The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in the phase space in multi-body decays of bottom and charmed mesons. In this study, we examine the CP violation in the decay channel $ {\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0} $ in the phase-space region where the intermediate resonances $ \overline{K}^{*}(892)^{0} $ and $ {\overline{K}^{*}_{0}(700)} $ dominate. In particular, the forward-backward asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are investigated. The nontrivial correlation between FBA and FB-CPA is analyzed. The analysis indicates that FB-CPAs around the resonance $ \overline{K}^{*}(892)^{0} $ can be as large as approximately 35%, which can be potentially accessible by Belle and Belle-II collaborations in the near future.

China

Jian-Yu Yang

Yu-Jie Zhao

Jing-Juan Qi

Zhen-Hua Zhang

The forward-backward asymmetry induced CP asymmetry in ${{\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0}}$ in phase space around the resonances ${{\overline{K}}^{*}(892)^{0}}$ and ${{\overline{K}}^{*}_{0}(700)}$ * Supported by National Natural Science Foundation of China (12475096, 12405115, 12192261) and Scientific Research Fund of Hunan Provincial Education Department (22A0319)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

Given the 3 × 3 Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix <italic>V</italic>, we define a new set of rephasing invariants in terms of the &#8220;trios&#8221; of its nine elements: <math altimg='si1.svg'><mrow><msubsup><mi>&#9674;</mi><mrow><mi>&#945;</mi><mi>&#946;</mi><mi>&#947;</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>k</mi></mrow></msubsup><mo>&#8801;</mo><mrow><mo>(</mo><msub><mi>V</mi><mrow><mi>&#945;</mi><mi>i</mi></mrow></msub><msub><mi>V</mi><mrow><mi>&#946;</mi><mi>j</mi></mrow></msub><msub><mi>V</mi><mrow><mi>&#947;</mi><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><mi>det</mi><mi>V</mi></mrow></math> with <italic>&#945;</italic>&#8239;&#8800;&#8239; <italic>&#946;</italic>&#8239;&#8800;&#8239; <italic>&#947;</italic> and <italic>i</italic>&#8239;&#8800;&#8239; <italic>j</italic>&#8239;&#8800;&#8239; <italic>k</italic> running respectively over ( <italic>u, c, t</italic>) and ( <italic>d, s, b</italic>). We find that <math altimg='si2.svg'><mrow><mrow><mrow><mi mathvariant='normal'>I</mi></mrow><mi>m</mi></mrow><msubsup><mi>&#9674;</mi><mrow><mi>&#945;</mi><mi>&#946;</mi><mi>&#947;</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>k</mi></mrow></msubsup><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi mathvariant='script'>J</mi></mrow></math> holds, where <math altimg='si3.svg'><mi mathvariant='script'>J</mi></math> is the well-known Jarlskog invariant of weak CP violation. Analogous rephasing invariants <math altimg='si4.svg'><mrow><msubsup><mi>&#10731;</mi><mrow><mi>&#945;</mi><mi>&#946;</mi><mi>&#947;</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>k</mi></mrow></msubsup><mo>&#8801;</mo><mrow><mo>(</mo><msub><mi>U</mi><mrow><mi>&#945;</mi><mi>i</mi></mrow></msub><msub><mi>U</mi><mrow><mi>&#946;</mi><mi>j</mi></mrow></msub><msub><mi>U</mi><mrow><mi>&#947;</mi><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><mi>det</mi><mi>U</mi></mrow></math> can be defined for the 3&#8239;&#215;&#8239;3 Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix <italic>U</italic>, where <italic>&#945;</italic>&#8239;&#8800;&#8239; <italic>&#946;</italic>&#8239;&#8800;&#8239; <italic>&#947;</italic> and <italic>i</italic>&#8239;&#8800;&#8239; <italic>j</italic>&#8239;&#8800;&#8239; <italic>k</italic> run respectively over ( <italic>e, &#956;, &#964;</italic>) and (1, 2, 3). Taking into account small non-unitarity of <italic>U</italic> based on the canonical seesaw mechanism for neutrino mass generation, we calculate <math altimg='si5.svg'><mrow><mrow><mrow><mi mathvariant='normal'>I</mi></mrow><mi>m</mi></mrow><msubsup><mi>&#10731;</mi><mrow><mi>&#945;</mi><mi>&#946;</mi><mi>&#947;</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>k</mi></mrow></msubsup></mrow></math> with the help of a full Euler-like block parametrization of the seesaw flavor structure and demonstrate that their leading terms converge to a universal invariant <math altimg='si6.svg'><msub><mi mathvariant='script'>J</mi><mi>&#957;</mi></msub></math> in the unitarity limit of <italic>U</italic>.

Shu Luo

Zhi-zhong Xing

New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements

Several proposed future lepton colliders are capable of producing trillions of Z-bosons, including FCC-ee, CEPC, LEP3 and LEP-Z. Such Tera-Z factories can discover new elementary particles with couplings to the Z-boson that are orders of magnitude smaller than current bounds. For couplings near the currently excluded parameter regions they could produce sufficiently large samples to study the new particles’ properties in detail, thereby serving as both a discovery and precision machine in one. Using simple analytic estimates, we quantify the dependence of the expected event yield in long-lived particle searches on the number of produced Z-bosons and on the detector dimensions. From this, we derive estimates for both the discovery reach and the measurement precision attainable at such facilities. While the precision of such estimates of course falls short of proper simulations, the analytic approach is suitable for a quick assessment of the sensitivity for a given design. We illustrate this with two examples, heavy neutral leptons and axion-like particles. Under optimistic assumptions, these could be produced in the millions and billions, respectively, effectively turning future lepton colliders into exotics factories.

Belgium

Germany

Marco Drewes

Croatia

Juraj Klarić

Yuan-Zhen Li

New particles at the Z-pole:

<p>We discuss physics-informed renormalization group flows (PIRGs) for general operators. We show that operator PIRGs provide comprehensive access to all correlation functions of the quantum field theory under investigation. The operator PIRGs can be seen as a completion of the PIRG approach, whose qualitative computational simplification and structural insights are now fully accessible for general applications. The potential of this setup is assessed within a simple analytic example of the zero-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ϕ</mi><mn>4</mn></msup></math>-theory, for which the generating functions of the fundamental field are computed within a vertex expansion, using the one- to ten-point functions.</p>

Friederike Ihssen

Jan M. Pawlowski

Physics-informed operator flows and observables

Italy

Stefano Noi

Ramona Gröber

Manoj Mandal

Erratum: Two-loop running effects in Higgs physics in Standard Model Effective Field Theory

The notion of time in general relativity must arise from an internal clock, i.e., a degree of freedom in the gravitational theory internal to the system that can serve the role of a physical clock. One such internal notion of time is the York time, corresponding to constant extrinsic curvature slicing of spacetime. We study the Hartle-Hawking wavefunction of asymptotically $\textit{AdS}$ JT gravity as a function of York time. Using both canonical quantization and the JT gravity path integral, we explicitly calculate this wavefunction and show that it satisfies a Schrodinger equation with respect to York time. We find the corresponding York Hamiltonian, which turns out to be manifestly Hermitian. Our analysis cleanly avoids operator ordering ambiguities. The dependence of the wavefunction on York time should be thought of as emerging from a unitary basis transformation of the gravitational length basis states used to compute the wavefunction, and not from time evolution of the state in the dual boundary theory.

India

Onkar Parrikar

Japan

Sunil Sake

York time in JT gravity

Recently, a theoretical framework was set up in Miramontes et al. (Eur Phys J C 85:1055, 2025), which allows for the symmetry-preserving inclusion of full quark-gluon vertices in the description of the meson dynamics. In the present work, we develop a special truncation within this approach, which leads to a tractable set of functional equations that satisfy the fundamental chiral Ward-Takahashi identities. Specifically, in the chiral limit that we consider, this truncation allows us to simplify considerably the quark-gluon Schwinger–Dyson equation, without significant loss of quantitative accuracy. Importantly, this implies a substantial reduction of complexity of the renormalized Bethe–Salpeter equation: it is composed by a pair of one-loop diagrams that contain the full quark-gluon vertex, and a single two-loop diagram that is instrumental for the masslessness of the pion in the chiral limit. A detailed numerical analysis reveals that the incorporation of the aforementioned two-loop diagram is instrumental for the corresponding eigenvalue to reach unity. The key relation between the quark mass function and the pion wave function is shown to be satisfied to within the numerical precision of the loop integrals, which is at the level of about one percent or better. The field-theoretic ingredients required for the extension of this analysis beyond the chiral limit are briefly discussed.

M. Ferreira

Spain

A. Miramontes

J. Morgado

J. Papavassiliou

J. Pawlowski

Pion physics with dressed quark-gluon vertices

In this study, we investigate the possibility of enhancing the di-jet resonance searches by tagging the final state radiation (FSR) jet using an event-level deep neural network. It is found that solely relying on the 4-momenta of the leading three jets allows the algorithm to achieve good discriminating power that can identify the hardest FSR jet in the signal while rejecting other soft jets. Once the invariant mass is corrected with the tagged FSR jet, the mass resolution of the signal is greatly enhanced, and the sensitivity of the search is also improved by more than 10%. By crafting the input variables carefully, the algorithm introduces minimal mass sculpting for the background, and its applicability extends to a broad mass range. This work proves that FSR jet tagging can potentially enhance di-jet resonance searches, suiting various stages of the physics programmes at the Large Hadron Collider (LHC) and High-Luminosity LHC (HL-LHC).

Bingxuan Liu

Yuxuan Shen

Yuanshunzi Sui

Enhancing di-jet resonance searches via a final-state radiation jet tagging algorithm * Bingxuan Liu is supported by Shenzhen Campus of the Sun Yat-sen University under project 74140-12255011, and by the Young Scientists Fund (C Class) of the National Natural Science Foundation of China (12405122). Both Yuxuan Shen and Yuanshunzi Sui are supported by College Students’ Innovative Entrepreneurial Training Plan Program

We investigate the collider signatures of a maximally flavor-violating $ U(1)_{L_\mu-L_\tau} $ model, where a new gauge boson $ Z^\prime $ and scalar triplets induce lepton flavor-changing interactions in the $\textit{μ}$-$\textit{τ}$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $ m_{Z^\prime} $ and the effective parameters $ \tilde{g}/m_{Z^\prime} $ , whereas it remains largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $ m_{Z^\prime} $ , and beam polarization can significantly suppress the Standard Model backgrounds while enhancing new physics contributions. We find that, in the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results show that multi-lepton final states are powerful probes of the $ U(1)_{L\mu - L_\tau} $ framework and can offer valuable guidance for future searches at muon and electron-positron colliders.

Jianing Qin

Fei Huang

Honglei Li

Zhi-Long Han

Jin Sun

Collider probes of four-lepton final states in maximally flavor-violating ${U(1)_{L_\mu-L_\tau}} $ model * Supported by National Natural Science Foundation of China (12505112, 11805081), Shandong Province Natural Science Foundation (ZR2024QA138, ZR2022MA056) and State Key Laboratory of Dark Matter Physics, University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC- 202404) and Jin Sun is supported by IBS under the project code, (IBS-R018-D1)