In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

China

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

In this paper, we construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch–Xing (FX) parametrization, which is obtained by trivializing arguments of the matrix elements in the third row and third column. We further analyze rephasing invariant structure of the FX phase <italic>&#948;</italic> <inf>FX</inf> under an approximation <math altimg='si1.svg'><mrow><msubsup><mi>U</mi><mrow><mn>13</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, where the 1&#8211;3 element of the diagonalization matrix of charged leptons <italic>Ue</italic> is neglected. With an additional approximation <math altimg='si2.svg'><mrow><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase <math altimg='si3.svg'><msubsup><mi>&#948;</mi><mrow><mrow><mi mathvariant='normal'>F</mi></mrow><mi>X</mi></mrow><mi>&#957;</mi></msubsup></math> and the contribution from the relative phase <math altimg='si4.svg'><mrow><msubsup><mi>&#961;</mi><mn>1</mn><mo>&#8242;</mo></msubsup><mo linebreak='goodbreak'>&#8722;</mo><msubsup><mi>&#961;</mi><mn>2</mn><mo>&#8242;</mo></msubsup></mrow></math> between the lighter 1-2 generations. The phase <italic>&#948;</italic> <inf>FX</inf> for finite <math altimg='si5.svg'><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup></math> is understood as a generalization of the compact expression. This result covers almost all perturbative calculations of CP phases for the CKM and MNS matrices with hierarchical charged fermions.

Japan

Masaki J.S. Yang

Rephasing invariant structure of CP phase in Fritzsch–Xing parametrization for simplified mixing matrices

Motivated by the first LHCb searches for the rare $$ {\overline{B}}_{s,d}^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $\textit{J}$/$\textit{ψ}$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $\textit{B}$-meson LCDA, the maximum branching ratios of $$ {\overline{B}}_s^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ and $$ {\overline{B}}_d^0 $$ → $\textit{J}$/$\textit{ψμ}$ $\textit{μ}$ , integrated over the dimuon invariant mass squared $\textit{q}$ from 1 GeV to ( $$ {m}_{B_{s,d}} $$ − $\textit{m}$ ) , can reach up to 2.21 × 10 and 7.69 × 10 at the leading order in $\textit{α}$ , respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $$ \mathcal{B}{\left.\left({\overline{B}}_s^0\to J/\psi {\mu}^{+}{\mu}^{-}\right)\right|}_{q^2\ge 1{\textrm{GeV}}^2} $$ = 2.88 × 10 and $$ \mathcal{B}{\left.\left({\overline{B}}_d^0\to J/\psi {\mu}^{+}{\mu}^{-}\right)\right|}_{q^2\ge 1{\textrm{GeV}}^2} $$ = 1.07 × 10 . In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $\textit{J}$/$\textit{ψ}$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.

Xin-Qiang Li

Yan Shi

Ya-Dong Yang

Xing-Bo Yuan

Chun-Yang Zhao

$$ {\overline{B}}_{s,d}^0 $$ → $\textit{J}$/$\textit{ψμ}$ + $\textit{μ}$ − decays in QCD factorization

This paper presents a systematic study of hyperon non-leptonic two-body decays induced by light quark transitions, particularly the $ s \rightarrow u\bar{u}d $ process, within the framework of $\textit{SU}$(3) flavor symmetry. The effective weak Hamiltonian is decomposed into irreducible $\textit{SU}$(3) representations, including the 27-plet and octet components, and applied to analyze decays of octet and decuplet baryons and charmed baryons. Both the irreducible representation amplitude (IRA) approach and the topological diagrammatic analysis (TDA) are employed to construct decay amplitudes and constrain the parameter space. $\textit{SU}$(3) symmetry-breaking effects arising from the strange quark mass are incorporated systematically. A global fit to current experimental data allows us to extract form factors and predict branching ratios and asymmetry parameters for several decay channels. Our results demonstrate the predictive power of $\textit{SU}$(3) flavor symmetry while highlighting significant symmetry-breaking effects, especially in amplitudes related to the 27-plet. Notably, the $ \Sigma^+ \rightarrow p\pi^0 $ decay channel exhibits a deviation exceeding $ 1\sigma $ from experimental measurements, suggesting the possible presence of new decay mechanisms or contributions beyond the Standard Model. Besides, we also evaluate the size of symmetry breaking. However, the large uncertainty of the experimental data makes it difficult to precisely determine the value of symmetry breaking. We strongly recommend that future experimental efforts aim to reduce the measurement uncertainties, especially for the processes $ \Lambda^0\to p\pi^- $ and $ \Lambda^0\to n\pi^0 $ , which have larger experimental errors compared to other data and play an important role in determining the symmetry breaking parameter. This study provides a systematic framework for future tests of the Standard Model and the search for new physics in hyperon decays.

Xin Wu

Qi Chen

Ye Xing

Zhi-Peng Xing

Ruilin Zhu

$\textit{SU}$(3) flavor symmetry analysis of hyperon non-leptonic two body decays * Ruilin Zhu is supported by NSFC (12322503, 12075124) and the Natural Science Foundation of Jiangsu (BK20211267). Zhi-Peng Xing is supported by NSFC (12375088, 12335003, 12405113). Ye Xing is supported by NSFC (12005294)

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

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

Scalar singlets under the Standard Model gauge group appear naturally in many well-motivated New Physics scenarios, such as the composite Higgs models. Unlike the Higgs boson in the Standard Model, they can induce large flavour-changing neutral currents (FCNCs) in the top sector. We investigate systematically the effects of a light scalar singlet $\textit{S}$ with top-quark FCNC couplings, by including the low-energy constraints from the $\textit{B}$ → $\textit{μ}$ decay, the muon anomalous magnetic moment ($\textit{g}$ − 2) and the neutron Electric Dipole Moment (EDM). We also perform a detailed Monte-Carlo simulation of the channel $\textit{pp}$ → $\textit{tS}$ + $\textit{j}$ with $\textit{S}$ → $\textit{μ}$ and $\textit{S}$ → $$ b\overline{b} $$ , and investigate the LHC sensitivity to the $\textit{tcS}$ couplings. It is found that the scalar singlet $\textit{S}$ can induce scalar-type contributions to the $\textit{B}$ $\textit{→ μ}$ decay, which do not suffer from the helicity suppression and contain a large CKM factor $$ {V}_{cs}^{\ast }{V}_{tb} $$ . As a result, constraints on the $\textit{tcS}$ couplings from the measured branching ratio $$ \mathcal{B} $$ ($\textit{B}$ → $\textit{μ}$ ) are quite stringent, being even stronger than the expected LHC sensitivity in some parameter spaces. Besides the CP-conserving $\textit{tcS}$ couplings, we have also considered the case of CP-violating $\textit{tcS}$ couplings, with $$ {y}_{R,L}^{ct}=\left|{y}_{R,L}^{ct}\right|{e}^{i{\theta}_{R,L}} $$ . It is found that the CP observables $$ {\mathcal{A}}_{\Delta {\varGamma}_s}^{\mu \mu} $$ and $$ {\mathcal{S}}_{\mu \mu} $$ of the $\textit{B}$ $\textit{→ μ}$ decay are sensitive to the phase $\textit{θ}$ , while the neutron EDM can provide bounds on the phase difference $\textit{θ}$ − $\textit{θ}$ . Therefore, they are complementary to each other in probing the CP phases of the $\textit{tcS}$ couplings.

Biao-Feng Hou

Ming-Wang Zhang

Phenomenological anatomy of top-quark FCNCs induced by a light scalar singlet

Motivated by the latest CDF W-mass measurement as well as the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly and the discrepancies observed in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions, we propose an extension of the Standard Model (SM) with the <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math>-singlet vector-like fermion partners that are featured by additional <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> gauge symmetry. The fermion partners have the same SM quantum numbers as of the right-handed SM fermions, and can therefore mix with the latter after the electroweak and the <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> symmetry breaking. As a result, desirable loop-level corrections to the <math><msub><mrow><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>μ</mi></mrow></msub></math>, the W-boson mass <math><msub><mrow><mi>m</mi></mrow><mrow><mi>W</mi></mrow></msub></math> and the Wilson coefficient <math><msub><mrow><mi>C</mi></mrow><mrow><mn>9</mn></mrow></msub></math> in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions can be obtained. The final allowed parameter space is also consistent with the constraints from the <math><mi>Z</mi><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay, the neutrino trident production and the LHC direct searches for the vector-like quarks and leptons.

Ze-Jun Xie

Correlating the CDF -mass Shift With the Muon − 2 and the → Transitions

Recently, the Belle II collaboration announced the first measurement of the branching ratio <math> <mi>B</mi> <mfenced> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </mfenced> </math> $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level <math> <mi>b</mi> <mo>→</mo> <mi>sν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math> $$ b\to s\nu \overline{\nu} $$ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio <math> <mi>B</mi> <mfenced> <mrow> <msup> <mi>B</mi> <mn>0</mn> </msup> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </mfenced> </math> $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B 0 → K *0 + inv and B s → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B + → π + + inv and K + → π + + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q 2 distributions of the B → K (*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator <math> <msub> <mi>Q</mi> <mi>qχ</mi> </msub> <mo>=</mo> <mfenced> <mrow> <msub> <mover> <mi>q</mi> <mo>¯</mo> </mover> <mi>p</mi> </msub> <msub> <mi>γ</mi> <mi>μ</mi> </msub> <msub> <mi>q</mi> <mi>r</mi> </msub> </mrow> </mfenced> <mfenced> <mrow> <mover> <mi>χ</mi> <mo>¯</mo> </mover> <msup> <mi>γ</mi> <mi>μ</mi> </msup> <mi>χ</mi> </mrow> </mfenced> </math> $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ with a fermionic dark matter mass m χ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q 2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction F L of K * in the B → K * + inv decays within the DLEFT. By combining the decay spectra and F L , almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes.

Meng Shen

Deciphering the Belle II data on <math> <mi>B</mi> <mo>→</mo> <mi>Kν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math> $$ B\to K\nu \overline{\nu} $$ decay in the (dark) SMEFT with minimal flavour violation

The recently updated measurement of the W-boson mass by the CDF collaboration exhibits a 7σ deviation from the SM expectation, which may imply a sign of new physics beyond the SM. The observed discrepancy could be explained by new fermions that carry the electroweak gauge charges and affect the vacuum polarization of gauge bosons. Notably, if the new fermions also have the same quantum numbers as of the SM quarks, they can mix with the latter and thus modify the penguin diagrams governing the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions. Therefore, the W-boson mass shift could be related to the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> anomalies observed by the LHCb collaboration during the past few years. To investigate this possibility, we consider in this letter a model containing a vector-like top partner gauged under a new <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> symmetry. It is found that the latest CDF <math><msub><mrow><mi>m</mi></mrow><mrow><mi>W</mi></mrow></msub></math> measurement and the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> anomalies can be simultaneously accommodated at 2σ level.

Correlating the CDF -boson Mass Shift With the → Anomalies

Within the Standard Model, we investigate the <math><mi>C</mi><mi>P</mi></math> violations and the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays basing on the factorization-assisted topological-amplitude (FAT) approach and the topological amplitude (TA) approach of Cheng and Chiang [Phys. Rev. D 104, 073003 (2021).]. We find that the <math><mi>C</mi><mi>P</mi></math> violations in these decays <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math> can exceed the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> in the two approaches and consist of three parts: the indirect <math><mi>C</mi><mi>P</mi></math> violations in <math><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> mixing <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>mix</mi></mrow></msubsup></math>, the direct <math><mi>C</mi><mi>P</mi></math> violations in charm decays <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>dir</mi></mrow></msubsup></math>, and the new <math><mi>C</mi><mi>P</mi></math> violation effects <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>int</mi></mrow></msubsup></math>, which are induced from the interference between two tree (Cabibbo-favored and doubly Cabibbo-suppressed) amplitudes with the neutral kaon mixing. The indirect <math><mi>C</mi><mi>P</mi></math> violations in <math><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> mixing play a dominant role in <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math>; the new <math><mi>C</mi><mi>P</mi></math> violation effects have a non-negligible contribution to <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math>. We estimate the numerical results of the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries <math><msubsup><mi>R</mi><mrow><msub><mi>K</mi><mi>S</mi></msub><mo>−</mo><msub><mi>K</mi><mi>L</mi></msub></mrow><msup><mi>D</mi><mo>±</mo></msup></msubsup></math> and find that there exists a large difference between the numerical results in the FAT approach and that of the TA approach. We present the numbers of <math><msup><mi>D</mi><mo>±</mo></msup></math> events-times-efficiency needed to observe the <math><mi>C</mi><mi>P</mi></math> violations and the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries at the level of 3 standard deviations (<math><mrow><mn>3</mn><mi>σ</mi></mrow></math>). We also find that if one adopts the values of the decay time parameters <math><msub><mi>t</mi><mn>0</mn></msub><mo>=</mo><mn>3.0</mn><msub><mi>τ</mi><mi>S</mi></msub></math> and <math><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>10.0</mn><msub><mi>τ</mi><mi>S</mi></msub></math>, the new <math><mi>C</mi><mi>P</mi></math> violation effect <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></mrow><mrow><mi>int</mi></mrow></msubsup></math> would dominate the <math><mi>C</mi><mi>P</mi></math> violation in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays and could be observed with <math><mn>6.7</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> and <math><mn>6.5</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> <math><msup><mi>D</mi><mo>±</mo></msup></math> events-times-efficiency in the FAT approach and the TA approach, respectively. Our results could be tested by the LHCb (Large Hadron Collider beauty), Belle II, and BESIII experiments.

Ru-Min Wang

Xiao-Dong Cheng

Study of <math><mi>C</mi><mi>P</mi></math> violation in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays