The magnitude of the direct CP asymmetry generated during the weak decay of hadrons is attributed to the weak phase and certain strong phases. The weak phase originates from the CKM matrix, while a strong phase may result from the resonance effect produced by the mixing of vector mesons $ V\left\{\rho^{0}(770),\,\omega(782),\,\phi(1020)\right\} $ to $ \pi^+ \pi^- $ meson pairs. $ \rho^{0}(770) $ can decay directly into $ \pi^+ \pi^- $ meson pairs; both $ \omega(782) $ and $ \phi(1020) $ can also decay into $ \pi^+ \pi^- $ meson pairs, with a small contribution from isospin symmetry breaking. The main contribution for the middle state vector meson $ \rho^{0}(770)-\omega(782)-\phi(1020) $ interference is the mix of $ \rho^{0}(770) $ , $ \omega(782)-\rho^{0}(770) $ , and $ \phi(1020)-\rho^{0}(770) $ . We calculated the CP asymmetry and decay branching ratio for $ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \pi^0 (\bar K ^{0}) $ within the framework of QCD factorization and compared them with previous studies. We also analyzed the $ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \eta(\eta^{(')}) $ decay process. The results show that the CP asymmetry of these four decay processes is significantly enhanced, especially for the $ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \bar K ^{0} $ decay process. Moreover, the decay branching ratio also changes under the resonance effect. These results might provide support for the experimental analysis of the $ \bar B^{0}_s $ meson.

China

Xi-Liang Yuan

Chao Wang

Zhuang-Dong Bai

Gang Lü

Role and contribution of the resonance effect for the decay process of ${ \bar {\boldsymbol B}^{\bf 0}_{\boldsymbol s} \boldsymbol\rightarrow \boldsymbol\pi^{+}\boldsymbol\pi^{-}{\boldsymbol P}}$ * Supported by National Natural Science Foundation of China (Project No.11805153) and Natural Science Foundation of Henan Province (Project No.252300420319)

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

<p>We report a study of the hadronic transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>28.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> mesons recorded by the Belle detector. We present the first evidence for the near-threshold transition <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, the analog of the near-threshold charm sector decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, with a branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo minsize="2ex" stretchy="true">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo minsize="2ex" stretchy="true">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.55</mn><mo>±</mo><mn>0.19</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We also obtain branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>2.39</mn></mrow><mrow><mo>−</mo><mn>0.19</mn></mrow><mrow><mo>+</mo><mn>0.20</mn></mrow></msubsup><mo>±</mo><mn>0.24</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo minsize="2ex" stretchy="true">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo minsize="2ex" stretchy="true">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mrow><mn>0.47</mn></mrow><mrow><mo>−</mo><mn>0.12</mn></mrow><mrow><mo>+</mo><mn>0.13</mn></mrow></msubsup><mo>±</mo><mn>0.06</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, confirming the measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math> transitions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mi>P</mi></math>–wave states. The ratio for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>2</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn></math> transitions is also measured and found to differ by 3.3 standard deviations from the expected value in the QCD multipole expansion.</p>

Z.S. Stottler

T.K. Pedlar

B.G. Fulsom

I. Adachi

K. Adamczyk

H. Aihara

S. Al Said

D.M. Asner

H. Atmacan

T. Aushev

R. Ayad

V. Babu

Sw. Banerjee

M. Bauer

P. Behera

K. Belous

J. Bennett

F. Bernlochner

M. Bessner

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

G. Bonvicini

J. Borah

A. Bozek

P. Branchini

T.E. Browder

A. Budano

M. Campajola

L. Cao

D. Červenkov

M.C. Chang

B.G. Cheon

K. Chilikin

H.E. Cho

K. Cho

S.K. Choi

Y. Choi

S. Choudhury

D. Cinabro

S. Das

G. De Nardo

G. De Pietro

R. Dhamija

F. Di Capua

Z. Doležal

T.V. Dong

S. Dubey

P. Ecker

D. Epifanov

T. Ferber

D. Ferlewicz

V. Gaur

A. Garmash

A. Giri

P. Goldenzweig

E. Graziani

T. Gu

Y. Guan

K. Gudkova

C. Hadjivasiliou

T. Hara

K. Hayasaka

S. Hazra

M.T. Hedges

D. Herrmann

W.S. Hou

C.L. Hsu

K. Inami

N. Ipsita

A. Ishikawa

R. Itoh

M. Iwasaki

Y. Iwasaki

W.W. Jacobs

S. Jia

Y. Jin

A.B. Kaliyar

T. Kawasaki

C. Kiesling

C.H. Kim

D.Y. Kim

K.H. Kim

Y.K. Kim

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> at Belle