propose one-to-one correspondence reconstruction for electron-positron Higgs factories. For each visible particle, one-to-one correspondence aims to associate relevant detector hits with only one reconstructed particle and accurately identify its species. To achieve this goal, we develop a novel detector concept featuring 5-dimensional calorimetry that provides spatial, energy, and time measurements for each hit, and a reconstruction framework that combines state-of-the-art particle flow and artificial intelligence algorithms. In the benchmark process of Higgs to di-jets, over 90% of visible energy can be successfully mapped into well-reconstructed particles that not only maintain a one-to-one correspondence relationship but also associate with the correct combination of cluster and track, improving the invariant mass resolution of hadronically decayed Higgs bosons by 25%. Performing simultaneous identification on these well-reconstructed particles, we observe efficiencies of 97% to nearly 100% for charged particles ($e^{\pm}$, $\mu^{\pm}$, $\pi^{\pm}$, $K^{\pm}$, $p/\bar{p}$) and photons ($\gamma$), and 75% to 80% for neutral hadrons ($K_L^0$, $n$, $\bar{n}$). For physics measurements of Higgs to invisible and exotic decays, golden channels to probe new physics, one-to-one correspondence could enhance discovery power by 10% to up to a factor of two. This study demonstrates the necessity and feasibility of one-to-one correspondence reconstruction at electron-positron Higgs factories.

hep-ex

Measurements of decay branching fractions of the Higgs boson to hadronic final states at the CEPC

The Circular Electron Positron Collider (CEPC) is a large-scale particle accelerator designed to collide electrons and positrons at high energies. One of the primary goals of the CEPC is to achieve high-precision measurements of the properties of the Higgs boson, facilitated by the large number of Higgs bosons that can be produced with significantly low contamination. The measurements of Higgs boson branching fractions into $b\overline{b} /c\overline{c} /gg$ and $\tau\overline{\tau} /WW^{*} /ZZ^{*} $, where the $W$ or $Z$ bosons decay hadronically, are presented in the context of the CEPC experiment, assuming a scenario with 5600 fb$^{-1}$ of collision data at a center-of-mass energy of 240 GeV. In this study the Higgs bosons are produced in association with a $Z$ boson, with the $Z$ boson decaying into a pair of muons $(\mu^{+}\mu^{-})$, which have high efficiency and high resolution. In order to separate all decay channels simultaneously with high accuracy, the Particle Flow Network (PFN), a graph-based machine learning model, is considered. The precise classification provided by the PFN is employed in measuring the branching fractions using the migration matrix method, which accurately corrects for detector effects in each decay channel. The statistical uncertainty of the measured branching ratio is estimated to be 0.55% in $H\to b\overline{b}$ final state, and approximately 1.5%-16% in $H\to c\overline{c} /gg/\tau\overline{\tau}/WW^{*} /ZZ^{*} $ final states. In addition, the main sources of systematic uncertainties to the measurement of the branching fractions are discussed.

hep-ex

Discovery Potential of Future Electron-Positron Colliders for a 95 GeV Scalar

The Large Electron Positron collider observed an indication for a new Higgs boson with a mass around $95$\,GeV-$100$\,GeV in the process $e^+e^-\to Z^*\to ZS$ with $S\to b\bar b$. The interest in this excess re-emerged with the di-photon signature at $\approx$\,95\,GeV at the Large Hadron Collider. In fact, a combined global significance of $3.4\sigma$ is obtained once $WW$ and $\tau\tau$ signals are included in addition. In this article, we perform a feasibility study for discovering such a new scalar $S$ at future electron-positron colliders using the recoil-mass method applied to $e^{+} e^{-} \to ZS$ with $Z \rightarrow \mu^{+} \mu^{-}$ and $S \to b \bar{b}$. For this, we employ a Deep Neural Network to enhance the separation between the Standard Model background and the signal, reducing the required integrated luminosity necessary for discovery by a factor of two to three. As a result, an $SU(2)_L$ singlet Higgs with a mass of $\approx$\,95\,GeV can be observed with more than 5$\sigma$ significance at a 250\,GeV centre-of-mass energy collider with $5~ {\rm ab}^{-1}$ integrated luminosity if it has a mixing angle of at least $0.1$ with the Standard Model Higgs, which means that a discovery can be achieved within the whole 95\% confidence-level region preferred by Large Electron Positron excess. Furthermore, including more decay channels such as $S\to \tau\tau$ and $Z\to e^+e^-$ further enhances the discovery potential of future $e^+e^-$ accelerators, like CEPC, CLIC, FCC-ee and ILC.

hep-ph

Radiative Leptonic Decay of Heavy Quarkonia

This study examines the properties of heavy quarkonia $X$ by treating them as bound states of $Q$ and $\bar{Q}$ at the LO level within the NRQCD framework, where $Q$ represents either a charm or a bottom quark. The branching ratios for the radiative leptonic decays $X\rightarrow γl^{+} l^{-}$ are revisited and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of $X$. Furthermore, we apply Lorentz transformations from the rest frame of $X$ to the center-of-mass frame of $l^+ l^-$ to establish the connection between the widths ${Γ_{X \rightarrow γl^{+} l^{-}}}$ and ${Γ_{X \rightarrow l^{+} l^{-}}}$. When comparing the connection with those documented in the literature (divided by $2π$) for various $X$ states, such as $J/Ψ$, $Ψ(2S)$, $Υ(1S)$, and $Υ(2S)$, relative differences typically around or below 10\% can be found, which is comparable to the NLO corrections of $O(α)$ and $O(v^4)$. However, we observe a significant disparity in the ratio between ${Γ_{Ψ(2S) \to γτ^+ τ^-}}$ and ${Γ_{Ψ(2S) \to τ^+ τ^-}}$, with our prediction being four times larger than those in the literature. The outcomes derived from this study held practical implications in describing the QED radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and the searches for new physics.

hep-ph