arXiv subjects

Yu-Dong Zhang

Publications and source records attributed to Yu-Dong Zhang.

18 recordsLinked to original sources

arXiv2025

Rare $W \to B_c + γ$ decay up to the NNLO and NLL accuracy in QCD

We perform a detailed theoretical study of the rare radiative decay of the $W$ boson into a $B_c$ meson and an on-shell photon. The decay amplitude is described by two independent form factors, which are calculated up to the next-to-next-to-leading order (NNLO) in QCD within the nonrelativistic QCD (NRQCD) factorization formalism. Since the two typical energy scales, the $W$-boson mass $m_W$ and the $B_c$-meson mass $m_{B_c}$, involved in the process are widely separated, large logarithms of $m_W^2/m_{B_c}^2$ present in the NRQCD short-distance coefficients are also resummed to all orders in $α_s$ up to the next-to-leading logarithmic (NLL) accuracy, by employing the light-cone factorization approach. Taking into account all these corrections, we then perform a phenomenological exploration of this rare decay. It is found that, relative to the leading-order result, the decay width of the process is reduced by the next-to-leading-order and NNLO corrections, with a net effect of $\sim19\%$ and of $\sim31\%$, respectively. Furthermore, the NLL resummation can considerably alter the fixed-order NRQCD predictions, especially for the $\mathcal{O}(α_s)$ correction. We also find that the radiative corrections increase the renormalization scale dependence of the branching fraction, which is however significantly reduced by the NLL resummation. The dependence of the branching fraction on the heavy-quark masses $m_{b,c}$ is also investigated, which shows a monotonic decrease (increase) with $m_c$ ($m_b$).

hep-ph↗

arXiv2025

Medical World Model: Generative Simulation of Tumor Evolution for Treatment Planning

Providing effective treatment and making informed clinical decisions are essential goals of modern medicine and clinical care. We are interested in simulating disease dynamics for clinical decision-making, leveraging recent advances in large generative models. To this end, we introduce the Medical World Model (MeWM), the first world model in medicine that visually predicts future disease states based on clinical decisions. MeWM comprises (i) vision-language models to serve as policy models, and (ii) tumor generative models as dynamics models. The policy model generates action plans, such as clinical treatments, while the dynamics model simulates tumor progression or regression under given treatment conditions. Building on this, we propose the inverse dynamics model that applies survival analysis to the simulated post-treatment tumor, enabling the evaluation of treatment efficacy and the selection of the optimal clinical action plan. As a result, the proposed MeWM simulates disease dynamics by synthesizing post-treatment tumors, with state-of-the-art specificity in Turing tests evaluated by radiologists. Simultaneously, its inverse dynamics model outperforms medical-specialized GPTs in optimizing individualized treatment protocols across all metrics. Notably, MeWM improves clinical decision-making for interventional physicians, boosting F1-score in selecting the optimal TACE protocol by 13%, paving the way for future integration of medical world models as the second readers.

cs.CV↗

arXiv2024

Electromagnetic and hadronic decay of fully heavy tetraquark

In this study, we compute the electromagnetic and hadronic decay widths of the S-wave fully heavy tetraquark $T_{4Q}$ ($Q=c$ or $b$) at lowest order in $α_s$ and $v$, in the framework of nonrelativistic QCD. The short-distance coefficients are determined through the standard procedure of matching. The nonperturbative long-distance matrix elements are related to the phenomenological four-body Schrödinger wave functions at the origin, whose values are taken from literature. The branching fractions are predicted to be around $10^{-4}$ and $10^{-7}-10^{-6}$ for the $T_{4c}$ hadronic decay and electromagnetic decay, respectively. Combing our results with the $T_{4c}$ production cross sections at the LHC, we also predict the event numbers for various decay channels. With integrated luminosity $\mathcal{L}=100 \,{\rm fb}^{-1}$, it is expected that the event numbers can reach $10^3$ for $T_{4c}\to γγ$, and $10^6$ for $T_{4c}\to {\rm LH}$, at the LHC. The detecting prospect is promising. In addition, the decay widths of $T_{4b}$ are estimated based on simple dimensional analysis as well as velocity scaling rule.

hep-ph↗

arXiv2023

Automatic Diagnosis of Myocarditis Disease in Cardiac MRI Modality using Deep Transformers and Explainable Artificial Intelligence

Myocarditis is a significant cardiovascular disease (CVD) that poses a threat to the health of many individuals by causing damage to the myocardium. The occurrence of microbes and viruses, including the likes of HIV, plays a crucial role in the development of myocarditis disease (MCD). The images produced during cardiac magnetic resonance imaging (CMRI) scans are low contrast, which can make it challenging to diagnose cardiovascular diseases. In other hand, checking numerous CMRI slices for each CVD patient can be a challenging task for medical doctors. To overcome the existing challenges, researchers have suggested the use of artificial intelligence (AI)-based computer-aided diagnosis systems (CADS). The presented paper outlines a CADS for the detection of MCD from CMR images, utilizing deep learning (DL) methods. The proposed CADS consists of several steps, including dataset, preprocessing, feature extraction, classification, and post-processing. First, the Z-Alizadeh dataset was selected for the experiments. Subsequently, the CMR images underwent various preprocessing steps, including denoising, resizing, as well as data augmentation (DA) via CutMix and MixUp techniques. In the following, the most current deep pre-trained and transformer models are used for feature extraction and classification on the CMR images. The findings of our study reveal that transformer models exhibit superior performance in detecting MCD as opposed to pre-trained architectures. In terms of DL architectures, the Turbulence Neural Transformer (TNT) model exhibited impressive accuracy, reaching 99.73% utilizing a 10-fold cross-validation approach. Additionally, to pinpoint areas of suspicion for MCD in CMRI images, the Explainable-based Grad Cam method was employed.

cs.CV↗

arXiv2023

Two-Loop QCD Corrections to C even Bottomonium Exclusive Decays to Double $J/ψ$

In the framework of nonrelativistic QCD (NRQCD) factorization, we compute both the polarized and the unpolarized decay widths for the processes $η_b(χ_{bJ})\to J/ψJ/ψ$, accurate up to next-to-next-to-leading-order (NNLO) in $α_s$. For the first time, we confirm that the NRQCD factorization does hold at NNLO for the process involving triple quarkonia. We find the radiative corrections are considerable. In particular for $χ_{b2}$, both $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections are sizable and negative, and can significantly reduce the leading order prediction. At NNLO, the branching fractions are $8.2\times 10^{-7}$, $6.2\times 10^{-6}$, $7.2\times 10^{-7}$ and $2.7\times 10^{-6}$ for $η_b$, $χ_{b0}$, $χ_{b1}$ and $χ_{b2}$ decay, respectively. Our theoretical predictions are consistent with the upper limits measured by the {\tt Belle} Collaboration. Moreover, we investigate the dependence of the theoretical predictions on the ratio of the charm quark mass and the bottom quark mass. By fixing $m_b$ and varying $m_c$ from $1.25$ to $1.9$ GeV, we find the branching fraction can change a factor of $2$, $3$, and $6$ for $η_b$, $χ_{b0}$, and $χ_{b1}$, respectively. In the phenomenological analysis, with the integrate luminosity $\mathcal{L}=100\,{\rm fb}^{-1}$, we expect about $(5-10)\times 10^3$ $η_b(χ_{bJ})\to J/ψJ/ψ\to \ell \bar{\ell}\ell \bar{\ell}$ events produced at the {\tt LHC}, thus it might be hopeful to search for these processes. On the other hand, there are less than $100$ $η_b(χ_{bJ})\to J/ψJ/ψ$ signal events at the B factory, so it seems the experimental measurements on these channels are quite challenging based on current dataset.

hep-ph↗

arXiv2023

$Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy

Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute QCD next-to-next-to-leading order (NNLO) corrections to the helicity amplitudes as well as the decay width of $Z\to H+γ$, where $H$ can be $η_Q (Q=c,b), J/ψ$, or $Υ$. In addition, we resum the next-to-leading logarithms (NLL) of ${m_Z^2}/{m_Q^2}$ to all orders of $α_s$ for the leading-twist helicity amplitude by employing the light-cone factorization approach. It is worth mentioning that we obtain the analytic expressions of the truncated NLL at $α_s^2$. We find that the $\mathcal{O}(α_s)$ corrections are around 10\% for $η_c$ and $Υ$ productions, however insignificant for $J/ψ$ and $η_b$ productions. The $\mathcal{O}(α_s^2)$ corrections are moderate for charmonium production, while very small for bottomonium production. Moreover, it is found that the NLL resummation can considerably alter the NRQCD prediction, especially for $J/ψ$ production. Combining the NRQCD and light-cone computation, we make phenomenological predictions on the decay widths and branching fractions. In addition, we investigate the dependence of the theoretical results on the heavy quark mass, and find the branching fraction of $Z\to H+γ$ monotonically decreases as $m_Q$ increases.

hep-ph↗

arXiv2023

$Z$ boson radiative decays to a $P$-wave quarkonium at NNLO and LL accuracy

In this work, we study the radiative decay of $Z$ boson to a $P$-wave quarkonium $H$ in association with a photon, where $H$ can be $χ_{QJ}$, $h_Q$ with $Q=c,b$ and $J=0,1,2$. The helicity amplitudes and the unpolarized decay widths are evaluated up to QCD next-to-next-to-leading order (NNLO) within the framework of nonrelativistic QCD (NRQCD). For the first time, we check the NRQCD factorization for $h_Q$ exclusive production at two-loop order. The leading logarithms (LL) of $m_Z^2/m_Q^2$ in the leading-twist short-distance coefficients, which may potentially ruin the perturbative convergence, are resummed to all orders of $α_s$ by employing the light-cone factorization. We find the radiative corrections are considerable for $χ_{Q2}$ and $h_Q$ productions, while are moderate or even minor for other channels. We also notice that the LL resummation can change the leading-order predictions for decay widths by more than 25\% for $χ_{c0,2}$ and $h_c$ productions, and by around 50\% for $χ_{c1}$ production. However, effects of the LL resummation on the next-to-leading-order and NNLO predictions are notably mitigated. Some phenomenological explorations are also performed.

hep-ph↗

arXiv2022

Deep Learning for Brain Age Estimation: A Systematic Review

Over the years, Machine Learning models have been successfully employed on neuroimaging data for accurately predicting brain age. Deviations from the healthy brain aging pattern are associated to the accelerated brain aging and brain abnormalities. Hence, efficient and accurate diagnosis techniques are required for eliciting accurate brain age estimations. Several contributions have been reported in the past for this purpose, resorting to different data-driven modeling methods. Recently, deep neural networks (also referred to as deep learning) have become prevalent in manifold neuroimaging studies, including brain age estimation. In this review, we offer a comprehensive analysis of the literature related to the adoption of deep learning for brain age estimation with neuroimaging data. We detail and analyze different deep learning architectures used for this application, pausing at research works published to date quantitatively exploring their application. We also examine different brain age estimation frameworks, comparatively exposing their advantages and weaknesses. Finally, the review concludes with an outlook towards future directions that should be followed by prospective studies. The ultimate goal of this paper is to establish a common and informed reference for newcomers and experienced researchers willing to approach brain age estimation by using deep learning models

eess.IV↗

arXiv2022

Automated Diagnosis of Cardiovascular Diseases from Cardiac Magnetic Resonance Imaging Using Deep Learning Models: A Review

In recent years, cardiovascular diseases (CVDs) have become one of the leading causes of mortality globally. CVDs appear with minor symptoms and progressively get worse. The majority of people experience symptoms such as exhaustion, shortness of breath, ankle swelling, fluid retention, and other symptoms when starting CVD. Coronary artery disease (CAD), arrhythmia, cardiomyopathy, congenital heart defect (CHD), mitral regurgitation, and angina are the most common CVDs. Clinical methods such as blood tests, electrocardiography (ECG) signals, and medical imaging are the most effective methods used for the detection of CVDs. Among the diagnostic methods, cardiac magnetic resonance imaging (CMR) is increasingly used to diagnose, monitor the disease, plan treatment and predict CVDs. Coupled with all the advantages of CMR data, CVDs diagnosis is challenging for physicians due to many slices of data, low contrast, etc. To address these issues, deep learning (DL) techniques have been employed to the diagnosis of CVDs using CMR data, and much research is currently being conducted in this field. This review provides an overview of the studies performed in CVDs detection using CMR images and DL techniques. The introduction section examined CVDs types, diagnostic methods, and the most important medical imaging techniques. In the following, investigations to detect CVDs using CMR images and the most significant DL methods are presented. Another section discussed the challenges in diagnosing CVDs from CMR data. Next, the discussion section discusses the results of this review, and future work in CVDs diagnosis from CMR images and DL techniques are outlined. The most important findings of this study are presented in the conclusion section.

eess.IV↗

arXiv2022

Probabilistic combination of eigenlungs-based classifiers for COVID-19 diagnosis in chest CT images

The outbreak of the COVID-19 (Coronavirus disease 2019) pandemic has changed the world. According to the World Health Organization (WHO), there have been more than 100 million confirmed cases of COVID-19, including more than 2.4 million deaths. It is extremely important the early detection of the disease, and the use of medical imaging such as chest X-ray (CXR) and chest Computed Tomography (CCT) have proved to be an excellent solution. However, this process requires clinicians to do it within a manual and time-consuming task, which is not ideal when trying to speed up the diagnosis. In this work, we propose an ensemble classifier based on probabilistic Support Vector Machine (SVM) in order to identify pneumonia patterns while providing information about the reliability of the classification. Specifically, each CCT scan is divided into cubic patches and features contained in each one of them are extracted by applying kernel PCA. The use of base classifiers within an ensemble allows our system to identify the pneumonia patterns regardless of their size or location. Decisions of each individual patch are then combined into a global one according to the reliability of each individual classification: the lower the uncertainty, the higher the contribution. Performance is evaluated in a real scenario, yielding an accuracy of 97.86%. The large performance obtained and the simplicity of the system (use of deep learning in CCT images would result in a huge computational cost) evidence the applicability of our proposal in a real-world environment.

eess.IV↗

arXiv2022

Higher-order QCD corrections to $Υ$ decay into double charmonia

In this work, we study the exclusive decay of $Υ$ into $J/ψ$ in association with $η_c$ ($χ_{c0,1,2}$). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of $Υ\rightarrow J/ψ+χ_{c1}$ is obtained as $3.73^{+5.10+0.10}_{-2.06-1.19}\times 10^{-6}$, which agrees well with the Belle measurement, i.e., ${\rm Br}(Υ\rightarrow J/ψ+χ_{c1})=(3.90\pm1.21\pm0.23)\times10^{-6}$. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for $Υ(2S)\to J/ψ+χ_{c1}$, where some tension exists between theory and experiment. Having the polarized decay widths, we study the $J/ψ$ polarization, which turn out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super B factory thanks to the high luminosity.

hep-ph↗

arXiv2022

Source-free unsupervised domain adaptation for cross-modality abdominal multi-organ segmentation

Domain adaptation is crucial for transferring the knowledge from the source labeled CT dataset to the target unlabeled MR dataset in abdominal multi-organ segmentation. Meanwhile, it is highly desirable to avoid the high annotation cost related to the target dataset and protect the source dataset privacy. Therefore, we propose an effective source-free unsupervised domain adaptation method for cross-modality abdominal multi-organ segmentation without source dataset access. The proposed framework comprises two stages. In the first stage, the feature map statistics-guided model adaptation combined with entropy minimization is developed to help the top segmentation network reliably segment the target images. The pseudo-labels output from the top segmentation network are used to guide the style compensation network to generate source-like images. The pseudo-labels output from the middle segmentation network is used to supervise the learning progress of the desired model (bottom segmentation network). In the second stage, the circular learning and pixel-adaptive mask refinement are used to further improve the desired model performance. With this approach, we achieved satisfactory abdominal multi-organ segmentation performance, outperforming the existing state-of-the-art domain adaptation methods. The proposed approach can be easily extended to situations in which target annotation data exist. With only one labeled MR volume, the performance can be levelled with that of supervised learning. Furthermore, the proposed approach is proven to be effective for source-free unsupervised domain adaptation in reverse direction.

cs.CV↗

arXiv2022

An overview of artificial intelligence techniques for diagnosis of Schizophrenia based on magnetic resonance imaging modalities: Methods, challenges, and future works

Schizophrenia (SZ) is a mental disorder that typically emerges in late adolescence or early adulthood. It reduces the life expectancy of patients by 15 years. Abnormal behavior, perception of emotions, social relationships, and reality perception are among its most significant symptoms. Past studies have revealed that SZ affects the temporal and anterior lobes of hippocampus regions of the brain. Also, increased volume of cerebrospinal fluid (CSF) and decreased volume of white and gray matter can be observed due to this disease. Magnetic resonance imaging (MRI) is the popular neuroimaging technique used to explore structural/functional brain abnormalities in SZ disorder, owing to its high spatial resolution. Various artificial intelligence (AI) techniques have been employed with advanced image/signal processing methods to accurately diagnose SZ. This paper presents a comprehensive overview of studies conducted on the automated diagnosis of SZ using MRI modalities. First, an AI-based computer aided-diagnosis system (CADS) for SZ diagnosis and its relevant sections are presented. Then, this section introduces the most important conventional machine learning (ML) and deep learning (DL) techniques in the diagnosis of diagnosing SZ. A comprehensive comparison is also made between ML and DL studies in the discussion section. In the following, the most important challenges in diagnosing SZ are addressed. Future works in diagnosing SZ using AI techniques and MRI modalities are recommended in another section. Results, conclusion, and research findings are also presented at the end.

cs.LG↗

arXiv2021

Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium

Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay $Υ\to η_c(χ_{cJ})+γ$. Both the helicity amplitudes and the helicity decay widths are obtained. It is the first computation for the processes involving both bottomonium and charmonium at two-loop accuracy. By employing the Cheng-Wu theorem, we are able to convert most of complex-valued master integrals (MIs) into real-valued MIs, which makes the numerical integration much efficient. Our results indicate the $\mathcal{O}(α_s)$ corrections are moderate for $η_c$ and $χ_{c2}$ production, and are quite marginal for $χ_{c0}$ and $χ_{c1}$ production. It is impressive to note the NLO corrections considerably reduce the renormalization scale dependence in both the decay widths and the branching fractions for $χ_{cJ}$, and slightly improve that for $η_c$. With the NRQCD matrix elements evaluated via the Buchmüller-Tye potential model, we find the decay width for $η_c$ production is one-order-of-magnitude larger than $χ_{cJ}$ production, which may provide a good opportunity to search for $Υ\to η_c+γ$ in experiment. In addition, the decay width for $χ_{c1}$ production is several times larger than those for $χ_{c0,2}$. Finally, we find the NLO NRQCD prediction for the branching fraction of $Υ\to χ_{c1}+γ$ is only half of the lower bound of the experimental data measured recently by {\tt Belle}. Moreover, there exists serious contradiction between theory and experiment for $Υ\to η_c+γ$. The discrepancies between theory and experiment deserve further research efforts.

hep-ph↗

arXiv2021

Automatic Diagnosis of Schizophrenia in EEG Signals Using CNN-LSTM Models

Schizophrenia (SZ) is a mental disorder whereby due to the secretion of specific chemicals in the brain, the function of some brain regions is out of balance, leading to the lack of coordination between thoughts, actions, and emotions. This study provides various intelligent deep learning (DL)-based methods for automated SZ diagnosis via electroencephalography (EEG) signals. The obtained results are compared with those of conventional intelligent methods. To implement the proposed methods, the dataset of the Institute of Psychiatry and Neurology in Warsaw, Poland, has been used. First, EEG signals were divided into 25 s time frames and then were normalized by z-score or norm L2. In the classification step, two different approaches were considered for SZ diagnosis via EEG signals. In this step, the classification of EEG signals was first carried out by conventional machine learning methods, e.g., support vector machine, k-nearest neighbors, decision tree, naïve Bayes, random forest, extremely randomized trees, and bagging. Various proposed DL models, namely, long short-term memories (LSTMs), one-dimensional convolutional networks (1D-CNNs), and 1D-CNN-LSTMs, were used in the following. In this step, the DL models were implemented and compared with different activation functions. Among the proposed DL models, the CNN-LSTM architecture has had the best performance. In this architecture, the ReLU activation function with the z-score and L2-combined normalization was used. The proposed CNN-LSTM model has achieved an accuracy percentage of 99.25%, better than the results of most former studies in this field. It is worth mentioning that to perform all simulations, the k-fold cross-validation method with k = 5 has been used.

eess.SP↗

arXiv2021

Sequential Learning on Liver Tumor Boundary Semantics and Prognostic Biomarker Mining

The boundary of tumors (hepatocellular carcinoma, or HCC) contains rich semantics: capsular invasion, visibility, smoothness, folding and protuberance, etc. Capsular invasion on tumor boundary has proven to be clinically correlated with the prognostic indicator, microvascular invasion (MVI). Investigating tumor boundary semantics has tremendous clinical values. In this paper, we propose the first and novel computational framework that disentangles the task into two components: spatial vertex localization and sequential semantic classification. (1) A HCC tumor segmentor is built for tumor mask boundary extraction, followed by polar transform representing the boundary with radius and angle. Vertex generator is used to produce fixed-length boundary vertices where vertex features are sampled on the corresponding spatial locations. (2) The sampled deep vertex features with positional embedding are mapped into a sequential space and decoded by a multilayer perceptron (MLP) for semantic classification. Extensive experiments on tumor capsule semantics demonstrate the effectiveness of our framework. Mining the correlation between the boundary semantics and MVI status proves the feasibility to integrate this boundary semantics as a valid HCC prognostic biomarker.

cs.CV↗

arXiv2020

Uncertainty-driven ensembles of deep architectures for multiclass classification. Application to COVID-19 diagnosis in chest X-ray images

Respiratory diseases kill million of people each year. Diagnosis of these pathologies is a manual, time-consuming process that has inter and intra-observer variability, delaying diagnosis and treatment. The recent COVID-19 pandemic has demonstrated the need of developing systems to automatize the diagnosis of pneumonia, whilst Convolutional Neural Network (CNNs) have proved to be an excellent option for the automatic classification of medical images. However, given the need of providing a confidence classification in this context it is crucial to quantify the reliability of the model's predictions. In this work, we propose a multi-level ensemble classification system based on a Bayesian Deep Learning approach in order to maximize performance while quantifying the uncertainty of each classification decision. This tool combines the information extracted from different architectures by weighting their results according to the uncertainty of their predictions. Performance of the Bayesian network is evaluated in a real scenario where simultaneously differentiating between four different pathologies: control vs bacterial pneumonia vs viral pneumonia vs COVID-19 pneumonia. A three-level decision tree is employed to divide the 4-class classification into three binary classifications, yielding an accuracy of 98.06% and overcoming the results obtained by recent literature. The reduced preprocessing needed for obtaining this high performance, in addition to the information provided about the reliability of the predictions evidence the applicability of the system to be used as an aid for clinicians.

eess.IV↗

arXiv2020

Study on $η_{c2}(η_{b2})$ electromagnetic decay into double photons

Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute the helicity amplitude as well as the decay width of $η_{Q2}$ ($Q=c,b$) electromagnetic decay into two photons up to next-to-next-to-leading order (NNLO) in $α_s$ expansion. For the first time, we verify the validity of NRQCD factorization for the D-wave quarkonium decay at NNLO. We find that the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections to the helicity amplitude are negative and moderate, nevertheless both corrections combine to suppress the leading-order prediction for the decay width significantly. By approximating the total decay width of $η_{Q2}$ as the sum of those for the hadronic decay and the electric $E1$ transition, we obtain the branching ratios ${\rm Br}(η_{c2}\to 2γ)\approx 5\times10^{-6}$ and ${\rm Br}(η_{b2}\to 2γ)\approx 4\times10^{-7}$. To explore the potential measurement on $η_{Q2}$, we further evaluate the production cross section of $η_{Q2}$ at LHCb at the lowest order in $α_s$ expansion. With the kinematic constraint on the longitudinal rapidity $4.5>y>2$ and transverse momentum $P_T>(2-4)m_Q$ for $η_{Q2}$, we find the cross section can reach $2-50$ nb for $η_{c2}$, and $1-22$ pb for $η_{b2}$. Considering the integrated luminosity $\mathcal{L}=10\, {\rm fb}^{-1}$ at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV, we estimate that there are several hundreds events of $pp\to η_{c2}\to 2γ$. Since the background is relatively clean, it is promising to reconstruct $η_{c2}$ through its electromagnetic decay. On the contrary, due to small branching ratio and production cross section, it is quite challenging to detect $η_{b2}\to 2γ$ at LHCb.

hep-ph↗