We generalize chiral perturbation theory with spinless matter fields in the fundamental representation of SU($\textit{N}$) to curved spacetime in the presence of an external gravitational field. This work is motivated by recent interest in investigating energy-momentum tensor matrix elements of matter fields. The complete chiral Lagrangian is constructed, including both minimal extensions from flat spacetime and new curvature-induced terms, up to the next-to-next-to-leading order in the chiral expansion, $$ \mathcal{O}\left({p}^3\right) $$ . We perform a systematic one-loop renormalization of the generating functional using the background field method combined with the heat-kernel technique, and explicitly compute the resulting ultraviolet divergences.

China

Cheng-Cheng Li

Xiong-Hui Cao

Feng-Kun Guo

Renormalization of chiral perturbation theory with spinless matter field in curved spacetime

In light of recent high-precision data taken by the BESIII Collaboration, we reconsider the dipion transition <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. The strong pion-pion final-state interactions are taken into account model independently by using dispersion theory. We find that we can reproduce the substructure near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> threshold observed experimentally without introducing an extra resonance state. While a helicity-flip amplitude plays an important role for the formation of the dip in the invariant-mass distribution, the virtual exchange of the charmoniumlike exotic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> state improves the fit quality only slightly.

Yun-Hua Chen

Germany

Xiang-Kun Dong

Christoph Hanhart

Bastian Kubis

Decoding the structure near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass threshold in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays

We propose a novel method to identify the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>. The two poles owe their origin to different quark flavor irreducible representations in the meson-baryon coupled-channel interactions, thus they should be individually manifested in reactions that provide good flavor eigenstate sources. Hadronic decays of charmonia into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi mathvariant="normal">Σ</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mi mathvariant="normal">Σ</mi><mi>π</mi></math> are such reactions, and the flavor octet and singlet poles can be approximately singled out in these two decay modes. This SU(3) flavor filter works even considering the flavor symmetry breaking. With the huge charmonium data sets collected, it is therefore promising to solve the long-standing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> puzzle employing the proposed flavor filter.

Ying-Bo He

Xiao-Hai Liu

Li-Sheng Geng

Ju-Jun Xie

Identifying the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></mrow></math> using an SU(3) flavor filter

The discoveries of the hidden-charm <italic>P<inf>c</inf></italic> pentaquarks by the LHCb Collaboration have been not confirmed by other experiments yet. It is desirable to investigate the feasibility of observing them in other experiments. We present an order-of-magnitude estimate of the cross section of the <math altimg='si1.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi>p</mi><mover accent='true'><mi>p</mi><mo>&#175;</mo></mover></mrow></math> process, where the hidden-charm pentaquarks may be searched for, and find it to be of <math altimg='si6.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mn>4</mn><mspace width='0.33em' /><mtext>fb</mtext><mo>)</mo></mrow></math> when the <math altimg='si7.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> c.m. energy is about between 6 and 7 GeV. The cross section for <math altimg='si8.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><msub><mi>P</mi><mi>c</mi></msub><mover accent='true'><mi>p</mi><mo>&#175;</mo></mover></mrow></math> is then estimated to be <math altimg='si9.svg'><mrow><mo>&#8818;</mo><mi mathvariant='script'>O</mi><mo>(</mo><mn>0.1</mn><mspace width='0.33em' /><mtext>pb</mtext><mo>)</mo></mrow></math>. Thus, it is promising to search for <italic>P<inf>c</inf></italic> at the future high-luminosity super tau-charm facilities with annual integrated luminosity about 1 ab <math altimg='si10.svg'><msup><mrow /><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></math>. We also predict the branching fraction of <math altimg='si11.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>&#8594;</mo><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi>p</mi><mover accent='true'><mi>p</mi><mo>&#175;</mo></mover></mrow></math> to be of <math altimg='si12.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mn>2</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>6</mn></mrow></msup><mo>)</mo></mrow></math>, which can be tested at <italic>B</italic> factories.

Xiao-Yu Zhang

Yi-Lin Song

Production of <math altimg='si5.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi>p</mi><mover accent='true'><mi>p</mi><mo>&#175;</mo></mover></mrow></math> in electron-positron collisions

In this paper, we model <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> as a <math altimg='si15.svg'><mrow><mn>4</mn><mi>S</mi></mrow></math>- <math altimg='si16.svg'><mrow><mn>3</mn><mi>D</mi></mrow></math> bottomonium mixture and <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> as a <math altimg='si18.svg'><mrow><mn>5</mn><mi>S</mi></mrow></math>- <math altimg='si19.svg'><mrow><mn>4</mn><mi>D</mi></mrow></math> mixture, and predict the properties of a new bottomonium state, <math altimg='si68.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10950</mn><mo>)</mo></mrow></math>, as the mixing partner of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math>. The mixing angles are derived from dielectron decay widths and mass shifts of these bottomonia. We consider open-bottom meson loops in the decays of the <math altimg='si8.svg'><mi>D</mi></math>-wave bottomonium components, based on a nonrelativistic effective field theory power counting. We show that the <math altimg='si7.svg'><mi>S</mi></math>- <math altimg='si8.svg'><mi>D</mi></math> mixing scheme is consistent with the experimental data of the decays of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math> ( <math altimg='si69.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math>) and <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math> ( <math altimg='si70.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math>). Predictions for the dielectron widths and partial decay widths into <math altimg='si71.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub><mi>&#969;</mi></mrow></math> for <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> and <math altimg='si68.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10950</mn><mo>)</mo></mrow></math> are presented.

Zheng-Li Luo

Decays of <math altimg='si21.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> and <math altimg='si17.svg'><mrow><mstyle mathvariant='normal'><mi>&#933;</mi></mstyle><mo>(</mo><mn>10753</mn><mo>)</mo></mrow></math> into <math altimg='si3.svg'><mrow><mi>&#969;</mi><msub><mi>&#967;</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></mrow></math>

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

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

Pablo Goldenzweig

Jiayin Gu

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

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation

A comprehensive analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi><mo stretchy="false">→</mo><mi>π</mi><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice quantum chromodynamics (QCD) data at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. In the present analysis, the amplitudes for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix formalism. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, the rigorous Roy-Steiner-type equation approach allows us to determine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave scattering lengths, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>0.9</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.28</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mo>−</mo><mrow><mo stretchy="false">(</mo><mn>0.3</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.02</mn></mrow><mrow><mo>+</mo><mn>0.05</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math> [also known as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math>] pole position, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mi>κ</mi></msub></msqrt><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>96</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>41</mn></mrow></msubsup><mo>−</mo><mi>i</mi><mn>19</mn><msubsup><mn>8</mn><mrow><mo>−</mo><mn>17</mn></mrow><mrow><mo>+</mo><mn>38</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

Qu-Zhi Li

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

We perform a rigorous analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> lattice data in the inelastic region, the lattice data from the crossed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, the masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> at the same pion mass from previous study, and the Regge model. Predictions on the elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering phase shifts and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math> pole content are made. Contrary to the virtual pole scenario obtained using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix method in the literature, we find that lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> remains a broad resonance at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

Rigorous Roy-Steiner equation analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at unphysical quark masses

The Efimov effect is an intriguing three-body quantum phenomenon. Searching for Efimov states within the realms of nuclear and hadronic physics presents a challenge due to the inherent inability of natural physical systems to exhibit adjustable two-body scattering lengths. In this study, we examine the potential existence of Efimov states in the $\textit{D}$ $\textit{D}$ $\textit{D}$ and $\textit{DD}$ $\textit{D}$ three-hadron systems. Utilizing a pionless effective field theory framework, we determine that the presence of Efimov states in the spectrum of the $\textit{D}$ $\textit{D}$ $\textit{D}$ system is contingent upon the existence of an ($\textit{I, J}$) = (1$\textit{,}$ 2) $\textit{D}$ $\textit{D}$ two-body bound system. If only the $$ {T}_{cc}^{+} $$ and its heavy quark spin partner $$ {T}_{cc}^{\ast +} $$ exist while there is no near-threshold pole in all other $\textit{S}$-wave $\textit{D}$ $\textit{D}$ scattering amplitudes, no Efimov effect is expected in the $\textit{D}$ $\textit{D}$ $\textit{D}$ systems.

Hai-Long Fu

Yong-Hui Lin

Hans-Werner Hammer

Ulf-G. Meißner

Georgia

Akaki Rusetsky

Xu Zhang

Exploring Efimov states in $\textit{D}$