Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

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)

<p>We propose an extension of the QCD sum rules, termed the resonance sum rules, to access resonance poles in the complex energy plane. By strategically introducing a contour in the complex plane and conformal mapping, the method intends to reach resonance poles on the second Riemann sheet. To validate this approach, we apply resonance sum rules to the square-well potential model, for which the pole locations are known. The analysis demonstrates a successful extraction of the pole positions and residues for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave resonances. The results are in good agreement with the analytic solutions, with discrepancies within 5% for the pole positions and 20% for the residues. This framework provides a basis for future applications to realistic hadronic resonances, promising new insights into spectral properties of QCD.</p>

Zi-Xi Ou-Yang

Japan

Philipp Gubler

Makoto Oka

Guang-Juan Wang

Jia-Jun Wu

Resonance sum rules: An application to the square-well potential

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)

We propose a search strategy at the HL-LHC for a new neutral particle $\textit{X}$ that couples to $\textit{W}$-bosons, using the process $ p p \to W^{\pm} X (\to W^{+} W^{-}) $ with a tri-$\textit{W}$-boson final state. Focusing on events with two same-sign leptonic $\textit{W}$-boson decays into muons and a hadronically decaying $\textit{W}$-boson, our method leverages the enhanced signal-to-background discrimination achieved through a machine-learning-based multivariate analysis. Using the heavy photophobic axion-like particle (ALP) as a benchmark, we evaluate the discovery sensitivities on both production cross section times branching ratio $ \sigma(p p \to W^{\pm} X) \times \text{Br}(X \to W^{+} W^{-}) $ and the coupling $ g_{aWW} $ for particle mass over a wide range of 170–3000 GeV at the HL-LHC with center-of-mass energy $ \sqrt{s} = 14 \, \text{ TeV} $ and integrated luminosity $ {\cal{L}} = 3 \, \text{ab}^{-1} $ . Our results show significant improvements in discovery sensitivity, particularly for masses above 300 GeV, compared to existing limits derived from CMS analyses of Standard Model (SM) tri-$\textit{W}$-boson production at $ \sqrt{s} = 13 \, \text{ TeV} $ . This study demonstrates the potential of advanced selection techniques in probing the coupling of new particles to $\textit{W}$-bosons and highlights the HL-LHC's capability to explore physics beyond the SM.

Ying-nan Mao

Kechen Wang

Yiheng Xiong

Sensitivities of new resonance couplings to $\textit{W}$-bosons at the LHC * Ying-nan Mao and Yihen Xiong are supported by the National Natural Science Foundation of China (12205227). Kechen Wang is supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102), and the research program of the Wuhan University of Technology (2020IB024). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology

The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar $$ D{\overline{D}}^{\ast } $$ system, where the well-known exotic state $\textit{χ}$ (3872) is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics.

Kang Yu

Zhi Yang

Finite volume Hamiltonian method for two-particle systems containing long-range potential on the lattice

<p>A comprehensive study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave heavy tetraquark states with identical quarks and antiquarks, specifically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo>,</mo><msup><mi>Q</mi><mo>′</mo></msup><mo>=</mo><mi>c</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>b</mi></mrow></math>), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mo>/</mo><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mi>s</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>/</mo><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi><mi>q</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>q</mi><mo>=</mo><mi>u</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi></mrow></math>), are studied in a unified constituent quark model. This model contains the one-gluon exchange and confinement potentials. The latter is modeled as the sum of all two-body linear potentials. We employ the Gaussian expansion method to solve the full four-body Schrödinger equations, and search bound and resonant states using the complex-scaling method. We then identify 3 bound and 62 resonant states. The bound states are all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> states with the isospin and spin-parity quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>: two bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> states with the binding energies, 153 MeV and 4 MeV below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup></math> threshold, and a shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> state at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>15</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold. The deeper <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> bound state aligns with the lattice QCD predictions, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> bound state, still has a much larger binding energy than the recently observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> by LHCb collaboration. No bound states are identified for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math>. Our analysis shows that the bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math> states are more probable with a larger mass ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>Q</mi></msub><mo>/</mo><msub><mi>m</mi><msup><mi>Q</mi><mo>′</mo></msup></msub></math>. Experimental investigation for these states is desired, which will enrich our understanding of hadron spectroscopy and probe insights into the confinement mechanisms within tetraquarks.</p>

Qi Meng

Mass spectra of full-heavy and double-heavy tetraquark states in the conventional quark model

In this work, we conduct a three-coupled-channel analysis of the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> structure, focusing on the <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math>, and <math><mi>ρ</mi><msub><mi>η</mi><mi>c</mi></msub></math> channels, based on the one-boson exchange model. Drawing from previous study on the exotic state <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>, we only utilize one more parameter to construct the interactions between the channels. Our model successfully reproduces the experimental line shapes of the invariant mass distribution at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.23</mn></math> and 4.26 GeV for the three channels. Additionally, the finite-volume energy levels in our model show agreement with current lattice QCD conclusion. Detailed analysis suggests that the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> peaks in the <math><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math><mi>ρ</mi><msub><mi>η</mi><mi>c</mi></msub></math> distributions primarily arise from the triangle loop involving the <math><msub><mi>D</mi><mn>1</mn></msub><mover><mi>D</mi><mo>¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> intermediate system. In the <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> distribution, the threshold peak is generated by the cascade decay mechanism enhanced by a triangle diagram. Moreover, we find a virtual pole located far from the threshold, indicating that <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> peaks are not associated with a physical pole. We conclude that the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> peaks are predominantly caused by the threshold cusp.

Three-coupled-channel analysis of <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>3900</mn><mo>)</mo></math> involving <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, <math><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, and <math><mi>ρ</mi><msub><mi>η</mi><mi>c</mi></msub></math>