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.

China

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)

In this paper we bootstrap de Sitter wavefunction coefficients (WFCs) involving fermionic operators. Starting with a fixed total-energy pole order, we systematically impose the conformal Ward identities (CWI) together with cutting-rule constraints. We derive the relevant cutting rules for fermionic exchange for the first time, enabling a complete determination of fermionic three- and four-point WFCs. We show that CWI fixes the leading total-energy-pole residue to the flat-space amplitude and subleading residues to curvature induced corrections to bulk vertices. The structure of the Ward-Takahashi identities are similarly fully determined. As an application, we derive four massless spin-1/2 WFC due to graviton exchange. We also revisit the tension between conserved spin-3/2 operators and de Sitter geometry. We demonstrate that the reality conditions appropriate to dS and Euclidean AdS (EAdS) lead to distinct three-point WFCs for two spin-3/2 operators and the stress tensor. Consequently, the residue of the leading total-energy pole for the four-point WFC receives graviton- and photon-exchange contributions with opposite signs in dS, whereas they appear with the same sign in EAdS. This result is reminiscent of the classic analysis by Pilch, van Nieuwenhuizen, and Sohnius, though formulated in an on-shell framework.

Taiwan

Wei-Ming Chen

Yu-tin Huang

Zi-Xun Huang

Yohan Liu

Fermionic boundary correlators in (EA)dS space

The Galactic Center GeV Excess (GCE) remains a compelling but enigmatic signal from the inner regions of our galaxy. Muonphilic dark matter (DM), which couples exclusively to muons via a new mediator, provides a viable explanation for the GCE and relic density while naturally evading constraints from direct detection, collider searches, and other multimessenger observations. Based on the viable nonresonant parameter space identified in previous global fits, we perform a comprehensive study on the prospects for discovering such muonphilic DM in the context of a future 3 TeV muon collider, focusing on simplified models with a $Z_2$ -even mediator. Four distinct search strategies are investigated: visible on-shell mediator decays ( $\mu^{+}\mu^{-}\gamma$ final state), invisible on-shell mediator decays (mono-photon plus missing energy), mono-photon production via off-shell mediators, and vector boson fusion production. Through a detailed signal-background analysis using cut-and-count methods, we project the exclusion limits at $ 95 $ % confidence level for seven representative models across a wide range of mediator masses. Our results demonstrate that the projected limits cover a significant portion of viable parameter space that explains the GCE, establishing a muon collider as a decisive machine for testing the muonphilic DM hypothesis.

Wanyun Chen

Haoqi Li

Chih-Ting Lu

Qiulei Wang

Exploring muonphilic dark matter with the $\textit{Z}$ $_{2}$-even mediator at muon colliders * Chih-Ting Lu, Wanyun Chen and Haoqi Li are supported by the National Natural Science Foundation of China (NNSFC) (12335005, 12575118) and the Special funds for postdoctoral overseas recruitment, Ministry of Education of China

Positive and negative flows of the Chen-Lee-Liu model and its various reductions, including Burgers hierarchy, are formulated within the framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator. Two classes of vacua, namely zero vacuum and constant non-zero vacuum can be realized within a centerless Heisenberg algebra. The tau functions for soliton solutions are obtained by a dressing method and vertex operators are constructed for both types of vacua. We are able to select and classify the soliton solutions in terms of the type of vertices involved. A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method by letting them interact with various integrable defects.

Brazil

Ireland

Y.F. Adans

United States

H. Aratyn

C.P. Constantinidis

J.F. Gomes

G.V. Lobo

T.C. Santiago

New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations

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)

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.

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)

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

Heavy Majorana neutrinos ($\textit{N}$) are predicted in many models of physics beyond the Standard Model. In this work, we explore the production and detection prospects of TeV-scale heavy neutrinos ( $ m_N \gtrsim 1 $ TeV) at a future 3 TeV Compact Linear Collider (CLIC). We focus on two distinct decay topologies: (i) $ N \to \ell^\pm W^\mp $ with hadronic $\textit{W}$ boson decay, leading to a final state with one charged lepton and a hadronic fat jet $ J_W $ ; and (ii) $ N \to \nu h $ with subsequent Higgs decay $ h \to b\bar{b} $ , yielding a Higgs-tagged fat jet $ J_h $ and $\not {E}_T$ . Based on comprehensive detector-level simulations and background analysis, we present both $ 2\sigma $ exclusion limits and $ 5\sigma $ discovery reaches in the $ m_N $ – $ |V_{\ell N}|^2 $ plane. We further extract 95% confidence level upper limits on the mixing parameter $ |V_{\ell N}|^2 $ and perform a detailed comparison with existing constraints from direct searches at future colliders and indirect global fits. Our findings demonstrate that a 3 TeV CLIC can improve the sensitivity to $ |V_{\ell N}|^2 $ by about two orders of magnitude compared with the projected reaches of future hadron colliders while remaining competitive with other CLIC search channels.

Yao-Bei Liu

Jing-Wei Lian

Searches for heavy neutrinos at a 3 TeV CLIC in fat jet final states * Yao-Bei Liu is supported by the Natural Science Foundation of Henan Province, China (252300421988), Jing-Wei Lian is supported by the National Natural Science Foundation of China (12447140) and the Natural Science Foundation of Henan Province, China (252300421771)

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)

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)