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)

We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor action. In the probe approximation, we perform an inverse reconstruction of the model functions by parameterizing them with neural networks and solving the EMD equations via a differentiable ODE solver (a neural ODE framework), calibrating the model to a reference thermodynamic table for $(2+1)$ -flavor QCD at finite temperature and finite baryon chemical potential. The reconstructed model functions are then parameterized and kept fixed across thermodynamic states. Next, viewing the EMD sector as an effective description of pure Yang-Mills theory, we fix its parameters by fitting the $\mu_B=0$ lattice pure-glue EoS using a hybrid optimization strategy. Finally, we go beyond the probe limit and solve the coupled EMD+KKSS equations with back-reaction, using the pure-glue-calibrated EMD sector as a fixed input and varying the KKSS couplings to compare with the $\mu_B=0$ two-flavor lattice EoS. We find a visible mismatch and a high-temperature behavior in which the back-reacted dimensionless ratios approach a nearly $\beta_1$ -insensitive plateau close to the pure-glue baseline, providing a simple structural diagnostic for the present flavor-sector truncation.

Yutian Deng

Mei Huang

Lin Zhang

Holographic QCD equation of state constrained by lattice QCD: neural-ODE for probe-limit and a back-reaction test * Start-up funding from Sun Yat-sen University (SYSU) (Y. Deng and L. Zhang); National Natural Science Foundation of China (NSFC) (12235016) (L. Zhang and M. Huang) and 12221005 (M. Huang)

In this work, we focus on the possible linear relationship between short-range correlations (SRCs) and the EMC effect for partons in nuclei. First, we test a linear relationship pertaining to gluons in bound nuclei; it is manifested as a correlation between the slope of the reduced cross-section ratio in deep inelastic scattering (DIS) and the cross-section of sub-threshold $ J/\psi $ photoproduction. For comparison, results from four different global analysis groups of nuclear parton distribution functions (nPDFs) are utilized. These results show a good linear correlation between the gluons in bound nuclei and the slope of the reduced cross-section ratio, consistent with the possible presence of nuclear effects in the gluon distributions. Second, we investigate the linear relationship of quarks in the proton-induced Drell-Yan process. The corresponding results for quarks show strong sensitivity to the parameterizations forms adopted by the different groups. These findings enhance our understanding of the substructure in bound nuclei and provide a valuable reference for future global fitting of nPDFs.

Shu-Man Hu

Wei Wang

Ji Xu

Xing-Hua Yang

Shuai Zhao

Testing a linear relation: short-range correlations and the EMC effect for gluons and quarks in nuclei * Supported in part by the National Natural Science Foundation of China (12125503, 12335003, 12105247, 12305106, 12475098)

We present a systematic analysis of the Higgs signal strengths at 125 GeV and 95 GeV in a non-supersymmetric $ U(1)_X $ model with vector-like fermions ( $ U(1)_X $ VLFM). This framework extends the Standard Model (SM) by introducing an additional $ U(1)_X $ gauge symmetry, three right-handed neutrinos, two singlet Higgs fields ($\textit{ϕ}$ and $\textit{S}$), and one generation of vector-like quarks and leptons. The scalar fields mix in the neutral CP-even sector, yielding two Higgs-like states around 95 GeV and 125 GeV. We perform a $ \chi^2 $ analysis that combines the Higgs signal strength measurements at 125 GeV from ATLAS and CMS, including the $ \gamma\gamma $ , $ WW^* $ , $ ZZ^* $ , $ b\bar{b} $ , and $ \tau\bar{\tau} $ channels, together with the 95 GeV excesses observed in the diphoton and $ b\bar{b} $ final states reported by CMS and LEP. Our results indicate that the $ U(1)_X $ VLFM successfully reproduces the observed signal strengths of the 125 GeV Higgs while simultaneously explaining the 95 GeV excess. The parameters $ g_X $ , $ g_{YX} $ , $ v_S $ , $ v_P $ , and the new Yukawa couplings play a crucial role in achieving this consistency.

Rong-Zhi Sun

Shu-Min Zhao

Meng-Zi Cao

Song Gao

Portugal

Xing-Xing Dong

Higgs Bosons at 95 and 125 GeV in the $\textit{U}$(1) $\textit{X}$ VLFM * Supported by National Natural Science Foundation of China (NNSFC) (2075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), the Project of the China Scholarship Council (CSC) (202408130113). This work is also supported by Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the project UID/00777/2025 (https://doi.org/ 10.54499/UID/00777/2025)

The internal structure of the light scalar state $ a_0(1450) $ has not been definitively determined; it may comprise multiple possible configurations. Among these, it may be regarded as a $ q\bar{q} $ state. Based on this possibility, we use QCD light-cone sum rules to study the semileptonic decay process $ D \to a_0(1450)\ell \nu_\ell $ with $ \ell=(e, \mu) $ and to test this hypothesis. First, we construct two twist-2 light-cone distribution-amplitude schemes based on the light-cone harmonic-oscillator model, and present their moments $ \langle\xi^{n}\rangle |_{\mu} $ and Gegenbauer moments $ a_{n}(\mu) $ at $ \mu_0=1\; {\rm{GeV}} $ and $ \mu_k= 1.4\; {\rm{GeV}} $ for $ n=(1,3,5) $ . In the large-recoil region, we obtain the transition form factors (TFFs): $ f_+^{({\rm{S}}1)}(0) = $ $ 0.836_{-0.119}^{+0.116} $ , $ f_+^{({\rm{S}}2)}(0)=0.767_{-0.105}^{+0.106} $ , and $ f_-(0)=0.630_{-0.077}^{+0.078} $ . A simplified series expansion $ z(q^2, t) $ is used to extrapolate the TFFs to the entire physical $ q^2 $ region. For $ q^2=10^{-5} \; {\rm{GeV}}^2 $ , we compute the angular distribution of the differential decay width ${{\rm d}\Gamma}/{{\rm d}\cos\theta_\ell }$ over the range $ \cos\theta_\ell \in [-1,1] $ . Subsequently, we obtain the differential decay widths and branching fractions for $ D^0 \to a_0(1450)^- \ell^+ \nu_\ell $ and $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $ , with branching fractions of order $ 10^{-6} $ . Finally, we analyze three angular observables for the semileptonic decay process $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $ : the forward–backward asymmetry $ {\cal{A}}_{\rm{FB}} $ , the lepton polarization asymmetry $ {\cal{A}}_{\lambda_\ell} $ , and the $ q^2 $ -differential flat term $ {\cal{F}}_{\rm{H}} $ .

Ya-Lin Song

Yin-Long Yang

Ye Cao

Xue Zheng

Hai-Bing Fu

Searching the possibility of $\textit{a}$ $_{0}$(1450) scalar state being a q q state structure via charmed meson semileptonic decays * Supported in part by the National Natural Science Foundation of China (12265010), and the Guizhou Provincial Department of Science and Technology (MS[2025]219, CXTD[2025]030)

We report stronger evidence for the $X(7200)$ state and markedly improved measurements of the $X(6900)$ resonance parameters based on a combined analysis of the di- $J/\psi$ mass spectrum using published data from LHCb, ATLAS, and CMS. Through simultaneous fits to the datasets from all three experiments, we observe the $X(6900)$ with overwhelming significance ( $ \gt 12\sigma$ ) and determine its mass and width with improved precision. For the $X(7200)$ , we find consistent signals across multiple interference models, with significances ranging from $3.7\sigma$ to $6.6\sigma$ ; in the best-fit model (the CMS three-resonance scheme), the significance reaches $6.6\sigma$ , providing substantially stronger evidence for this state. Our results underscore the essential role of interference effects in fully charmed tetraquark spectroscopy and offer new constraints on their production mechanisms at the LHC.

Yuan Wang

Ran Li

Bin Zhong

Ya-Qian Wang

Enhanced evidence of $\textit{X}$(7200) and improved measurements of $\textit{X}$(6900) parameters from a combined LHCb-ATLAS-CMS analysis * Supported by the National Natural Science Foundation of China (NSFC) (12475077)

We study a minimal $$\mathbb {Z}_2$$ -symmetric extension of the Standard Model containing two singlet fermions and a singlet scalar that interact with the SM particles through the Higgs-portal. We identify regions of parameter space in which all three new particles are kinematically stable, giving rise to a multi component dark matter (DM) scenario. The parameter space consistent with the observed dark matter relic abundance are determined, and the contribution of each component to the total relic density is evaluated. While the DM–nucleon elastic scattering cross sections of the two fermionic dark matter components are loop-suppressed, the corresponding cross section of the scalar dark matter particle arises at tree level and is therefore expected to dominate. We find a viable region of the parameter space in which the scalar dark matter candidate with mass range of approximately 125–400 GeV, evades current direct detection (DD) bounds while contributing only a small fraction of the observed relic density. In contrast, the fermionic dark matter possesses a loop-suppressed DD cross section that lies below the neutrino floor and can constitute a substantial fraction of the total relic density.

Iran

Karim Ghorbani

Multi component dark matter in a minimal model

We discuss the correspondence between highly excited strings and black holes in the presence of angular momentum. At fixed imaginary angular velocity $\textit{ν}$, we show that free strings exhibit a Hagedorn instability due to a thermal-winding mode turning tachyonic. This allows us to determine the exact Hagedorn temperature $\textit{β}$ ($\textit{ν}$) for bosonic, type II, and heterotic strings. Using the effective field theory for the thermal-winding mode around the $\textit{ν}$-dependent background, we find a novel ‘rotating string star’ saddle (perturbatively in the angular velocity) and study its properties. This configuration describes a self-gravitating bound state of highly excited rotating strings. As in the non-rotating case, the saddle is qualitatively shown to interpolate between the rotating strings phase and a rotating black hole. We also comment on the implications of these results for anti-de Sitter space.

Israel

Josef Seitz

United States

Erez Urbach

A spin on Hagedorn temperatures and string stars

<p>We investigate dilepton production from an isospin-asymmetric hot and dense medium in order to explore the role of isospin imbalance in electromagnetic spectral properties. We focus in particular on modifications of the dilepton production rate associated with the onset of pion condensation, which can occur in the presence of a finite isospin chemical potential. We employ the Nambu–Jona-Lasinio model with isoscalar-vector interaction. We examine the phase structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow></math> plane and estimate the vector current correlator-resummed dilepton rate for an effective quark chemical potential. We find that the interplay between isospin asymmetry, pion condensation, and vector interactions leads to nontrivial modifications of the dilepton yield. In particular, we observe two key features of the pion condensed phase: an enhancement at lower invariant mass and a prominent plateaulike structure which also help clearly identify the pion condensed phase from a chirally broken/restored phase. These results highlight the potential sensitivity of dilepton observables to pion-condensed phase of QCD matter, with possible implications for future low-energy heavy-ion collision experiments as well as isospin-rich environments such as neutron star matter.</p>

Romania

Poland

Aritra Bandyopadhyay

India

Chowdhury Aminul Islam

Krzysztof Redlich

Japan

Chihiro Sasaki

Dilepton production as a probe of pion condensation in hot and dense QCD matter

<p>In this work, we investigate the behavior of the light vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson in the presence of a symmetric nuclear medium at zero temperature. We calculate the mass, decay constant of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson, and leading twist distribution amplitudes (DAs) in the light-front quark model in vacuum, which are further investigated at different baryonic densities. We also predict the Mellin moments of the DAs and decay width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> process in both vacuum and medium. The evolution of DAs is carried out by the leading order (LO) Efremov-Radyushkin-Brodsky-Lepage method and compared with available predictions. For better understanding of medium effects on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson, we have also predicted the in-medium charge [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>C</mi></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>], magnetic [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>], and quadrupole [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mi>Q</mi></msub><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math>] form factors. The in-medium charge radii, magnetic moment, and quadrupole moment have also been predicted in this work. We have found that the nuclear medium induces appreciable modifications on the mass, weak decay constant, decay width, and distribution amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson. However, the charge radii, magnetic moment, and quadrupole moment are observed to exhibit weaker sensitivity to changes in baryonic density.</p>

Anshu Gautam

 Tanisha

Satyajit Puhan

Arvind Kumar

Harleen Dahiya

Spectroscopy of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson in a symmetric nuclear medium