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ResoSeg: Resonance Tagger using Transformer and Segment Model
Chunkai Li, Junhao Yin, Ke Li, Jingde Chen
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 85%
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Summary
The paper introduces ResoSeg, a deep learning model for resonance tagging in high-energy physics that combines particle-level segmentation and event-level classification. Applied to the BESIII experiment, ResoSeg reconstructs the eta_c meson from the decay chain e+e- -> pi+ pi- hc, hc -> gamma eta_c, eta_c -> anything. It outperforms conventional channel-specific methods by more than double in efficiency, generalizes to unseen energy points and other production modes via transfer learning, and is robust to variations in resonance parameters.
Entities (8)
Relation Signals (7)
ResoSeg → appliedto → BESIII
confidence 95% · We present the first application of segmentation to resonance tagging at BESIII and introduce ResoSeg
ResoSeg → implementedin → PyTorch
confidence 95% · We implement the ResoSeg model in PyTorch [28]
ResoSeg → reconstructs → eta_c
confidence 95% · We demonstrate the reconstruction of eta_c with e+e- -> pi+ pi- hc, hc -> gamma eta_c, eta_c -> anything
ResoSeg → inspiredby → Segment Anything Model (SAM)
confidence 90% · The decoder is inspired by SAM [26], an image segmentation model
ResoSeg → inspiredby → Particle Transformer (ParT)
confidence 90% · The encoder of the model consists of Particle Embedding, Pair Embedding, and Particle Attention Blocks, drawing inspiration from ParT [2]
ResoSeg → outperforms → conventional 16-channel approach
confidence 90% · Experimental results show that the average combined efficiency of ResoSeg is more than double that of the conventional 16-channel approach
BESIII-eta_c dataset → uses → Truth-Matching Algorithm
confidence 90% · The model is trained on BESIII-eta_c dataset, which is constructed with per-track true labels obtained via a Truth-Matching Algorithm
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Abstract
Abstract:Deep learning has been widely applied across many areas of experimental high-energy physics, yet existing models address only event-level classification or object tagging and therefore still require reconstruction algorithms tailored to each decay channel. We present the first application of segmentation to resonance tagging at BESIII and introduce ResoSeg, a deep learning model that jointly performs particle-level segmentation and event-level classification, enabling a one-pass analysis of resonance to anything decays while precisely reconstructing the relevant resonance properties. We demonstrate the reconstruction of $\eta_c$ with $e^+e^-\to\pi^+\pi^-h_c$, $h_c\to\gamma\eta_c$, $\eta_c\to\text{anything}$. The model is trained on BESIII-$\eta_c$ dataset, which is constructed with per-track true labels obtained via a Truth-Matching Algorithm. Experimental results show that the average combined efficiency of ResoSeg is more than double that of the conventional 16-channel approach across energy points from 4.19 to 4.60\,GeV. The model generalizes to unseen energy points, adapts to other $\eta_c$ production modes through transfer learning, and remains robust against variations in the $\eta_c$ mass, width, and branching fractions, providing a general, resonance-aware model applicable beyond $\eta_c$ and BESIII. The source code is available at this https URL.
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- Source: https://arxiv.org/abs/2609.12610v1
- Canonical: https://arxiv.org/abs/2609.12610v1
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ResoSeg: Resonance Tagger using Transformer and Segment Model Chunkai Li Affiliation: Nankai University, Tianjin, 300071, China Ke Li Email: like@ihep.ac.cn Affiliation: Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China Affiliation: University of Chinese Academy of Sciences, Beijing, 100049, China. Jingde Chen Affiliation: Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China Affiliation: University of Chinese Academy of Sciences, Beijing, 100049, China. Junhao Yin Email: yinjh@nankai.edu.cn Affiliation: Nankai University, Tianjin, 300071, China September 11, 2026 Abstract Deep learning has been widely applied across many areas of experimental high-energy physics, yet existing models address only event-level classification or object tagging and therefore still require reconstruction algorithms tailored to each decay channel. We present the first application of segmentation to resonance tagging at BESIII and introduce ResoSeg, a deep learning model that jointly performs particle-level segmentation and event-level classification, enabling a one-pass analysis of resonance to anything decays while precisely reconstructing the relevant resonance properties. We demonstrate the reconstruction of ηc _c with e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→γηch_c→γ _c, ηc→anything _c . The model is trained on BESIII-ηc _c dataset, which is constructed with per-track true labels obtained via a Truth-Matching Algorithm. Experimental results show that the average combined efficiency of ResoSeg is more than double that of the conventional 16-channel approach across energy points from 4.19 to 4.60 GeV. The model generalizes to unseen energy points, adapts to other ηc _c production modes through transfer learning, and remains robust against variations in the ηc _c mass, width, and branching fractions, providing a general, resonance-aware model applicable beyond ηc _c and BESIII. The source code is available at https://github.com/oashen/ResoSeg. I Introduction As a fundamental part of the Standard Model, the quark model classifies ordinary hadrons into mesons and baryons, but also predicts exotic states beyond this picture, such as multi-quark states, glueballs, and hybrids [1]. In experimental high-energy physics, most hadrons are unstable and appear as resonant states—short-lived intermediate particles that manifest as peaks in the invariant mass distributions of their decay products. The identification and precise reconstruction of these resonant states are essential for mapping the hadron spectrum, testing QCD predictions, and searching for exotic forms of matter. Machine learning, particularly deep learning, has seen broad adoption in experimental high-energy physics. Existing models, however, typically focus on event-level classification or object tagging, i.e., determining whether a given event corresponds to the signal process of interest or contains a certain type of jet. Powerful classifiers such as Particle Transformer (ParT) [2], SPANet [3] and GN3 [4] have achieved state-of-the-art performance in jet tagging, and have also been widely applied to event classification at lepton colliders [5, 6, 7]. The study of intermediate resonances is especially important at lepton colliders. Compared with hadron colliders, lepton colliders such as BESIII, Belle I, and CEPC operate with substantially lower background levels; therefore, the key challenge is not background suppression but rather increasing the available signal statistics. Despite their success, these models do not substantially improve signal statistics significantly in this context: they do not provide per-track information about the origin of particles relative to intermediate resonances. Consequently, analyses that adopt such models still require dedicated reconstruction algorithms tailored to each specific decay channel to reconstruct the four-momentum of the target resonance, leaving the overall analysis paradigm unchanged. Segmentation, which assigns a semantic label to each element of an input, offers a natural solution to this limitation. When adapted to experimental high-energy physics, track-level segmentation enables the direct identification of which tracks originate from a given intermediate resonance, allowing the simultaneous reconstruction of resonance to anything decay chains in a single inference pass, thereby substantially increasing the available data statistics compared with conventional channel-by-channel approaches. Crucially, it provides access to the full kinematic properties of the resonance without relying on decay-channel-specific reconstruction algorithms, transforming the way analyses are performed. The study of hadron spectroscopy and exotic hadron candidates is a central program at multiple experiments, including BESIII, Belle I, and LHCb. A common requirement across these analyses is the identification and reconstruction of intermediate resonances—for example, ηc _c and J/ψJ/ψ at BESIII, B and D mesons at LHCb, and B mesons at Belle I—whose decay products must be disentangled from the remaining particles in the event. In all cases, the precision of the resonance reconstruction directly determines the sensitivity of the physics measurement. In this article, we propose ResonanceSegmenter (ResoSeg), a unified model that combines event-level classification with particle-level segmentation. ResoSeg simultaneously determines whether an event contains a signal process and assigns a semantic category to each reconstructed track, thereby identifying the target resonance and labeling its decay products in a single model. Specifically, ResoSeg first embeds the track features into a high-dimensional latent space via an embedding layer, and then segments the tracks within this latent space, thereby determining whether each track originates from the target resonance and reconstructing the resonance. We focus on the ηc _c meson as our primary demonstration case, but the ResoSeg model is inherently general and can be readily extended to other resonances and experiments. As the lightest ground-state charmonium [8], ηc _c serves as a fundamental spectroscopic benchmark, yet its reconstruction is notoriously challenging: it possesses hundreds of possible decay channels [8], most with tiny branching fractions, and no single dominant mode, making channel-by-channel reconstruction impractical. Traditional reconstruction methods typically concentrate on the 16 decay channels with relatively large branching fractions and cleaner backgrounds, and have achieved considerable success [9, 10, 11]. Building on this success, we aim to further improve the reconstruction performance with ResoSeg to obtain even better results. I BESIII detector The BESIII detector [12] records symmetric e+e−e^+e^- collisions provided by the BEPCII storage ring [13] in the center-of-mass energy range from 1.84 to 4.95 GeV, with a peak luminosity of 1.1×1033cm−2s−11.1× 10^33\;cm^-2s^-1 achieved at s=3.773GeV s=3.773\;GeV. Large data samples have been collected in this energy region [14]. 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 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 surrounded by an octagonal flux-return yoke made of steel, interleaved with resistive-plate-counter muon-identification modules. The charged-particle momentum resolution at 1GeV/c1~ GeV/c is 0.5%0.5\%, and the dE/dx dE/ dx resolution is 6%6\% for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5%2.5\% (5%5\%) at 11 GeV in the barrel (end cap) region. The time resolution in the plastic scintillator TOF barrel region is 68 ps, while that in the end cap region was 110 ps. The end cap TOF system was upgraded in 2015 using multigap resistive plate chamber technology, providing a time resolution of 60 ps, which benefits 33% of the data used in this analysis [15, 16, 17]. Since it began operation, BESIII has played a leading role in the discovery and investigation of exotic states, also known as the XYZ states [18]. More than 30 new particles have been obseved by BESIII experiment [8]. Many of the new particles are observed from the reconstruction of final states involving ηc _c, for example, Zc(3900)→π+hc[hc→γηc],ρ+ηcZ_c(3900)→π^+h_c\;[h_c→γ _c],\;ρ^+ _c, etc [19, 20, 21, 22, 23]. I BESIII-ηc _c Dataset In this section, we provide an overview of the BESIII-ηc _c dataset. In this work, the signal channel is e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→γηch_c→γ _c, ηc→anything _c ; the background channel is e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→anythingh_c except γηcγ _c. The dataset comprises the inclusive decay modes of the ηc _c resonance. Each event includes an event-level true label that indicates whether the event is a signal event, and particle-level true labels that classify all reconstructed tracks from the BESIII detector into three categories: 1. fake tracks or background-event tracks; 2. real tracks originating from the intermediate ηc _c resonance; 3. real tracks not originating from the intermediate ηc _c resonance (e.g., the π+π−π^+π^- from e+e−e^+e^- annihilation, and the γ from hch_c decay). Simulation setup. The Monte Carlo (MC) dataset is simulated with standard Monte Carlo event generators used by the BESIII experiment. All particle decays are modeled with EVTGEN [24] using branching fractions either taken from the Particle Data Group (PDG) [8], when available, or otherwise estimated with LUNDCHARM [25]. True label. The true labels needed for supervised learning are obtained via a Truth-Matching Algorithm. In this algorithm, we define an average invariant mass resolution Res Res to evaluate the quality of the truth matching, Res=∑resonances|Mrec−Mtruth|Mtruth. Res= _ resonances |M_ rec-M_ truth|M_ truth. (1) The best matching result is the one with the minimum Res Res value. The matched ηc _c invariant mass spectrum obtained with this method is shown in Fig. 1, together with the distribution obtained by the conventional method. The good agreement indicates that the Truth-Matching Algorithm successfully obtains the true labels. The efficiency of the Truth-Matching Algorithm varies with the decay channel and the center-of-mass energy. For the decay channel e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→γηch_c→γ _c, ηc→anything _c , the average efficiency at the center-of-mass energies of 4.22 GeV, 4.26 GeV, and 4.39 GeV is 5.68%. Figure 1: The matched ηc _c invariant mass spectrum compared with the distribution obtained by the conventional method. Input features. Information about the charged and neutral tracks in each event is taken as the input. The number of tracks per event is not fixed, but generally does not exceed 50, with the majority distributed in the range of 7 to 15. Charged tracks with sufficiently large momentum typically leave responses in the MDC, TOF, and EMC. Their responses in the MDC allow us to reconstruct their trajectories as helices, while those in the TOF and EMC, together with the MDC response, help with particle identification (PID). Neutral tracks (usually photons) leave responses only in the EMC and can be reconstructed as electromagnetic showers. For each track, the following three types of information are chosen: MDC track information, EMC shower information, and PID information. • MDC track information. This item contains the charge q, the distances vrv_r, vzv_z from the reconstructed track to the nearest point of the interaction point, and the five helix parameters (d0,ϕ0,κ,z0,tanλd_0,\; _0,\;κ,\;z_0,\; λ) of each track. • EMC shower information. This item contains the polar angle θ and azimuthal angle ϕφ describing the shower position, the second moment A20A_20 and lateral moment A42A_42 characterizing the shower shape, and the total deposited energy E in the EMC, along with their uncertainties dθdθ, dϕdφ, and dEdE. • PID information. This item contains the PID classification results obtained from the BESIII PID algorithm. The class of a charged track is determined as the hypothesis with the highest probability output by the PID algorithm. The label for neutral tracks is 0, while for charged tracks, the labels for the e, μ, π, K, p hypotheses are 1, 2, 3, 4, and 5, respectively. Training, validation and test sets. The dataset includes three center-of-mass energy points: 4.22 GeV, 4.26 GeV, and 4.39 GeV. For each energy point, 0.8 million events are generated for both the signal channel and the background channel, resulting in a total of 4.8 million events. They are split into training, validation, and test sets in a ratio of 8:1:1. Furthermore, to validate the generalization ability of the model and its performance in realistic physics analysis scenarios, we also use the official BESIII inclusive MC dataset at 4.26 GeV as a test set. This dataset contains events of all known hadronic decay processes of e+e−e^+e^-. This inclusive MC dataset is required to satisfy the following preselections: 1. At least one set of γ, π+π^+, π−π^- candidates satisfies 3.45GeV/c2<RM(π+π−)<3.65GeV/c23.45\ GeV/c^2<RM(π^+π^-)<3.65\ GeV/c^2 and 2.80GeV/c2<RM(γπ+π−)<3.20GeV/c22.80\ GeV/c^2<RM(γπ^+π^-)<3.20\ GeV/c^2; 2. The event must be correctly and fully reconstructed, i.e., passing a kinematic fit to itself. After the preselections, the remaining number of events is 222,125. Evaluation metrics. The labeling of intermediate resonances can be essentially divided into two tasks: event-level classification and particle-level segmentation. For event-level classification, we use accuracy Acc and recall as evaluation metrics. For particle-level segmentation, we also need to evaluate the model’s performance at the event level. To this end, we adopt the IoU score, as defined in Eq. 2, which is commonly used in image segmentation. The IoU score is an event-level metric with values in the range [0,1][0,1]. The closer the value is to 1, the closer the model’s output matches the true labels for that event. We quantify segmentation performance using the average IoU score per category and the event-level perfect match rate (PMR), which is defined as the fraction of events with a perfect IoU score of 1 for all categories. IoU=ModelOutput∩TrueLabelModelOutput∪TrueLabel, IoU= Model\;Output∩ True\;Label Model\;Output∪ True\;Label, (2) Combining both aspects, we use the model signal reconstruction efficiency ϵrel,sig=NfinalNTM _ rel,\;sig= N_ finalN_ TM (i.e., the relative efficiency of the model), where NTMN_TM denotes the number of signal events passing the Truth-Matching Algorithm, and NfinalN_final is the number of signal events correctly reconstructed after model inference. For the inclusive MC test set, we use the background rejection rate Rej=1/ϵB Rej=1/ _B to evaluate the model performance, where ϵB _B is the background mistag efficiency. IV Model Architecture (a) ResoSeg (b) Two Way Attention Block Figure 2: The architecture of (a) ResoSeg (b) Two Way Attention Block. An overview of the ResoSeg architecture is presented in Fig. 2. The encoder of the model consists of Particle Embedding, Pair Embedding, and Particle Attention Blocks, drawing inspiration from ParT [2]. The decoder is inspired by SAM [26], an image segmentation model. Similar to ParT, since the input tracks are permutation invariant under token exchange, ResoSeg does not introduce any positional encoding. Additionally, it introduces interaction input features as an inductive bias to participate in the self-attention computation among the input particles. For an event with N tracks (including both charged and neutral tracks), the Tracks input includes a list of C features for every track and forms a shape (N,C)(N,C), while the Interactions input is a matrix of C′C features for every pair of particles with shape (N,N,C′)(N,N,C ). For the interaction features used to describe track-pair information, we adopt several features that differ from those used in ParT; these features are optimized by Bayesian optimization [27], which is discussed in Sec. VI. Specifically, for a pair of tracks a, b with 4-vectors pa=(Ea,Pa→)p_a=(E_a, P_a) and pb=(Eb,Pb→)p_b=(E_b, P_b), charges qaq_a and qbq_b, we calculate the following four features: M2=(Ea+Eb)2−|Pa→+Pb→|2,RM2=(Ecms−Ea−Eb)2−|Pcms→−Pa→−Pb→|2,Q=qa∗qb,kt=min(PT,a,PT,b)(ya−yb)2+(ϕa−ϕb)2, split&M^2=(E_a+E_b)^2-| P_a+ P_b|^2,\\ &RM^2=(E_ cms-E_a-E_b)^2-| P_ cms- P_a- P_b|^2,\\ &Q=q_a*q_b,\\ &k_t=min(P_T,a,P_T,b) (y_a-y_b)^2+( _a- _b)^2, split (3) where PT,i=(Px,i2+Py,i2)1/2P_T,i=(P_x,i^2+P_y,i^2)^1/2 is the transverse momentum, for i=a,bi=a,\;b and EcmsE_ cms is the center-of-mass energy. In particular, RM2RM^2 explicitly includes the event-level center-of-mass energy and momentum, thereby providing global kinematic context that is not captured by the individual track features alone. Since M2M^2, RM2RM^2 and ktk_t typically have a long-tail distribution, we use their logarithmic forms. The tracks and interactions inputs are each followed by an MLP that projects them to d- and d′d -dimensional embeddings, which are then fed into the Particle Attention Blocks to produce the encoded latent representations XLX^L that are passed to the SAM Decoder. The outputs of the SAM Decoder are the score for the entire event and the score for each track. The event score indicates how likely the event is to be a signal event, while the track score indicates the category of the track. Particle Attention Block. The Particle Attention Block is essentially the same as the one used in ParT, except that the activation function is replaced from GELU to SwiGLU. Each Particle Attention Block consists of a P-MHA, a two-layer MLP, and residual connections [2]. SAM Decoder. The SAM Decoder is the core component of ResoSeg. The SAM Decoder we use follows the original SAM design [26] closely, differing only in its inputs and outputs. Regarding the inputs, XLX^L is the sole input, without any prompt tokens. Regarding the outputs, the original SAM performs a binary classification task, while ours performs a multi-class classification task. In image segmentation, a mask is a pixel-wise label map that assigns a semantic class to every pixel. In ResoSeg, the segmentation target is a set of tracks instead of pixels, so the mask corresponds to assigning a semantic class to each track. The Mask Token is a learnable embedding that encodes this track-level mask information and interacts with particle features to generate the final track scores. For each event, we randomly initialize the Event Token and Mask Token, both of which have shape (1,d)(1,d). These tokens pass through M layers of Two Way Attention Block together with XLX^L. As in SAM, each Two Way Attention Block includes a self-attention on the Event Token and Mask Token (except for the first layer) and two cross-attentions between these two tokens and the Particle Embedding. After all Two Way Attention Block layers, the tokens undergo one more token-to-particle attention as a final update. Subsequently, the Event Token is passed through an MLP to output the Event Score; the Mask Token and the updated XMLX^L_M pass through their own MLPs, respectively, reducing their dimensions to d′×Nclassd × N_class and d′d . Here, NclassN_class is the number of categories for the particle-level segmentation. Then, a reshape operation transforms the Mask Token of shape (1,d′×Nclass)(1,d × N_class) into shape (Nclass,d′)(N_class,d ) to enable multi-class classification. Finally, a point-wise product is performed between the Mask Token and XMLX^L_M to produce the track score output. Losses. Both the event-level classification and particle-level segmentation tasks use cross-entropy as the loss. The total loss is a linear combination of the two losses. ℒ=f1×ℒevent+f2×ℒparticleL=f_1×L_event+f_2×L_particle (4) Implementation. We implement the ResoSeg model in PyTorch [28]. The baseline model has a total of L=4L=4 Particle Attention Blocks and M=2M=2 Two Way Attention Blocks. It uses a particle embedding of dimension d=64d=64, encoded from the input particle features using a three-layer MLP with (64,256,64)(64,256,64) nodes per layer, with GELU nonlinearity and layer normalization (LN) in between. The interaction input features are encoded using a four-layer pointwise 1D convolution with (64,64,64,4)(64,64,64,4) channels, with GELU nonlinearity and batch normalization in between, to yield a d′=8d =8-dimensional interaction matrix. All MHA blocks, including the P-MHA in the Particle Attention Block and the self-attention and cross-attention in the SAM Decoder, have 8 heads and an expansion factor of 4 for the MLP. For the particle-level segmentation task, the number of classification categories is Nclass=3N_class=3, corresponding to the three true-label categories provided in the dataset. The MLP before the point-wise product reduces the dimensions of both the Mask Token and the Particle Embedding to d′=d/4=16d =d/4=16. We use a dropout rate of 0.1 for all attention blocks. We also investigated using uncertainty weighting [29] to dynamically adjust the loss coefficients f1f_1 and f2f_2, but found no significant improvement over a fixed equal weighting; therefore, we simply set f1=f2=0.5f_1=f_2=0.5. We further tested gated attention (GA) [30] and conditional layer normalization (CLN) [31], but neither led to a noticeable performance gain; the detailed results are presented in Sec. VII. The hyperparameters were tuned within a reasonable range, providing a solid baseline. The total number of learnable parameters in the model is 557 thousand. V Experiments We conduct experiments on the BESIII-ηc _c dataset and present the results in Sec. V.1. The dataset is designed for the specific process described in Sec. I. ResoSeg trained on this dataset serves as a pre-trained model. We then adopt a transfer learning approach by changing the target decay channel to ψ(2S)→γηc(2S)ψ(2S)→γ _c(2S), ηc(2S)→γhc _c(2S)→γ h_c, hc→γηch_c→γ _c to evaluate its generalization capability to other ηc _c decay channels; the results are shown in Sec. V.2. We perform robustness tests against variations in the ηc _c mass, width, and branching fractions, with the results presented in Sec. V.3. V.1 Result on the BESIII-ηc _c dataset V.1.1 Setup We use the full BESIII-ηc _c dataset as the training data and optimize the parameters with the Adam [32] optimizer. The batch size is 1024, and the model is trained for 100 epochs. The learning rate follows a linear warmup and cosine annealing schedule: the first 20% of epochs are used for warmup, and the last 10% for annealing, with a stable learning rate of 0.0001. At the end of each epoch, the model is evaluated on the validation set and a checkpoint is saved. The checkpoint with the lowest validation loss is then used to evaluate the model’s performance on the test set. V.1.2 Post-processing After obtaining the model predictions, all tracks can be classified into three categories. To better reconstruct the ηc _c resonance and the entire event, we perform the following operations on these tracks: for tracks identified as real tracks from ηc _c, we sum their four-momenta to reconstruct the ηc _c resonance; for those identified as real tracks not from ηc _c, we require at least one neutral track and two charged tracks, and find the best γπ+π−γπ^+π^- combination by minimizing |M(γπ+π−ηc)−Mcms||M(γπ^+π^- _c)-M_cms|. V.1.3 Result The reconstructed mass spectra of ηc _c and γηcγ _c on the test set, together with those derived from the true labels, are shown in Fig. 3. The ResoSeg outputs reproduce the genuine signal shapes well. (a) ηc _c (b) γηcγ _c Figure 3: The reconstructed mass spectra of ηc _c and γηcγ _c on the test set, compared with those derived from the true labels. Performance is evaluated using the metrics described in Sec. I. For benchmarking purposes, a ParT model with identical hyperparameters is trained on the same dataset, and the results of both models are summarized in Table 1. Here, the reported ϵrel,sig _ rel,\;sig is the signal efficiency obtained after imposing the ηc _c and hch_c mass-window selections together with the event score requirement; the specific selections are 2.85GeV/c2<M(ηc)<3.05GeV/c22.85\;GeV/c^2<M( _c)<3.05\;GeV/c^2, 3.40GeV/c2<M(γηc)<3.58GeV/c23.40\;GeV/c^2<M(γ _c)<3.58\;GeV/c^2, and event score >0.9>0.9. In contrast, Rej90 Rej_90 is evaluated using only the event score selection, at the event score threshold that yields a relative signal efficiency of 90%. ResoSeg achieves strong performance across all metrics. In event-level classification, the high Acc and recall indicate that the model can effectively distinguish signal from background events. In particle-level segmentation, the high PMR shows that the model reconstructs the majority of signal events exactly, while the high average IoU indicates that the vast majority of both “real tracks from ηc _c” and “real tracks not from ηc _c” are correctly classified. The favorable ϵrel,sig _ rel,\;sig and Rej90 Rej_90 further ensure that ResoSeg retains as much signal as possible while suppressing background effectively. Within the BESIII-ηc _c dataset, ResoSeg and ParT exhibit comparable performance at the event level. On the more complex inclusive MC test set, ResoSeg shows a clear advantage in the two-dimensional ϵrel,sig _ rel,\;sig versus Rej comparison, where ϵrel,sig _ rel,\;sig is evaluated using only the event score selection, as shown in Fig. 4. The results demonstrate that ResoSeg can achieve a substantially higher Rej while maintaining competitive signal efficiency. More importantly, ResoSeg can recover the full four-momentum information of both the ηc _c resonance and hch_c resonance, providing further potential for background suppression. This suggests that ResoSeg offers a greater advantage in the analysis of resonance to anything decays. Figure 4: The two-dimensional comparison of ϵrel,sig _ rel,\;sig and Rej for ResoSeg and ParT, where ϵrel,sig _ rel,\;sig is evaluated using only the event score selection. Table 1: The evaluation metrics of ParT and ResoSeg on the BESIII-ηc _c dataset and the inclusive MC test set. For the average IoU, results are presented as “real tracks from ηc _c” / “real tracks not from ηc _c”. The ϵrel,sig _ rel,\;sig is the signal efficiency obtained after imposing the ηc _c and hch_c mass-window selections together with the event score requirement, while the Rej90 Rej_90 is evaluated using only the event score selection, at the event score threshold that yields a relative signal efficiency of 90%. Acc(%) Recall(%) Average IoU(×10−2× 10^-2) PMR(%) ϵrel,sig _ rel,\;sig(%) Rej90 Rej_90 ParT 95.93 98.93 \ \ \ 19.69 ResoSeg 97.31 98.84 96.12/95.20 87.91 79.79 47.82 Signal extraction on inclusive MC test set. We extract the signal from the event score distribution. The inclusive MC sample is randomly split into two parts: one part is used to extract the probability density functions (PDFs), and the other part is used to fit and extract the event yield. This process is repeated 10,000 times to perform an input/output check. The resulting pull=(Ninput−Noutput)/σoutput pull=(N_input-N_output)/ _output distribution is shown in Fig. 5, and the fit result from one of these iterations is shown in Fig. 6. The pull distribution is fitted with a Gaussian function, yielding a mean of 0.03±0.010.03± 0.01 and a σ of 1.12±0.011.12± 0.01, indicating that our method extracts the signal from the inclusive MC sample stably and accurately. Moreover, the fits yield extracted signals of high statistical significance. Figure 5: The pull=(Ninput−Noutput)/σoutput pull=(N_input-N_output)/ _output distribution of the input/output check, fitted with a Gaussian function. Figure 6: One representative fit from the input/output check. Efficiency and generalization to other energy points. The model is trained at three energy points, 4.22, 4.26, and 4.39 GeV. To test its generalization, we generate about 50 thousand events at each of 4.190, 4.245, 4.360, 4.420, and 4.600 GeV as test sets and evaluate the reconstruction efficiency on them. For comparison, we compute at the same energy points the combined efficiency ϵcombined=∑iℬi×ϵi _ combined= _iB_i× _i over the 16 decay channels of the conventional method, keeping the background levels in the inclusive MC samples comparable. Fig. 7(a) shows the combined efficiency of ResoSeg together with that of the conventional method. ResoSeg clearly achieves a significantly higher reconstruction efficiency; averaged over these energy points, its combined efficiency is about 2.6 times that of the conventional value. Fig. 7(b) shows the corresponding ϵrel,sig _ rel,\;sig, which remains high on energy points outside the training set but degrades noticeably as the center-of-mass energy increases. (a) The combined efficiency (b) The ResoSeg efficiency ϵrel,sig _ rel,\;sig Figure 7: The combined efficiency and the ResoSeg efficiency ϵrel,sig _ rel,\;sig at different energy points. Solid points represent energy points included in the training set, while hollow points represent extrapolated energy points. The gray line in (a) shows the combined efficiency of the conventional method, for which the background level in the inclusive MC sample is comparable to that of ResoSeg. V.2 Transfer learning The dataset used for transfer learning is essentially the same as that described in Sec. I, except that the signal channel is changed to ψ(2S)→γηc(2S)ψ(2S)→γ _c(2S), ηc(2S)→γhc _c(2S)→γ h_c, hc→γηch_c→γ _c, ηc→anything _c , the background channel to ψ(2S)→γηc(2S)ψ(2S)→γ _c(2S), ηc(2S)→γhc _c(2S)→γ h_c, hc→anythingh_c , and the center-of-mass energy to 3.686 GeV. The transfer learning dataset is also split into training, validation, and test sets in a ratio of 8:1:1. The post-processing procedure for ψ(2S)→γηc(2S)ψ(2S)→γ _c(2S), ηc(2S)→γhc _c(2S)→γ h_c, hc→γηch_c→γ _c, ηc→anything _c is slightly different from that for e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→γηch_c→γ _c, ηc→anything _c . We additionally require at least one photon in each of the three energy intervals (0,0.07]GeV(0,0.07]~GeV, [0.08,0.16]GeV[0.08,0.16]~GeV, and [0.2,+∞)GeV[0.2,+∞)~GeV, corresponding to the three photons not originating from ηc _c. The evaluation metrics for transfer learning with different data sizes are shown in Fig. 8; each training run uses 100 epochs. Each data point is obtained by averaging over multiple independent training runs, with the number of repetitions chosen according to the dataset size so as to keep the computational cost manageable. The statistical uncertainty of each data point is taken as the standard error of the mean (SEM) of these repeated runs and is shown as error bars in the figure. As few as 300 thousand events already yield good performance, and the metrics saturate once the data size reaches 800 thousand. Notably, the model’s ability to distinguish tracks not originating from ηc _c is markedly weaker on the transfer learning dataset than on the BESIII-ηc _c dataset, leading to slightly degraded PMR and ϵrel,sig _ rel,\;sig. This is physically plausible because the transfer learning dataset contains two low-energy photons among the three non-ηc _c tracks, which are inherently difficult to identify correctly. (a) Accuracy and recall (b) Average IoU score (c) PMR (d) ϵrel,sig _ rel,\;sig Figure 8: The evaluation metrics for transfer learning with different training set sizes. Each data point is obtained from multiple independent training runs, and the error bars represent the SEM of these runs. V.3 Robustness Evaluation Robustness is evaluated by shifting the mass (M) and width (Γ ) of the ηc _c in simulation, as well as by altering the branching fractions of ηc _c in the dataset. In the simulation, the default values of ηc _c mass and width are M=2.9839GeV/c2M=2.9839\ GeV/c^2 and Γ=0.032GeV/c2 =0.032\ GeV/c^2. Based on the uncertainties of the ηc _c from the PDG [8], we shift M by ±10σ± 10σ (0.004GeV/c20.004\ GeV/c^2) and ±5σ± 5σ (0.002GeV/c20.002\ GeV/c^2), and shift Γ by ±5σ± 5σ (0.0025GeV/c20.0025\ GeV/c^2) and ±2.5σ± 2.5σ (0.00125GeV/c20.00125\ GeV/c^2). We quantify robustness by the change in ϵrel,sig _ rel,\;sig, Δϵrel,sig=|ϵrel,sig,modified−ϵrel,sig,default|/ϵrel,sig,default _ rel,\;sig=| _ rel,\;sig,\,modified- _ rel,\;sig,\,default|/ _ rel,\;sig,\,default. Fig. 9 shows the average effect of mass shifts (a) and width shifts (b) over the three energy points. ResoSeg is robust to both mass and width shifts. (a) ϵrel,sig _ rel,\;sig against mass shift. (b) ϵrel,sig _ rel,\;sig against width shift. Figure 9: Average Δϵrel,sig _ rel,\;sig induced by (a) mass and (b) width shifts across the three energy points. Regarding branching fractions, the default configuration uses PDG-adjusted values. To test robustness, we change them to the BESIII default fractions and to uniform fractions. The average Δϵrel,sig _ rel,\;sig over the three energy points for the BESIII default fractions is 1.98%, and that for the uniform fractions is 4.92%, indicating that the model is quite robust. VI Bayesian Optimization of the Interaction Features Since the underlying physics of jets and quarkonium differs considerably, we design five additional features specifically for track-pair descriptions. Together with the four features adopted in ParT [2], we obtain a total of nine interaction features, as listed in Eq. (5): Δ=(ya−yb)2+(ϕa−ϕb)2,kt=min(PT,a,PT,b)Δ,z=min(PT,a,PT,b)/(PT,a+PT,b),M2=(Ea+Eb)2−|Pa→+Pb→|2,RM2=(Ecms−Ea−Eb)2−|Pcms→−Pa→−Pb→|2,Q=qa∗qb,|HelicityAngle|=|Pb∗→⋅z^|Pb∗→||,PolarAngle=Pa,z→+Pb,z→|Pa→+Pb→|,|ΔEEMC|=|Ea,EMC−Eb,EMC|, split& = (y_a-y_b)^2+( _a- _b)^2,\\ &k_t=min(P_T,a,P_T,b) ,\\ &z=min(P_T,a,P_T,b)/(P_T,a+P_T,b),\\ &M^2=(E_a+E_b)^2-| P_a+ P_b|^2,\\ &RM^2=(E_ cms-E_a-E_b)^2-| P_ cms- P_a- P_b|^2,\\ &Q=q_a*q_b,\\ &| Helicity\;Angle|= | P^*_b· z| P^*_b| |,\\ & Polar\;Angle= P_a,z+ P_b,z| P_a+ P_b|,\\ &| E_ EMC|=|E_a, EMC-E_b, EMC|, split (5) where Pi→=(Px,i,Py,i,Pz,i) P_i=(P_x,i,P_y,i,P_z,i) is the three-momentum in the laboratory frame, and P→i∗ P_i^* is that in the center-of-mass frame of the two-particle system, PT,i=(Px,i2+Py,i2)1/2P_T,i=(P_x,i^2+P_y,i^2)^1/2 is the transverse momentum in the laboratory frame, and Ei,EMCE_i, EMC is the deposit energy in EMC, for i=a,bi=a,\;b. To efficiently search the combinatorial feature space, we adopt Bayesian optimization, specifically the Efficient Global Optimization framework. We construct a Gaussian process surrogate model to provide predictive mean and variance for any feature subset . At each iteration, the next subset is selected by maximizing the Expected Improvement acquisition function, This procedure balances exploration and exploitation with a limited number of costly model retraining evaluations [27]. The optimal subset of interaction features is found to be [M2,RM2,Q,kt][M^2,\;RM^2,\;Q,\;k_t]. Table 2 compares the performance of this optimal subset with that of the default ParT interaction subset, when applied to both ResoSeg and ParT. It is evident that, for quarkonium, the optimized interaction features can significantly improve both ϵrel,sig _ rel,\;sig and Rej90 Rej_90 for ResoSeg, and also enhance Rej90 Rej_90 for ParT. Table 2: Evaluation metrics of ResoSeg and ParT using the optimal subset [M2,RM2,Q,kt][M^2,\;RM^2,\;Q,\;k_t] and the default ParT subset [M2,Δ,kt,z][M^2, ,k_t,z] on the test set. For the average IoU, results are presented as “real tracks from ηc _c” / “real tracks not from ηc _c”. The ϵrel,sig _ rel,\;sig is the signal efficiency obtained after imposing the ηc _c and hch_c mass-window selections together with the event score requirement, while the Rej90 Rej_90 is evaluated using only the event score selection, at the event score threshold that yields a relative signal efficiency of 90%. Acc(%) Recall(%) Average IoU(×10−2× 10^-2) PMR(%) ϵrel,sig _ rel,\;sig(%) Rej90 Rej_90 Optimal ResoSeg 97.31 98.84 96.12/95.20 87.91 79.79 47.82 Default ResoSeg 97.14 98.70 94.68/92.61 82.26 74.81 15.94 Optimal ParT 95.93 98.93 \ \ \ 19.69 Default ParT 96.16 99.16 \ \ \ 17.02 To quantify the individual contribution of each feature, we define its importance as the average change in ϵrel,sig _ rel,\;sig when the feature is included versus when it is excluded, averaged over all evaluated subsets. The resulting importances are presented in Fig. 10. M2M^2 and RM2RM^2 yield the most substantial improvements to the model, while the other features contribute only marginally in comparison. Figure 10: The importance of each interaction feature, quantified by the average change in ϵrel,sig _ rel,\;sig when the feature is included versus excluded. VII Gated attention and conditional layer normalization Based on the aforementioned model as a baseline, we introduce three model modifications: (1) replacing all attention layers in the model with gated attention (GA) [30]; (2) replacing all layer normalization with conditional layer normalization (CLN) [31], where the condition consists of the number of charged tracks with EMC information, the number of charged tracks without EMC information, the number of neutral tracks, and EcmsE_ cms; (3) applying both (1) and (2). The corresponding evaluation metrics are summarized in Table 3. Interestingly, when the interaction features exclude RM2RM^2 and include only [M2,Q,kt][M^2,Q,k_t], the model with CLN (denoted as noRM_CLN) outperforms the one without CLN (denoted as noRM) by a 6.61% improvement in PMR, a 5.87% gain in ϵrel,sig _ rel,\;sig, and a 44.68% improvement in Rej90 Rej_90. However, this improvement disappears when RM2RM^2 is included in the interaction features, likely because RM2RM^2 already contains the event-level information EcmsE_ cms, which serves a similar role to the condition used in CLN. Given that no significant difference is observed among these models, we opt not to introduce GA and CLN in the final model. Table 3: Evaluation metrics of the baseline and modified models on the test set. For the average IoU, results are presented as “real tracks from ηc _c” / “real tracks not from ηc _c”. The ϵrel,sig _ rel,\;sig is the signal efficiency obtained after imposing the ηc _c and hch_c mass-window selections together with the event score requirement, while the Rej90 Rej_90 is evaluated using only the event score selection, at the event score threshold that yields a relative signal efficiency of 90%. Acc(%) Recall(%) Average IoU(×10−2× 10^-2) PMR(%) ϵrel,sig _ rel,\;sig(%) Rej90 Rej_90 Baseline 97.31 98.84 96.12/95.20 87.91 79.79 47.82 GA 97.23 98.84 96.00/95.01 88.08 80.30 46.46 CLN 97.50 98.97 96.23/95.23 88.17 80.52 42.18 GA + CLN 97.11 99.09 95.90/95.01 87.23 80.56 34.71 noRM 96.71 99.08 94.78/92.73 82.21 76.10 26.77 noRM + CLN 97.42 99.01 96.07/94.92 87.64 80.57 38.73 VIII Conclusion and Discussion In this work, we integrate segmentation into experimental high-energy physics analyses and, for the first time, propose a model that simultaneously performs particle-level segmentation and event-level classification, thereby enabling the unified reconstruction of intermediate resonances in a single pass. To this end, we construct a dedicated BESIII-ηc _c dataset for the process e+e−→π+π−hce^+e^-→π^+π^-h_c, hc→γηch_c→γ _c, ηc→anything _c , and propose ResoSeg, which combines ParT’s particle-wise attention [2] with a SAM-inspired mask decoder [26]. At the event level, ResoSeg is comparable to ParT [2], and gives stronger background rejection on the more complex inclusive MC sample. By reconstructing the full four-momentum of the intermediate resonances, it provides further background suppression: at comparable background levels, the average combined efficiency of ResoSeg is 2.6 times that of the conventional method. These improvements enable more precise measurements of cross sections, masses, widths, and quantum numbers of exotic candidates such as the ZcZ_c states. In the inclusive MC sample, the model also separates signal from background stably, as verified by repeated input/output checks. ResoSeg also shows good generalization and robustness: it remains effective at extrapolated energy points from 4.19 to 4.60 GeV, adapts to an alternative ηc _c production chain via transfer learning, and is stable under shifts in the ηc _c mass, width, and fractions. Although demonstrated for ηc _c at BESIII, the approach is inherently general and can be transferred to other resonances and experiments, especially other lepton collider experiments. Future work will extend the model to additional resonances, address the data imbalance among the many ηc _c decay modes, and further optimize the architecture. Interference between resonance states, conventionally handled through partial-wave analysis, may instead be captured directly by deep learning in latent space, though a systematic treatment remains to be developed. Beyond resonance tagging, per-track semantic labels may also serve emerging paradigms such as foundation models for particle physics [33, 34, 35] and simulation-based inference [36, 37, 38]. 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