We investigate the direct $\rm CP $ violation in the decay $ D^\pm \to \pi^\pm \pi^+ \pi^- $ incorporating the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism. The integrated mixing intensities $ \overline \xi_{fa} $ and $ \overline \xi_{af} $ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $ \pi^+\pi^- $ pair lies near the $ f_0(980) $ resonance, this isospin-breaking mechanism can enhance the $\rm CP $ asymmetry. The enhancement is particularly pronounced when the $ f_0(980) $ carries a significant $ n\bar{n} $ quark component and the $ f_0(980) $ and $ \sigma(600) $ mixing angle is approximately $ 26^\circ $ . After accounting for non-factorizable effects, we find these corrections tend to partially cancel the leading-order contributions, resulting in a suppression of the $\rm CP $ violations relative to the naive factorization predictions. It is emphasized that the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism should be taken into account in both theoretical and experimental studies of $\rm CP $ violation in $\textit{B}$ or $\textit{D}$ meson decays.

China

Shi-Ji Cao

Jing-Juan Qi

Yi-Fan Zhao

Chao Wang

Zhen-Yang Wang

Xin-Heng Guo

Direct CP violation in ${ {\boldsymbol D}^{\bf\pm }\to {\boldsymbol\pi}^{\bf\pm} {\boldsymbol\pi}^{\bf +} {\boldsymbol\pi}^{\bf -}} $ with ${{\boldsymbol a}_{\bf 0}^{\bf 0}{\bf (980)-}{\boldsymbol f}_{\bf 0}{\bf (980)}} $ mixing * Supported by the National Natural Science Foundation of China (12405115, 12105149, 11805153, 12275024), and the High-Level Scientific Research Fund of Ningbo University (GJPY2026032)

Hadron-hadron interactions, being nonperturbative in nature, play a significant role in addressing phenomenological questions in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are typically expressed as a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about the interactions. However, source functions remain poorly constrained and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an 'inverse problem.' To address this, we propose a toy model based on Tikhonov regularization. Using a square-well potential with four distinct strengths, we calculate the CFs for inputs of single Gaussian source functions and mixed Gaussian source functions. The resulting CFs are then used to reconstruct the source functions via Tikhonov regularization. Our results show that the Gaussian source function can be successfully reconstructed, highlighting the potential of this approach for extracting realistic source functions from hadron pairs of interest.

Ao-Sheng Xiong

Qi-Wei Yuan

Ming-Zhu Liu

Fu-Sheng Yu

Zhi-Wei Liu

Li-Sheng Geng

Solving the inverse source problem in femtoscopy with a toy model * Supported in part by the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (JYB2025XDXM204) and the National Natural Science Foundation of China (W2543006, 12435007). Ming-Zhu Liu acknowledges support from the National Natural Science Foundation of China (12575086). Zhi-Wei Liu acknowledges support from the National Natural Science Foundation of China (12405133) and from the Shenzhen Science and Technology Program (ZDSYS20230626091501002). Fu-Sheng Yu and Ao-Sheng Xiong acknowledge support from the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-P2) and from the Fundamental Research Funds for the Central Universities (lzujbky-2023-stlt01, lzujbky-2024-oy02, lzujbky-2025-eyt01)

We have performed hyperfine spectroscopy of two transitions in ground-state deuterium and searched for violations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi><mi>T</mi></mrow></math> and Lorentz symmetry that would manifest as sidereal variations of the observed transition frequencies. Several nonrelativistic proton coefficients of the Standard-Model extension framework have been addressed. The spin-independent coefficients with momentum power <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>=</mo><mn>2</mn></math>, 4 are constrained for the first time. Bounds on spin-dependent coefficients are improved by exploiting a sensitivity enhancement originating from the relative momenta of the nucleons in the deuteron. The best previous constraints by hydrogen maser measurements are surpassed by 4 and 14 orders of magnitude for coefficients with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>=</mo><mn>2</mn></math> and 4, respectively.

Austria

A. Nanda

France

D. Comparat

O. Dulieu

S. Lahs

Canada

C. Malbrunot

L. Nowak

M.C. Simon

E. Widmann

Demonstration of Deuterium’s Enhanced Sensitivity to Symmetry Violations Governed by the Standard-Model Extension

Building upon our recent extension of the Gibbons–Werner (GW) method to bound massive particle orbits in static spherically symmetric (SSS) spacetimes [Huang $$et\ al.$$ , ], the present work further generalizes the framework to stationary axisymmetric (SAS) spacetimes. Although the general off-equatorial motion of massive particles in SAS spacetimes remains highly intricate, the equatorial case is of significant astrophysical importance and allows for a tractable analysis. Applying the GW method to equatorial bound orbits in SAS spacetimes presents two main challenges. The first arises from the orbital feature: the azimuthal self-intersecting of bound orbits, which we resolve through orbit segmentation, following the approach used in SSS spacetimes. The second stems from the Jacobi–Maupertuis Randers–Finsler (JMRF) metric: the loss of positive definiteness at large distances and the presence of the one-form (absent in the SSS case), which we address using our generalized GW method for SAS spacetimes [Huang $$et\ al.$$ , ]. As an explicit demonstration, we carry out the calculation in Kerr spacetime and obtain the deflection angle between two arbitrary points along the bound orbit of equatorial massive particles.

Yang Huang

Xiangyun Fu

Zhenyan Lu

Xin Qin

Xuan Zhou

Lei Hui

Extending Gibbons–Werner method to equatorial bound massive particles in stationary axisymmetric spacetimes

We investigate the charge-charge correlation (QQC) in electron-positron annihilation as a probe of charge dynamics in quantum chromodynamics. While generally divergent beyond leading order, we show that the QQC is infrared and collinear safe in the back-to-back limit, a property that we dub leading-power safety. This enables an analytic perturbative treatment that bypasses the reliance on nonperturbative track or fragmentation functions. Using soft-collinear effective field theory, we derive a factorization theorem and determine its logarithmic behavior analytically up to four loops in QCD, uncovering remarkable connections with the energy-energy correlation (EEC). Prior to this Letter, the behavior of the QQC beyond leading order was entirely unknown; we now establish its resummation to next-to-next-to-next-to-next-to-leading logarithmic (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LL</mi></mrow></math>) accuracy, placing it among the observables with the highest perturbative precision alongside the EEC. Our results are validated through a numerical analysis using event2, exhibiting excellent agreement with the predicted singular terms. This Letter establishes the QQC as a novel, calculable probe of charge dynamics and unveils a new window into the inner workings of non-Abelian gauge theories.

CERN

Pier Francesco Monni

Gherardo Vita

Zhen Xu

Hua Xing Zhu

Edge of Safety: Charge-Charge Correlation in the Back-to-Back Limit

The three-body decays of charmonium states provide a valuable laboratory for probing non-perturbative QCD dynamics and investigating light meson resonances. Three-body decays <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> are studied in this work ( <italic>P</italic> denotes the light pseudoscalar meson). Branching ratio analysis is performed for the <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> decays incorporating light vector ( <italic>V</italic>) meson resonance, light tensor ( <italic>T</italic>) meson resonance and light scalar ( <italic>S</italic>) meson resonance contributions. Based on the SU(3) flavor symmetry approach, we calculate the branching ratios under both the narrow width approximation and the finite width effect, and provide the predict results in the <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239;( <italic>V</italic>/ <italic>T</italic>) <italic>P</italic> <inf>3</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> processes. Furthermore, based on the significant <math altimg='si401.svg'><mrow><msubsup><mi>a</mi><mn>0</mn><mo>+</mo></msubsup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow></mrow></math> resonance signal in <math altimg='si136.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mi>&#951;</mi></mrow></math> decay, the predict results for <italic>&#967;</italic> <inf><italic>c</italic>1</inf>&#8239;&#8594;&#8239; <italic>SP</italic> <inf>3</inf>&#8239;&#8594;&#8239; <italic>P</italic> <inf>1</inf> <italic>P</italic> <inf>2</inf> <italic>P</italic> <inf>3</inf> are also obtained. While the resonance signals observed in current experiments are mainly concentrated in the <math altimg='si136.svg'><mrow><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>&#8594;</mo><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mi>&#951;</mi></mrow></math> decay, our results suggest potential resonance contributions in other channels. Especially in <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf>&#8239;&#8594;&#8239; <italic>KK&#960;</italic> channels, the predicted results show the significant resonance contributions from <italic>V</italic> mesons and <italic>T</italic> mesons, which is worth further experimental verification and exploration.

Bo Lan

Jie Zhu

Jin-Huan Sheng

Yuan-Guo Xu

Ru-Min Wang

Study of <italic>&#967;</italic> <inf><italic>c</italic>1,2</inf> decays to <italic>PPP</italic> via light meson resonances

We propose a nonlocal realization of the Stueckelberg portal between the Standard Model and dark sector, which decouple in the local limit. This implies that the mediator, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> dark photon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>A</mi><mo>′</mo></msup></math> with a Stueckelberg mass, interacts nonlocally with the Standard Model quarks and leptons. We study phenomenological implications of this scenario for the meson decays into semi-invisible and invisible channels. We discuss the experimental limitations on the model parameters, including the nonlocality scale.

Chile

Sergey Kovalenko

Sergey Kuleshov

Germany

Valery E. Lyubovitskij

JINR

Russia

Alexey S. Zhevlakov

Nonlocal portal to the dark sector

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to the fifth post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight 3. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the “Sparse Integral Reducer” (). We find perfect agreement in the overlap with all existing literature through the sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at the 5PM order.

Christoph Dlapa

Switzerland

Gregor Kälin

Zhengwen Liu

Rafael A. Porto

Nonlocal-in-time tail effects in gravitational scattering to fifth post-Minkowskian and tenth self-force orders

We analyze how the geodesic motion in the three- and four-vortex sectors of the Abelian-Higgs model at critical coupling is deformed by the excitation of a massive bound mode. We find that the geodesics corresponding to Bogomol’nyi-Prasad-Sommerfield (BPS) solutions with enhanced symmetry remain unchanged, although the direction of the actual motion depends on the mode-generated force, i.e., a force arising from the change of the mode frequency along the geodesic. In a generic case, for example, in head-on collisions between the axially symmetric one- and two-vortex or between two two-vortices, the vortex trajectories can differ strongly from the BPS geodesic. This enhances the chaotic behavior in the formation of the final state.

Spain

A. Alonso Izquierdo

M. Bachmaier

Japan

Poland

A. Wereszczynski

From BPS geodesics to mode-driven dynamics in the scattering of multiple BPS vortices

Two-neutron halo nuclei offer a fascinating probe into the behaviour of quantum few-body systems at the limits of binding. Although few nuclei have already been clearly identified, many of their properties remain poorly constrained. For example, 22C, one of the heaviest, still lacks a precise identification of its static and dynamic properties, such as its mass and dipole strength in the continuum. One main difficulty is that properties of two-neutron halo nuclei are inferred from indirect experimental data using a theoretical model. Therefore, accurately determining the characteristics of two-neutron halo nuclei requires an accurate theoretical model and careful quantification of the uncertainties. In this work, we examine 22C with a three-body model, seeing 22C as a 20C core and two halo neutrons, and quantify for the first time the uncertainties associated with the 20C- <italic>n</italic> interaction using a Bayesian approach. We propagate these uncertainties to properties of bound and scattering states of 22C, as well as its dipole strength. The comparison of our prediction for the matter radius to experimentally-derived values suggests that 22C is bound by less than 0.35 MeV and is dominated by a ( <italic>s</italic> <inf>1/2</inf>) 2 configuration. Our analysis of the dipole strength shows (i) that final-state interaction needs to be included for an accurate description, (ii) the uncertainties on the dipole strength function are about 50% and are mostly influenced by uncertainties on the 22C ground-state properties, i.e. its binding energy and single-particle structure, and (iii) partial-wave occupation of 22C depends on the scattering length and the <italic>d</italic> <inf>3/2</inf> resonance energy of the 20C- <italic>n</italic> unbound system. Such enhanced sensitivity of the dipole strength to both 21C and 22C properties motivates a precise measurement of the 22C dipole strength function, that will allow to precisely and accurately resolve the spectroscopy of these nuclei.

United States

Patrick McGlynn

Chloë Hebborn

Uncertainty quantified three-body model applied to the two-neutron halo 22C