We study the inelastic charmonium ( $ J/\psi $ , $ \psi(2S) $ ) and bottomonium ( $ \Upsilon(nS) $ ) photoproduction and fragmentation processes in $\textit{p}$-$\textit{p}$ and $ \rm Pb$ - $\rm Pb$ collisions at LHC energies, where the ultra-incoherent photon emission is included. Using the NRQCD factorization approach, an exact treatment is developed. This approach recovers the Weizsäcker-Williams approximation (WWA) near the $ Q^{2}\sim0 $ region, where the Martin-Ryskin and BCCKL methods are used to avoid double counting. We calculated the $ Q^{2} $ , $\textit{y}$, $\textit{z}$, $ \sqrt{s} $ , and $ p_{T} $ dependent and total cross sections. Inelastic photoproduction and fragmentation were observed to contribute to heavy quarkonium production, particularly at large $ p_{T} $ . In addition, the contribution of the ultra-incoherent photon channel, which increases rapidly with quarkonium mass, is significant and begins to dominate the photoproduction processes for large $ p_{T} $ . We also obtained the complete WWA validity scopes of inelastic heavy quarkonium photoproduction in heavy-ion collisions. The WWA had high accuracy at high energies and for $\rm Pb $ - $\rm Pb $ collisions. However, current photon spectra are derived beyond the WWA scope, and double counting can occur when considering different channels simultaneously.

China

Zhi-Lei Ma

Zhun Lu

Hao Liu

Li Zhang

Inelastic heavy quarkonium photoproduction in $\textit{p}$-$\textit{p}$ and Pb-Pb collisions at LHC energies * Supported in part by the National Natural Science Foundation of China (12305092, 12233006, 12150013), the Xingdian Talent Support Program for Youth Project, and by the Yunnan Fundamental Research Projects (202401AU070206). Hao Liu is supported by the Scientific Research and Innovation Project of Postgraduate Students in the Academic Degree of YunNan University (KC-242410212)

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 $\textit{Z}$ pole, the expected production of 4 Tera $\textit{Z}$ bosons will provide unique and highly precise measurements of $\textit{Z}$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $\textit{Z}$ 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 $\textit{τ}$ 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 $\textit{WW}$ 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. The role of machine learning for innovative detector design and advanced reconstruction algorithms is also stressed. The CEPC flavor physics program not only develops new capabilities for exploring flavor physics beyond existing projects but also enriches the physics opportunities of this machine. It should be remarked that, given the richness of the CEPC flavor physics, this manuscript is not meant to be a comprehensive survey, but rather an investigation of representative cases. Uncovering the full potential of flavor physics at the CEPC will require further dedicated explorations in the future.

Xiaocong Ai

United States

Wolfgang Altmannshofer

Peter Athron

Xiaozhi Bai

Lorenzo Calibbi

Germany

Lu Cao

Yuzhi Che

Chunhui Chen

Ji-Yuan Chen

Long Chen

Mingshui Chen

Shanzhen Chen

Xuan Chen

Shan Cheng

Cheng-Wei Chiang

Switzerland

Andreas Crivellin

Hanhua Cui

France

Olivier Deschamps

Sébastien Descotes-Genon

Xiaokang Du

Shuangshi Fang

Yu Gao

Yuanning Gao

Li-Sheng Geng

Pablo Goldenzweig

Jiayin Gu

Feng-Kun Guo

Yuchen Guo

Zhi-Hui Guo

Tao Han

Hong-Jian He

Jibo He

Miao He

Xiaogang He

Yanping Huang

Gino Isidori

Quan Ji

Jianfeng Jiang

Xu-Hui Jiang

Slovenia

Jernej F. Kamenik

Tsz Hong Kwok

Gang Li

Geng Li

Haibo Li

Haitao Li

Hengne Li

Honglei Li

Liang Li

Lingfeng Li

Qiang Li

Shu Li

Xiaomei Li

Xin-Qiang Li

Yiming Li

Yubo Li

Yuji Li

Zhao Li

Hao Liang

Zhijun Liang

Libo Liao

Zoltan Ligeti

Jia Liu

Jianbei Liu

Tao Liu

Yi Liu

Yong Liu

Zhen Liu

Xinchou Lou

Peng-Cheng Lu

Italy

Alberto Lusiani

Hong-Hao Ma

Kai Ma

Farvah Mahmoudi

Yajun Mao

Yaxian Mao

David Marzocca

Juan-Juan Niu

Soeren Prell

Huirong Qi

Sen Qian

Zhuoni Qian

Qin Qin

Ariel Rock

Jonathan L. Rosner

Manqi Ruan

Dingyu Shao

Chengping Shen

Xiaoyan Shen

Haoyu Shi

United Kingdom

Liaoshan Shi

Zong-Guo Si

Cristian Sierra

Huayang Song

Shufang Su

Wei Su

Zhijia Sun

Michele Tammaro

Dayong Wang

En Wang

Flavor physics at the CEPC: a general perspective * We acknowledge financial support from the National Natural Science Foundation of China (NSFC) (12125507, 12047503, 12035008, 2211530479, 12475094, 12135006, 12075097, 12375086, 2022YFA1601903, 12061141007, 12375091, 12342502, 12235018, 12335003, 12105100, 12475106, 11961141015, 12188102, 12175245, 12205171, 12321005, tsqn202312052, 2024HWYQ-005, 12405121, 12447167, 12061141006, 12405102, 12125503,12305115, 12075213, 12335005, 12235008); the Chinese Academy of Sciences (YSBR-101, XDB34030000); the National Key R&D Program of China (2022YFE0116900, 2023YFA1606703, 2022YFA1601901); the National Key Research and Development Program of China (2023YFA1606300); the Excellent Postdoctoral Program of Jiangsu Province (2023ZB891); the Shenzhen Science and Technology Program (202206193000001, 20220816094256002); the Natural Science Foundation for Distinguished Young Scholars of Henan Province (242300421046); the Beijing Municipal Natural Science Foundation (JQ22002); the Area of Excellence (AoE/P-404/18-3) and the General Research Fund (16304321) (both grants are issued by the Research Grants Council of Hong Kong S.A.R); the MOST National Key R&D Program (2023YFA1606303); the Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (Ministry of Education), Shanghai Jiao Tong University

In this study, we investigate a two-component scalar dark matter framework featuring two singlet scalar fields as dark matter candidates. To ensure vacuum stability, we employ copositive criteria for the scalar potential. We analyze four distinct copositive scenarios characterized by specific negative parameter configurations using direct detection constraints. A comprehensive parameter space scan is performed under joint constraints from the observed dark matter relic density and direct detection experiments. The different signs of couplings not only correspond to different copositive criteria but also contribute to different parameter spaces caused by interference. The allowed values of quartic couplings are different for the four different cases; however, they all require the new Higgs to play a dominant role in determining dark matter relic density within the viable parameter space.

Xin-Xin Qi

Hao Sun

Copositive criteria for a two-component dark matter model * Hao Sun is supported by the National Natural Science Foundation of China (12075043 and 12147205). XinXin Qi is supported by the National Natural Science Foundation of China (12447162)

Recent years have seen the development and growth of machine learning in high-energy physics. However, additional effort is required to continue exploring the use of machine learning to its full potential. To simplify the application of the existing algorithms and neural networks and to advance the reproducibility of the analysis, we developed HEP ML LAB ( $ \mathrm{hml}$ ), a Python-based, end-to-end framework for phenomenology studies. It covers the complete workflow from event generation to performance evaluation, and provides a consistent style of use for different approaches. We propose an observable naming convention to streamline the data extraction and conversion processes. In the KERAS style, we provide the traditional cut-and-count and boosted decision trees together with neural networks. We take the $W^+ $ tagging as an example and evaluate all built-in approaches with the metrics of significance and background rejection. With its modular design, HEP ML LAB is easy to extend and customize, and can be used as a tool for both beginners and experienced researchers.

Jing Li

HEP ML LAB: An end-to-end framework for applying machine learning to phenomenology studies * Hao Sun is supported by the National Natural Science Foundation of China (12075043)

General one-loop formulas for loop-induced processes $gg/\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, $\textit{e.g.,}$ Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models$\textit{.}$ Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and four-point functions following the output format of the packages $ {\tt LoopTools}$ and $ {\tt Collier}$ . Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes $\gamma \gamma\rightarrow hh$ are scanned over the parameter space of the Zee-Babu Model.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

One-loop analytical expressions for $\textit{gg}$/$\textit{γγ}$ → ϕ$_{i}$ϕ$_{j}$ in Higgs extensions of the standard model and their applications * This research is supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16). Khiem Hong Phan and Dzung Tri Tran express their gratitude to all the valuable support from Duy Tan University, for the 30th anniversary of establishment (Nov. 11, 1994 - Nov. 11, 2024) towards ''Integral, Sustainable and Stable Development''

<p>The vortex state properties of a pair of scalar particles produced in a strong circularly polarized electromagnetic standing wave field are investigated under the dipole approximation in the multiphoton regime. We find that vortex orientation is related to the intrinsic orbital angular momentum of created particles associating with the helicity of absorbed photons, while the magnitude of the orbital angular momentum, i.e., the topology charge, is determined by the number of absorbed photons. Moreover, the properties of particle creation and vortices formation can be understood by analyzing the pair production process in quasiparticle representation. This study provides new insights into the angular momentum transfer from field to particle in the scalar pair production process in vacuum. It is expected that there are similar findings about vortex features for different spin alignment in electron-positron pair production in strong fields via the topology charge as a new freedom.</p>

Hong-Hao Fan

Cui-Wen Zhang

Suo Tang

Bai-Song Xie

Vortex state properties in multiphoton scalar pair production

<p>We have formulated a generalized two level model for studying the vacuum electron-positron pair production in strong classical background fields via slowly varying envelope approximation. It can provide momentum spectra with fully spin resolved components for all possible combined spin states of the particle and antiparticle simultaneously in multidimensional time-dependent electric fields. Moreover, we have also investigated the validity of the two level model for fermions (scalar particles) by comparing the results with those by equal-time Dirac-Heisenberg-Wigner (Feshbach-Villars-Heisenberg-Wigner) formalism in different regimes of pair creation, i.e., multiphoton and tunneling dominated mechanisms. It is found that the results are consistent with each other, indicating the good approximation of the two level model. In particular, in terms of the two level model, we found that the contribution of the particle momentum spectra is the greatest when the spin states of the particle and antiparticle are parallel with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mn>1</mn></math>. It is believed that by this two level model one can extend researches on pair production for more different background fields, such as a slowly varying spatial-temporal one. Significantly, we demonstrate that the generalized two level model is equivalent to the spin resolved quantum kinetic theory. In comparison to the equal-time Dirac-Heisenberg-Wigner and Feshbach-Villars-Heisenberg-Wigner methods, the two-level model is simpler and has the potential to deliver faster computational performance.</p>

Orkash Amat

Yong-Feng Huang

Spin resolved momentum spectra for vacuum pair production via a generalized two level model

Electron-positron pair production is investigated in the multiphoton regime under polarized fields. Partial wave analysis can be applied to reveal the momentum spectral structure and identify the positions of valleys/peaks of the multiphoton rings by combining with <math><mi>C</mi><mi>P</mi></math> conservation. Moreover, considering the spin states of created pairs in partial wave analysis, the particle orbital angular momentum associated with the valleys/peaks can also be identified from multiphoton rings. It is found that the approximate analytical treatments for angular distribution by using partial wave analysis are consistent with those of the numerical calculation using the Dirac-Heisenberg-Wigner formalism. The results are helpful for understanding the angular momentum information in momentum spectra, and they also have an implication for revealing the vortex structure near the valleys where the amplitude nearly vanishes.

Li-Na Hu

Zi-Liang Li

Application of partial wave analysis in multiphoton pair production

Spin effect on the pair production under circularly polarized fields is investigated. Significantly different from what momentum spirals caused by two counterrotating fields with a time delay, we find for the first time that the spirals can also be induced due to the particle spin effect even if in a single field. We further examine the bichromatic combinational fields. The inhomogeneous spiral structures can be observed in the momentum spectrum; in particular, the spiral not only does exist in two cases of spin, but also is about 2 orders of magnitude amplified compared with that in the single field. Meanwhile, the spin asymmetry degree on the momentum distributions is investigated, and it was found that the effect of spin flip exists with an increased time delay between two fields. The spin asymmetry degree on the number density can reach to 98% in certain conditions. These results indicate that the signatures of created particles, especially the spiral structures, are strongly associated with information pertaining to the laser field as well as the created particle spin, which can deepen the understanding of vacuum pair production.

Spin effect induced momentum spiral and asymmetry degree in pair production

We investigate the effects of the asymmetric pulse shapes on electron-positron pair production in a field with three different cases of chirping via the real-time Dirac-Heisenberg-Wigner formalism. Our findings reveal the disappearance of interference effects with shorter falling pulse length, and the peak is concentrated on the left side of the momentum spectrum. As the falling pulse length extends, an incomplete multiring structure appears in the momentum spectrum. The number density of particles are very sensitive to the asymmetry of the pulse. With a long falling pulse, the number density can be significantly enhanced by over four orders of magnitude when certain frequency chirps are utilized. These results highlight the impact of the effective dynamically assisted mechanism and the frequency chirp on pair creation.

Neng-Zhi Chen

Asymmetric pulse effects on pair production in chirped electric fields