This study investigates the ultraviolet realization of semileptonic four-fermion operator $ O_{ledq}^{\alpha \beta 11} $ that incorporates Majorana dark matter (DM) in both lepton-flavor-conserving (LFC) and lepton-flavor-violating (LFV) scenarios at the one-loop level via box diagram, thereby effectively alleviating the lower bounds on the new physics scale. In addition, we investigate the interplay between model-independent constraints on the Wilson coefficients and DM direct detection, relic density, and collider searches in the context of fermion portal DM model with two mediators. We found that both the projected future constraint on the LFC Wilson coefficient $ C_{ledq}^{2211}/\Lambda^2 \lt $ $ (12.3\; \text{TeV})^{-2} $ from the measurements of neutrino non-standard interaction in the next-generation neutrino oscillation experiments, and the LFV constraint $ C_{ledq}^{1211}/\Lambda^2 \lt \left(2.2\times 10^3\; \text{TeV} \right)^{-2} $ from ongoing charged-lepton-flavor-violation searches, provide a complementary exploration of the parameter space encompassing the DM and scalar masses. With a colored mediator mass of approximately $ 2\; \text{TeV} $ , the sensitivity of the indirect constraints on the four-fermion operator can surpass those of collider searches and DM direct detection, in scenarios where the masses of the DM and scalar are close. By ensuring the correct DM relic density, however, we find that the collider searches and DM direct detection are more sensitive to the electroweak-scale DM and scalar than indirect constraints.

China

Yuxuan He

Gang Li

Jia Liu

Xiao-Ping Wang

Xiang Zhao

Lepton flavor of four-fermion operator and fermion portal dark matter * Gang Li and Xiang Zhao are supported by the National Natural Science Foundation of China (12347105, 12505127), the Guangdong Basic and Applied Basic Research Foundation (2024A1515012668). The work of Jia Liu is supported by the National Science Foundation of China (12235001, 12475103) and State Key Laboratory of Nuclear Physics and Technology (NPT2025ZX11). The work of Xiao-Ping Wang is supported by National Science Foundation of China (12375095) and the Fundamental Research Funds for the Central Universities

The 2HDM+S is the singlet extension of the two-Higgs-doublet model (2HDM). The singlet field and its mixing with the 2HDM Higgs sector lead to new contributions to the electroweak precision observables, in particular, the oblique parameters. In this study, we performed a systematic investigation of the impacts of each mixing angle on the oblique parameters. We adopted the mixing angles and physical Higgs masses as our parameters, which allow a mapping when a specific symmetry structure of the Higgs potential and various theoretical considerations are taken into account. We identified five benchmark cases, where at most one mixing angle was nonzero, and analyzed the 95% C.L. allowed parameter space using the oblique parameters. In the alignment limit of the 2HDM, we find that, other than the usual mass relations of $m_H\sim m_{H^\pm}$ or $m_A\sim m_{H^\pm}$ , electroweak precision measurements also impose an upper limit on the neutral Higgs masses. In the cases with nonzero singlet mixing with the 2HDM Higgses $\textit{H}$ or $\textit{A}$, we find approximate mass relations of $c^2_{\alpha_{HS}} m_{H} + s^2_{\alpha_{HS}}m_{h_S} = m_{H^\pm}$ or $c^2_{\alpha_{AS}} m_{A} + s^2_{\alpha_{AS}}m_{A_S} = m_{H^\pm}$ . These relations are universal to the 2HDM+S models, with or without further symmetry assumption. We also studied the non-alignment limit of the 2HDM+S, which typically has tighter constraints on the masses and mixing angles. Finally, we examined the complementarity between the electroweak precision analyses and the Higgs coupling precision measurements.

Cheng Li

Juxiang Li

Shufang Su

Wei Su

Electroweak precision constraints of the 2HDM+S * Cheng Li, Juxiang Li, and Wei Su are supported by the Natural Science Foundation of China (NSFC) (12305115), Shenzhen Science and Technology Program (202206193000001, 20220816094256002), Guangdong Provincial Key Laboratory of Gamma-Gamma Collider and Its Comprehensive Applications (2024KSYS001), and Guangdong Provincial Key Laboratory of Advanced Particle Detection Technology (2024B1212010005). Juxiang Li is also supported by the Fundamental Research Funds for the Central Universities, and the Sun Yat-sen University Science Foundation. Shufang Su is supported by the Department of Energy (DEFG02-13ER41976/DE-SC0009913)

Within the framework of the next-to-minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $ \tau\rightarrow e M^+ M^- $ decays: $ \tau \rightarrow e \pi^+\pi^- $ , $ \tau \rightarrow e \pi^+K^- $ , and $ \tau \rightarrow e K^+K^- $ . Based on the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensitive parameters and LFV sources are non-diagonal elements corresponding to the initial and final leptons. This work can provide a basis for discovering the existence of new physics (NP).

Rong-Zhi Sun

Shu-Min Zhao

Shuang Di

Portugal

Xing-Xing Dong

Study of ${\boldsymbol\tau\rightarrow {\boldsymbol e M^+ M^-}}$ decays in N-B-LSSM * Supported by National Natural Science Foundation of China (NNSFC) (12075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), the Project of the China Scholarship Council (CSC) (202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit (UIDB/00777/2020, UIDP/00777/2020)

<p>In this paper, we investigate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup><mo stretchy="false">→</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mi>K</mi><mn>0</mn></msup><mo>+</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mi>π</mi><mo>±</mo></msup><msup><mi>e</mi><mo>∓</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup><mo stretchy="false">→</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mi>K</mi><mn>0</mn></msup><mo>+</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>B</mi><mo>±</mo></msup><msup><mi>π</mi><mo>∓</mo></msup><msup><mi>e</mi><mo>±</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> decays; both of them consist of three parts: the indirect <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> mixing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>mix</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>mix</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math>, the direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>dir</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>dir</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math>, and the new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation effects <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>int</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>int</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math>, which originate from the interference between the amplitude of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><msup><mi>B</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup><mo stretchy="false">(</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>B</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>e</mi></msub><mo stretchy="false">)</mo></math> decay with the difference between the oscillating effect of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> and that of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mn>0</mn></msup></math>. The strong phase differences of the direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>dir</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>dir</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math> arise from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> mixing parameters. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math> are of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></math>, respectively. The new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation effect <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>int</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> plays a dominant role in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math>; the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math> is dominated by the indirect <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><mi>mix</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math>, so the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math> provides an ideal place to study the new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation effect. We derive another two asymmetry observables <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>p</mi></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>m</mi></mrow></msubsup></math>, which are dominated by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> mixing. The observables <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>m</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>p</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>p</mi><mi>p</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mi>m</mi><mi>m</mi></mrow></msubsup></math> are hopefully to be marginally observed at the LHC experiment and the HL-LHC experiment.</p>

Xiao-Dong Cheng

Zhen-Lu Weng

Ying-Ying Fan

Ru-Min Wang

Estimating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>B</mi><msup><mi>K</mi><mn>0</mn></msup><mo>+</mo><mi>B</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><mi>B</mi><msup><mi>π</mi><mo>±</mo></msup><msup><mi>e</mi><mo>∓</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> decays

A future $ e^+e^- $ collider could run at the $\textit{Z}$-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from the $\textit{WW}$ and $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

Hao-Qiao Li

Hai-Ning Yan

Jiayin Gu

Germany

Xiao-Ze Tan

Probing $\textit{Z}$/$\textit{W}$ pole physics at high-energy muon colliders via vector-boson-fusion processes * Supported by the National Natural Science Foundation of China (NSFC) (12035008, 12375091, 12347171), and the Innovation Program for Quantum Science and Technology (2024ZD0300101). Xiao-Ze Tan also acknowledges the support from Helmholtz – OCPC (Office of China Postdoctoral Council) Postdoctoral Fellowship Program

In this study, we investigated the neutrino transition magnetic moment in $ U(1)_X $ SSM. $ U(1)_X $ SSM is the $ U(1) $ extension of the Minimal Supersymmetric Standard Model (MSSM), and its local gauge group is extended to $S U(3)_C\times S U(2)_L \times U(1)_Y\times U(1)_X$ . To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to the MSSM, which can explain the results of neutrino oscillation experiments. The neutrino transition magnetic moment is induced by electroweak radiative corrections. By applying the effective Lagrangian method and on-shell scheme, we studied the associated Feynman diagrams and transition magnetic moment of neutrinos in the model. We fit experimental data for neutrino mass variances and mixing angles. Based on the range of data selection, the influences of different sensitive parameters on the results were analyzed. The numerical analysis shows that many parameters, such as $ g_X $ , $ M_2 $ , $ \mu $ , $ \lambda_H $ , and $ g_{YX} $ , have an effect on the neutrino transition magnetic moment. In our numerical results, the order of magnitude of $ \mu_{ij}^M/\mu_B $ is approximately $ 10^{-20} $ $ \sim $ $ 10^{-19} $ .

Long Ruan

Ming-Yue Liu

Xing-Yu Han

Xi Wang

Neutrino transition magnetic moment in $\textit{U}$(1) $\textit{X }$ SSM * Supported by National Natural Science Foundation of China (NNSFC, 12075074), Natural Science Foundation of Hebei Province (A2020201002, A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), Scholarship Council (CSC, 202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit UIDB/00777/2020 and UIDP/00777/2020

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

Motivated by the significant experimental progress in probing semileptonic decays <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> <math><mrow><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>μ</mi><mo>,</mo><mi>e</mi><mo>)</mo></mrow></math>, we analyze the branching ratios of the <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays with the nonresonant, the light scalar meson resonant, and the vector meson resonant contributions in this work. We obtain the hadronic amplitude relations between different decay modes by the SU(3) flavor analysis, and then predict relevant branching ratios of the <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays by the present experimental data with <math><mn>2</mn><mi>σ</mi></math> errors. Most of our predicted branching ratios are consistent with present experimental data within <math><mn>2</mn><mi>σ</mi></math> error bars, and others are consistent with the data within <math><mn>3</mn><mi>σ</mi></math> error bars. We find that the branching ratios of the nonresonant decays <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math>, and <math><mrow><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mspace></mspace><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> are on the order of <math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>)</mo></mrow></math>. The vector meson resonant contributions are dominant in the <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></mrow></math>, and <math><mrow><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mspace></mspace><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> decays. The nonresonant, the vector meson resonant, and the scalar resonant contributions are all important in the <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mi>η</mi><msup><mi>π</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays. The <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> and <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><mi>η</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> decays only receive both the nonresonant and the scalar resonant contributions, and both contributions are important in their branching ratios. According to our predictions, many decay modes could be observed in the experiments like BESIII, LHCb, and Belle II, and some decay modes might be measured in these experiments in the near future.

Yi Qiao

Yi-Jie Zhang

Yuan-Guo Xu

Four-body semileptonic charm decays <math><mi>D</mi><mo>→</mo><msub><mi>P</mi><mn>1</mn></msub><msub><mi>P</mi><mn>2</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> based on SU(3) flavor analysis

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.

Xing-Bo Yuan

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

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog