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)

<p>We investigate energy-momentum tensor (EMT) form factors and the spatial spin density distribution in the nucleon within a framework of the quantized Skyrme model with vector mesons. We construct both the canonical and Belinfante improved EMTs and analyze how pseudogauge uncertainty influences local spin and momentum densities while leaving the global nucleon properties unchanged. Using the inversion formulas from nucleon matrix elements in the forward limit, we extract the form factors, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, in both pseudogauges and the additional antisymmetric form factor, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">G</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, associated with the canonical EMT. We find that the pseudogauge choice leads to sizable differences in the local spin and momentum densities. In particular, the canonical EMT naturally encodes spin density through the antisymmetric tensor structure, while the Belinfante EMT is sensitive to the total angular momentum only. Our results illustrate explicitly how different pseudogauges correspond to different spatial interpretations of nucleon spin structure within the same underlying dynamics. These findings provide a concrete model realization of the pseudogauge ambiguity in QCD-inspired nucleon structure and offer useful intuition for interpreting spatial distributions.</p>

Japan

Kenji Fukushima

Tomoya Uji

Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons

<p>We extend our dispersive analyses on meson static properties to those of light baryons. The formalism treats the dispersion relation, which a baryonic correlation function obeys, as an inverse problem, solves for the involved spectral density with available operator-product-expansion (OPE) inputs directly, and extracts baryon static properties from the spectral density. We observe that the simultaneous implementation of the chiral-even and chiral-odd dispersive constraints unambiguously determines baryon masses and pole residues. A common set of quark and gluon condensates, which appear in OPE factorization and are universal, is found to accommodate the masses of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson, a proton, and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><mo stretchy="false">)</mo></math> baryon. The advantage of our approach over the conventional handling of QCD sum rules is advocated. This work encourages broad applications of our nonperturbative analytical method to baryon systems.</p>

Shuge Zeng

Hsiang-nan Li

Fanrong Xu

Light baryon static properties in a dispersive approach

Estimations of trigger efficiencies are essential to modern particle physics analyses. A data-driven method provides a framework in which to estimate these efficiencies from the properties of reconstructed candidates, described in this paper. This paper also presents the design, implementation and performance of a software package, TriggerCalib, which provides a first centralised implementation of these calculations and can be seamlessly employed in physics analyses. Additionally, the estimation of statistical and systematic uncertainties is discussed.

Germany

Johannes Albrecht

James Gooding

Switzerland

Maxim Lysenko

Abhijit Mathad

Alessandro Scarabotto

United States

Tomasz Skwarnicki

A framework and implementation for data-driven trigger efficiency estimation at LHCb

Confirming the existence of hybrid states remains challenging due to their experimental indistinguishability from tightly bound tetraquarks and loosely bound molecules. To address this issue, we employ QCD sum rules to systematically investigate the $$ \pi _1(1600) $$ and $$ \eta _1(1855) $$ as candidate tetraquark states with exotic quantum numbers $$ J^{PC} = 1^{-+}$$ . Within the hybrid framework, an $$ SU(3) $$ flavor nonet is expected, featuring two isoscalar configurations, $$ q{\bar{q}}g $$ and $$s{\bar{s}}g$$ , where $$q = u/d $$ . Moreover, the decay width of the $$ s{\bar{s}}g $$ state into the $$ K^* {\bar{K}}^* $$ channel ($\textit{VV}$) is found to be two orders of magnitude smaller than that into the $$ \eta \eta ^\prime $$ channel ($\textit{PP}$) [1]. In contrast, the tetraquark scenario predicts an $$ SU(3) $$ flavor 81-plet comprising three isoscalar states: $$ qq{\bar{q}}{\bar{q}} $$ , $$ qs{\bar{q}}{\bar{s}} $$ , and $$ ss{\bar{s}}{\bar{s}} $$ . Our analysis yields a mass of $$ 2.22^{+0.18}_{-0.26}~\textrm{GeV} $$ for the $$ ss{\bar{s}}{\bar{s}} $$ tetraquark state, which is expected to decay predominantly into the $$ \phi \phi $$ channel ($\textit{VV}$) and the $$ \eta f_1(1420) $$ channel, while its decay into the the $$ \eta \eta ^\prime $$ channel ($\textit{PP}$) is significantly suppressed. Therefore, experimental searches focusing on the $\textit{VV}$ decay channels are essential for discriminating between hybrid and tetraquark scenarios.

Niu Su

Er-Liang Cui

Yi-Wei Jiang

Hua-Xing Chen

A tetraquark 81-plet with $$J^{PC}=1^{-+}$$ or a hybrid nonet