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

We study the penguin-mediated   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mfenced> <mi>s</mi> </mfenced> </mrow> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mfenced> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </mfenced> <mi>ϕ</mi> </math>  $$ {\overline{B}}_{d(s)}\to {\overline{K}}^{\ast 0}\left({K}^{\ast 0}\right)\phi $$  transitions, proposing a new optimised observable L  K*ϕ  from the ratio of longitudinal branching ratios of these decays, with limited hadronic uncertainties and enhanced sensitivity to New Physics. This observable exhibits a deviation at the 1.48 σ level between its experimental value and its SM determination within QCD factorisation. This result can be accommodated together with the significant deviations found for the   <math> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mfenced> <mo>∗</mo> </mfenced> </msup> </math>  $$ {K}^{\left(\ast \right)}{\overline{K}}^{\left(\ast \right)} $$  modes in our earlier works if New Physics affects either the QCD penguin operator Q 4 or the chromomagnetic dipole operator Q 8g  for both b → d and b → s transitions. The allowed range for the Wilson coefficients C 4s,8gs  is narrower compared to C 4d,8gd  since the b → s transition channel   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mi>ϕ</mi> </math>  $$ {\overline{B}}_d\to {\overline{K}}^{\ast 0}\phi $$  is in better agreement with the SM. However, if we add the measured branching ratio for the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <mi>ϕ</mi> </math>  $$ {\overline{B}}_d\to {\overline{K}}^0\phi $$  to our analysis, the simultaneous explanation of all the experimental data for the   <math> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mfenced> <mo>∗</mo> </mfenced> </msup> </math>  $$ {K}^{\left(\ast \right)}{\overline{K}}^{\left(\ast \right)} $$  and the   <math> <msup> <mi>K</mi> <mo>∗</mo> </msup> <mfenced> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mfenced> <mo>∗</mo> </mfenced> </msup> </mfenced> <mi>ϕ</mi> </math>  $$ {K}^{\ast}\left({\overline{K}}^{\left(\ast \right)}\right)\phi $$  channels in terms of New Physics in the Wilson coefficients C 4d,s  or C 8gd,s  only, is not possible. This set of observables can be explained more easily if we assume New Physics in both f = d, s sectors, either in (C 4f  , C 6f  ) or (C 6f  , C 8gf  ). The addition of the branching ratios of the charged modes B − → K (∗)− ϕ to the above mix of observables results in a reduction of the parameter space for the (C 4f  , C 6f  ) scenario, while discarding the (C 6f  , C 8gf  ) scenario completely. This can be traced to the discrepancy of more than 1 σ between the experimental measurements of the branching ratios of the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> <mfenced> <msup> <mi>B</mi> <mo>−</mo> </msup> </mfenced> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <mfenced> <msup> <mi>K</mi> <mo>−</mo> </msup> </mfenced> <mi>ϕ</mi> </math>  $$ {\overline{B}}_d\left({B}^{-}\right)\to {\overline{K}}^0\left({K}^{-}\right)\phi $$  transitions. This should provide a strong incentive for the LHCb/Belle II experiments to measure the branching ratios of   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mn>0</mn> </mrow> </msup> <mi>ϕ</mi> </math>  $$ {\overline{B}}_d\to {\overline{K}}^{\left(\ast \right)0}\phi $$ ,   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mi>ϕ</mi> </math>  $$ {\overline{B}}_s\to {K}^{\ast 0}\phi $$  and particularly B − → K − ϕ to confirm or dismiss the conclusions hinted at by present data.

Spain

Aritra Biswas

Joaquim Matias

Gilberto Tetlalmatzi-Xolocotzi

Optimised observables and new physics prospects in the penguin-mediated decays B  d(s) → K (∗)0 ϕ

A system of dispersive representations of the Omnès–Khuri–Treiman–Sawyer–Wali type for the final-state interactions in the amplitudes of the  $$K\rightarrow \pi \pi \pi $$  <math> <mrow> <mi>K</mi> <mo>→</mo> <mi>π</mi> <mi>π</mi> <mi>π</mi> </mrow> </math>   weak transitions is constructed, under the assumptions that CP and isospin symmetries are conserved. Both the  $$\Delta I = 1/2$$  <math> <mrow> <mi>Δ</mi> <mi>I</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </math>   and  $$\Delta I = 3/2$$  <math> <mrow> <mi>Δ</mi> <mi>I</mi> <mo>=</mo> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </math>   transition channels are considered. The set of single-variable functions involved in these representations is identified, and the polynomial ambiguities in their definitions are discussed. Numerical solutions for the system of coupled integral relations satisfied by these functions are provided, and the determination of the subtraction constants in terms of the experimental information on the amplitudes in the decay region is addressed.

Véronique Bernard

Marc Knecht

Bachir Moussallam

A dispersive study of final-state interactions in  $$K\rightarrow \pi \pi \pi $$  <math> <mrow> <mi>K</mi> <mo>→</mo> <mi>π</mi> <mi>π</mi> <mi>π</mi> </mrow> </math>   amplitudes

We discuss the impact of the recent LHCb update on the two lepton-flavour universality ratios  $$R_K$$  <math> <msub> <mi>R</mi> <mi>K</mi> </msub> </math>   and  $$R_{K^*}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mo>∗</mo> </msup> </msub> </math>  , and the CMS update of  $$B({B_s \rightarrow \mu ^+\mu ^-})$$  <math> <mrow> <mi>B</mi> <mo>(</mo> <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> <mo>)</mo> </mrow> </math>   regarding the possibility of New Physics in  $$b\rightarrow s\ell ^+\ell ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays. We perform global fits of the New Physics Wilson coefficients defined in the model-independent approach of the Weak Effective Theory at the b-quark mass. We discuss three different frameworks for this analysis: (i) an update limited to the experimental data but using the same theoretical framework as in earlier works, (ii) a full update concerning both the experimental inputs and the theoretical framework, (iii) an analysis without the LHCb results on electron modes. The comparison between these various sets of results allows us to identify the differences stemming from the various components of the analysis: new experimental results, new inputs for the hadronic form factors, the role played by LHCb data on electron modes. As expected, the significance of all New Physics hypotheses gets reduced after the LHCb announcements on  $$R_{K^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>   while the hypothesis of a lepton-flavour-universal contribution to the Wilson coefficient of the semileptonic  $$O_{9\ell }$$  <math> <msub> <mi>O</mi> <mrow> <mn>9</mn> <mi>ℓ</mi> </mrow> </msub> </math>   operators (possibly with a very small lepton-flavour-universality violating component) is clearly reinforced. We also discuss the possibility of a long-distance charm-loop contribution through a mode-by-mode analysis and we find that the preferred values for the  $${\mathcal C}_{9\mu }$$  <math> <msub> <mi>C</mi> <mrow> <mn>9</mn> <mi>μ</mi> </mrow> </msub> </math>   Wilson coefficient are consistent throughout the different  $$b\rightarrow s\mu ^+\mu ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   modes and that there is no significant evidence of non-constant  $$q^2$$  <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math>   dependencies, which would indicate the presence of a long-distance charm-loop contribution beyond those already included.

Marcel Algueró

Bernat Capdevila

Martin Novoa-Brunet

To (b)e or not to (b)e: no electrons at LHCb

This article is an addendum to Ref. [1]. We discuss the correlation of <math><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> with the <math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> and <math><mi>B</mi><mo>→</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>s</mi></mrow></msub><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> modes in the model for NP contributions discussed in Ref. [1].Report Number: BARI-TH/22-737

Svjetlana Fajfer

Martín Novoa-Brunet

Addendum to “Implications of → Anomalies for Future Measurements of And ” [Phys. Lett. B 809 (2020) 135769]

We build a set of new observables using closely related non-leptonic penguin-mediated B  d  and B  s  decays:   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mo>,</mo> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <mo>,</mo> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0},{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0,{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$  and   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$  together with their CP conjugate partners. These optimised observables are designed to reduce hadronic uncertainties, mainly coming from form factors and power-suppressed contributions, and thus maximize their sensitivity to New Physics (NP). The deviations observed with respect to the Standard Model (SM) in the ratios of branching ratios of   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mfenced> <mrow> <mn>2.6</mn> <mi>σ</mi> </mrow> </mfenced> </math>  $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0}\left(2.6\sigma \right) $$  and   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <mfenced> <mrow> <mn>2.4</mn> <mi>σ</mi> </mrow> </mfenced> </math>  $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0\left(2.4\sigma \right) $$  can be explained by simple NP scenarios involving the Wilson coefficients   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  4 and   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  6 associated with QCD penguin operators and the coefficient   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  8g  of the chromomagnetic operator. The optimised observables for   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$  and   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$  show distinctive patterns of deviations with respect to their SM predictions under these NP scenarios. The pattern of deviations of individual branching ratios, though affected by significant hadronic uncertainties, suggests that NP is needed both in b → d and b → s transitions. We provide the regions for the Wilson coefficients consistent with both optimised observables and individual branching ratios. The NP scenarios considered to explain the deviations of   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$  and   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> </math>  $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0 $$  can yield deviations up to an order of magnitude among the observables that we introduced for   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$  and   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>→</mo> <msup> <mover> <mi>K</mi> <mo>¯</mo> </mover> <mn>0</mn> </msup> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ . Probing these new observables experimentally by improving the measurements of individual branching ratios of penguin-mediated decays would confirm the consistency of the deviations already observed and provide a highly valuable hint of NP in the non-leptonic sector.

A new puzzle in non-leptonic B decays

We derive a set of light-cone sum rules relating the S-wave B → Kπ hadronic form factors to the B-meson light-cone distribution amplitudes (LCDAs), taking into account the complete set of LCDAs up to and including twist four. These results complement the sum rules for the P-wave B → Kπ form factors obtained earlier. We then use the new sum rules to estimate the S-wave contributions to B → Kπℓℓ decays as a function of the Kπ invariant mass. We pay particular attention to the fact that the S-wave Kπ spectrum cannot be modelled by a sum of Breit-Wigner resonances, and employ a more consistent dispersive coupled-channel approach. We compare our predictions for branching ratios and angular observables with LHCb measurements in two different kinematic regions, around K ∗(892) and   <math> <msubsup> <mi>K</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>1430</mn> </mfenced> </math>  $$ {K}_0^{\ast }(1430) $$ . We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the B → Kπ form factors over a large kinematic range.

Alexander Khodjamirian

Javier Virto

Netherlands

K. Vos

Light-cone sum rules for S-wave B → Kπ form factors

Decays based on the b → sγ transition are expected to yield left-handed photons in the Standard Model, but could be particularly sensitive to New Physics contributions modifying the short-distance Wilson coefficients   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  7 and   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  7′ defined in the low-energy Effective Field Theory. These coefficients can be determined by combining observables of several modes, among which B  s  → ϕee at low q 2, in a kinematic range where the photon-pole is dominant. We investigate the impact of B  s  −   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math>  $$ \overline{B} $$   s  mixing on the angular observables available for this mode, which induces a time-dependent modulation governed by interference terms between mixing and decay that are sensitive to the moduli and phases of   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  7 and   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$  7′. These interference terms can be extracted through a time-dependent analysis but they also affect time-integrated observables. In particular, we show that the asymmetries   <math> <msubsup> <mi>A</mi> <mi>T</mi> <mfenced> <mn>2</mn> </mfenced> </msubsup> </math>  $$ {A}_T^{(2)} $$  and   <math> <msubsup> <mi>A</mi> <mi>T</mi> <mrow> <mfenced> <mo>Im</mo> </mfenced> <mo>;</mo> <mi>CP</mi> </mrow> </msubsup> </math>  $$ {A}_T^{\left(\operatorname{Im}\right); CP} $$  receive terms of potentially similar size from mixing-independent and mixing-induced terms, and we discuss how the constraints coming from the angular analysis of B  s  → ϕee at low q 2 should be interpreted in the presence of mixing.

Ioannis Plakias

Olcyr Sumensari

On the impact of meson mixing on B  s  → ϕee angular observables at low q 2

We consider the time-dependent analysis of rare <math><msub><mi>B</mi><mi>d</mi></msub></math> and <math><msub><mi>B</mi><mi>s</mi></msub></math> decays mediated by <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> transitions. The inclusion of time evolution allows us to construct novel observables with specific sensitivity to <math><mi>C</mi><mi>P</mi></math>-odd phases in these processes. The sensitivity to <math><mi>C</mi><mi>P</mi></math> violation of corresponding time-integrated measurements in the presence of flavor tagging is also explored. We provide precise predictions for these observables in the Standard Model and explore their sensitivity to new <math><mi>C</mi><mi>P</mi></math>-violating new physics contributions at present and planned future <math><mi>B</mi></math>-physics experiments. As such, these observables provide unique probes of <math><mi>C</mi><mi>P</mi></math> violation in <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> transitions.

Probing <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in exclusive <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> transitions

The physics potential of measuring   <math> <msubsup> <mi>B</mi> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </msubsup> </math>  $$ {B}_{(s)}^0 $$  → π 0 π 0 and   <math> <msubsup> <mi>B</mi> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </msubsup> </math>  $$ {B}_{(s)}^0 $$  → ηη decays via four-photon final states at Tera-Z phase of CEPC or FCC-ee is investigated in this paper. We propose an electromagnetic calorimeter (ECAL) with both high energy resolution and excellent separation power to efficiently reconstruct π 0 and η from hadronic final states with high photon multiplicity. The resulting B-meson mass resolution is approximately 30 MeV, allowing 3 σ separation between B 0 and   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$ . With the assistance of the b-jet tagging, the relative sensitivities to B 0 → π 0 π 0,   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → π 0 π 0, B 0 → ηη, and   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → ηη signal strengths at Tera-Z are projected as 0.45%, 4.5%, 18%, and 0.95%, respectively. Their dependence on various detector performances is also discussed. In addition, B 0 → π 0 π 0 and its two isospin-related modes are paid special attention due to their roles in the determination of the CKM angle α (ϕ 2). The anticipated precisions of their branching-ratio and CP-asymmetry measurements at Tera-Z are evaluated. We show that the measurement of the time-integrated B 0 → π 0 π 0 CP asymmetry at Tera-Z is complementary to B-factory ones. The precision on α combining Z- and B-factory results reaches 0.4°, lower than the systematic uncertainties attached to isospin breaking.

Yuexin Wang

Yongfeng Zhu

Prospects for   <math> <msubsup> <mi>B</mi> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </msubsup> </math>  $$ {B}_{(s)}^0 $$  → π 0 π 0 and   <math> <msubsup> <mi>B</mi> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </msubsup> </math>  $$ {B}_{(s)}^0 $$  → ηη modes and corresponding CP asymmetries at Tera-Z