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.

China

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

Collinear emission of $\textit{W}$ bosons off a high-energy muon induces a large muon-neutrino component among the Parton Distribution Functions (PDFs) of a muon. In this paper we study the phenomenology related to the $\textit{ν}$ PDF at future high-energy muon colliders. We examine total rates and differential distributions of the $$ e{\overline{\nu}}_e $$ and $\textit{Wγ}$ production processes, which receive a large, and often dominant, contribution from this PDF, allowing for a detailed experimental study. As a demonstration of the impact the $\textit{ν}$ PDF could have for searches of new physics, we study the charged-current pair production of a couple of heavy states, components of a SU(2) doublet. In both $$ e{\overline{\nu}}_e $$ production and charged-current pair production of heavy states, we compare results obtained using PDFs with those of a fixed-order simulation.

Rodolfo Capdevilla

Francesco Garosi

Austria

Bernd Stechauner

Testing the neutrino content of the muon at muon colliders

We study the role of the / -interference parton distribution function (PDF) in high-energy muon colliders. We review how this PDF emerges when electroweak interactions are applied to the collinear splitting process and show that the leading-order approximation is significantly suppressed due to an accidental cancellation. However, this suppression does not appear in the leading-logarithm resummed numerical result, where the / PDF is instead comparable to those of other electroweak gauge bosons. By extending the analytical approximation to next-to-leading order, we show the mechanism by which the suppression is lifted and provide a more accurate approximation to the numerical result. Furthermore, we explore the impact of the / PDF in several processes at future muon colliders. High-energy Compton scattering is identified as a promising process for observing experimentally this peculiar electroweak effect with high precision. We also quantify the impact of the / PDF on Higgs physics and, as a new physics example, in resonant single-production of axion-like particles (ALP).

Alfredo Stanzione

On the impact of the mixed Z/

We study the implications of the observed excess in  $$B^+ \rightarrow K^+ \nu \bar{\nu }$$  <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   under the assumption of Rank-One Flavour Violation, i.e. that New Physics couples to a single specific direction in flavour space. By varying this direction we perform analyses at the level of the low-energy EFT, the SMEFT, and with explicit mediators such as leptoquarks and colorless vectors ( $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   and  $$V^\prime $$  <math> <msup> <mi>V</mi> <mo>′</mo> </msup> </math>  ). We study correlations with other flavour, electroweak and collider observables, finding that the most interesting ones are with  $$K \rightarrow \pi \nu \bar{\nu }$$  <math> <mrow> <mi>K</mi> <mo>→</mo> <mi>π</mi> <mi>ν</mi> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>  ,  $$B_s \rightarrow \mu ^+ \mu ^-$$  <math> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>  , meson mixing and the LHC searches in  $$\tau ^+ \tau ^-$$  <math> <mrow> <msup> <mi>τ</mi> <mo>+</mo> </msup> <msup> <mi>τ</mi> <mo>-</mo> </msup> </mrow> </math>   high-energy tails. Among the various mediators, the scalar leptoquarks  $$\tilde{R}_2$$  <math> <msub> <mover> <mi>R</mi> <mo>~</mo> </mover> <mn>2</mn> </msub> </math>   and  $$S_1$$  <math> <msub> <mi>S</mi> <mn>1</mn> </msub> </math>   offer the best fits of the Belle-II excess, while being consistent with the other bounds. On the other hand, colorless vectors are strongly constrained by meson mixing and resonance searches in  $$p p \rightarrow \tau ^+ \tau ^-$$  <math> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <msup> <mi>τ</mi> <mo>+</mo> </msup> <msup> <mi>τ</mi> <mo>-</mo> </msup> </mrow> </math>  . In all cases we find that a flavour alignment close to the third generation is generically preferred.

Marco Nardecchia

Claudio Toni

Implications of  $$B \rightarrow K \nu {\bar{\nu }}$$  <math> <mrow> <mi>B</mi> <mo>→</mo> <mi>K</mi> <mi>ν</mi> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   under rank-one flavor violation hypothesis

We project the reach of future lepton colliders for measuring CKM elements from direct observations of $\textit{W}$ decays. We focus our attention to |$\textit{V}$ | and |$\textit{V}$ | determinations, using FCC-ee as case study. We employ state-of-the-art jet flavor taggers to obtain the projected sensitivity, and scan over tagger performances to show their effect. We conclude that future lepton collider can sizeably improve the sensitivity on |$\textit{V}$ | and |$\textit{V}$ |, albeit the achievable reach will strongly depend on the level of systematic uncertainties on tagger parameters.

Manuel Szewc

Direct CKM determination from W decays at future lepton colliders

Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Japan

Okuto Morikawa

Soma Onoda

Hiroshi Suzuki

Yet Another Lattice Formulation of 2D (1) Chiral Gauge Theory via Bosonization David Tong: lectures on gauge theory