Femtoscopy offers a sensitive probe of hadron emission sources and hadronic interactions. In this study, we examine relativistic corrections to scattering phase shifts and correlation functions using the two-body Dirac equation framework. We analyze the impact of the Darwin term and spin-dependent potentials, showing that these relativistic effects, especially spin-related interactions, significantly enhance the proton-proton correlation function. Our findings emphasize the necessity of including relativistic corrections for precise femtoscopic analyses.

United States

Zeyu Zeng

China

Baoyi Chen

Germany

Jiaxing Zhao

Relativistic corrections to hadron-hadron scattering phase shift and correlation function * Baoyi Chen is supported by the National Natural Science Foundation of China (NSFC) (12175165). Jiaxing Zhao is supported by the Helmholtz Research Academy Hessen for FAIR (HFHF)

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.

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

In this study, we compute the next-to-leading-order QCD corrections to the Dirac electromagnetic form factors of the Σ hyperons within the hard-collinear factorization framework at leading power. The corresponding short-distance coefficient functions are extracted from the relevant seven-point partonic correlation functions. We find that the one-loop radiative corrections to the leading-twist hard-scattering contributions are numerically significant over a broad range of momentum transfer. Combining the perturbatively calculated hard kernels with nonperturbative Σ distribution amplitudes determined from lattice QCD, we present state-of-the-art theoretical predictions for the Σ hyperon electromagnetic form factors.

Bo-Xuan Shi

Hui-Xin Yu

Xue-Chen Zhao

Next-to-leading-order QCD predictions for the Σ Dirac form factors * This research is supported by the National Natural Science Foundation of China (12475097, 12535006) and the Natural Science Foundation of Tianjin (25JCZDJC01190). Xue-Chen Zhao is supported by the Postdoctoral Fellowship Program of CPSF (GZB20250794)

In this work, we investigate novel traversable wormhole solutions within the framework of Asymptotically Safe Gravity (ASG), in the presence of a surrounding matter distribution described by the Dekel–Zhao profile. By considering the ASG renormalization group flow in the infrared (IR) regime, we show that quantum gravitational corrections allow these structures to exist at astrophysical scales, where the Dekel–Zhao matter distribution and ASG effects together determine the geometric stability and observational signatures of the wormhole. Thus, the scale-dependent gravitational coupling $\textit{G}$($\textit{k}$), derived from ASG in the IR regime, is incorporated directly into the field equations, providing a consistent description of quantum gravitational corrections at astrophysical scales. The combined effects of the running coupling (parameterized by $$\xi $$ ) and the dark matter characteristics determine the geometric structure and physical viability of the wormhole. The solutions satisfy the flare-out and asymptotic flatness conditions within restricted parameter domains. The Null Energy Condition is necessarily violated at the throat, with the ASG corrections strengthening the exotic behavior required to sustain the wormhole geometry. This interpretation is reinforced by the modified Tolman–Oppenheimer–Volkoff analysis, which shows that the repulsive quantum contributions induced by ASG counterbalance gravitational collapse. Phenomenologically, the shadow radius of the wormhole increases nearly linearly with $$\xi $$ , lying within the Event Horizon Telescope bounds for Sgr A* when $$\xi /M \simeq 0.8$$ –0.9, suggesting that ASG-corrected traversable wormholes in a dark matter environment described by the Dekel–Zhao profile may exhibit shadow properties compatible with current observational bounds in the strong-field regime.

Brazil

Jonathan Rebouças

Celio Muniz

Francisco Lustosa

Edson Otoniel

Quantum-improved wormholes in the Dekel–Zhao dark matter halo

<p>The spatial distributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>u</mi><mi>d</mi><mo stretchy="false">]</mo></math> diquark and heavy-light diquark of the SU(3)-flavor antitriplet charmed baryons are investigated by the two singly Cabibbo-suppressed hadronic weak decays, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>K</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math> within the nonrelativistic constituent quark model. The above two spatial distributions are reflected by the two parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>ρ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>λ</mi></msub></math>, which are the harmonic oscillator strength parameters of the charmed baryons. These two parameters obtain strong constraints from the decay widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>K</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math>. The larger the harmonic oscillator parameter is, the more compact the spatial distribution will become. The current <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>ρ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>λ</mi></msub></math> indicate that neither the light diquark nor the heavy-light diquark turns out to favor a compact structure. In addition, some selection rules, including the “<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> selection rule,” can be useful for the search of excited baryons in the heavy-flavor baryon hadronic weak decays.</p>

Peng-Yu Niu

Japan

Qian Wang

Qiang Zhao

Probing the diquark structure of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> in a combined analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>K</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math>

In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Jun Wang

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)

<p>The BESIII Collaboration has recently observed a resonant structure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, whose origin remains unresolved. In this study, we analyze the cross section line shape of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> by taking into account the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4415</mn><mo stretchy="false">)</mo></math> state and intermediate charmed meson loops. By treating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4415</mn><mo stretchy="false">)</mo></math> as both a pure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave state and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>−</mo><mi>D</mi></math> mixed states, and introducing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msubsup></math> resonance, we find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> peak at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> arises from the triangle singularity mechanism in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msubsup></math>-mediated rescattering processes, supporting its interpretation as a threshold effect rather than a conventional resonance.</p>

Xiao-Yun Wang

Liu-Lin Wang

Xiao-Hai Liu

Threshold effects as the origin of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> observed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>

Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

We carry out a systematic study of the 1$\textit{S}$-wave hidden and double charm-strange tetraquarks $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ in a nonrelativistic potential quark model framework with the explicitly correlated Gaussian method, and the mass spectra, color-spin configurations and possible decay modes are obtained. We find that although these states are all above their open flavor thresholds, their rearrangement decay widths are rather narrow which can be understood by the mismatching of the wave functions between the initial and final states. It implies that the tetraquarks of $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ may have a good chance to exist as genuine tetraquark states. It also shows that the color-spin configurations of the $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ systems are quite different. We find that for a physical state of $$cs\bar{c}\bar{s}$$ its color configurations can be dominated by either the $$|11\rangle _{c}$$ or $$|88\rangle _{c}$$ ones. It suggests that some hidden charm-strange tetraquark states may strongly couple to two color-singlet hadrons if the kinematics and dynamics allow. In contrast, we find that the color configurations $$|11\rangle _{c}$$ and $$|88\rangle _{c}$$ in a double charm-strange $$cc\bar{s}\bar{s}$$ state are rather compatible. It may suggest that an overall color-singlet tetraquark (i.e. a genuine color-singlet) should always play a role in the $$T_{cc\bar{s}\bar{s}}$$ states. We also demonstrate that our formalism contain the spin symmetry relations in the heavy quark symmetry and heavy quark spin symmetry limit which are the same as those derived in the Born–Oppenheimer model. Discussions taking into account some experimental candidates are presented, and suggestions on further experimental searches are also made.

Fengxiao Liu

Ru-Hui Ni

Xian-Hui Zhong

Hidden and double charm-strange tetraquarks and their decays in a potential quark model

One compelling way to probe dark matter is by looking for its gravitational effects on black holes. Inspired by the study of Cardoso et al. (Phys. Rev. D 105, 6, L061501 (2022)) on black holes in galaxies, this work investigates static, spherically symmetric black holes surrounded by Dekel-Zhao-type dark matter halos and influenced by a quintessential field. By adopting a double power-law profile, we derive explicit expressions for the cumulative mass, tangential velocity, and the modified metric, providing a coherent description of the horizon structure and thermodynamic properties. Depending on the core density, the spacetime may feature multiple horizons or even a naked singularity. Our analysis of null geodesics reveals that both dark matter and quintessence significantly affect photon trajectories and the resulting black hole shadow. By combining theoretical modeling with EHT observations of Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>, we place constraints on the halo density and quintessence parameter, directly connecting them to observable features. However, a stability analysis of circular photon orbits confirms that the photon sphere is inherently unstable, with its location and sensitivity strongly influenced by the surrounding matter. Finally, we analyze how the impact parameter <math altimg='si39.svg'><mover accent='true'><mi>b</mi><mo>&#732;</mo></mover></math> shapes photon trajectories around a black hole, determining the bending of null geodesics, the photon sphere location, and the event horizon structure, thereby illustrating the influence of spacetime geometry on light paths. This work highlights the intricate interplay between dark matter, quintessence, and black hole observables, bridging theoretical predictions with astrophysical measurements.

South Africa

Azerbaijan

A. Errehymy

Null geodesics and shadows of Dekel-Zhao-type dark matter black holes with a quintessential field: Constraints from EHT observations of M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>