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 explore signatures of lepton number violation (LNV) from decays of the discovered Higgs (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> bosons into a pair of right-handed neutrinos (RHNs). Due to the Majorana nature of RHNs, the final state can be the same-sign dilepton plus jets leading to two units of LNV. As a simple but plausible scenario, we investigate such a signal in models with a new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>X</mi></msub></math> gauge symmetry, which naturally introduces three RHNs for gauge anomaly cancellation and is spontaneously broken down by a vacuum expectation value of an isospin singlet scalar field (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>). In this scenario, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson can decay into a pair of RHNs via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> mixing and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Z</mi><mtext>−</mtext><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> mixing with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> being a new massive gauge boson, respectively. Estimating the LNV signal and corresponding backgrounds for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>±</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup><mn>4</mn><mi>j</mi></math> final states, we find bounds on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> mixing and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Z</mi><mtext>−</mtext><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> mixing as a function of a mass of RHNs at Higgs factories, e.g., at the High-Luminosity LHC with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>14</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, future <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></math> colliders at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>250</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, muon colliders at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, as well as at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> factories, e.g., CEPC and Future Circular Collider (FCC-ee) at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>91.2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We also discuss limits on the scalar mixing at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> collisions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math>) with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>346</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mn>775</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and 2 TeV, respectively.

Japan

Arindam Das

Takaaki Nomura

Kei Yagyu

Lepton number violation from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Higgs</mi><mo>/</mo><mi>Z</mi></math> decays into a pair of right-handed neutrinos

We perform a Wick rotation and analytic continuation from global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> to static <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></math> generators with a nonstandard adjoint action tied to dS bulk coordinates. To reproduce the real-scalar two-point function, we introduce a global defect operator that twists the inner product. We further show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mi>T</mi></math> symmetry is spontaneously broken in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> vacua with a central charge having an imaginary part. Finally, we derive integral identities for bulk and defect correlators, providing a unified framework for computing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></math> observables in the presence of global and local defects.

Xing Huang

Chen-Te Ma

dS/CFT correspondence from a defect operator

In this paper, we explore <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> quantum electrodynamics at finite density on a quantum computer, including two fermion flavors. Our method employs an established gauge-invariant Ansatz together with a quantum circuit structure that enforces Gauss’s law. As a proof of principle, we benchmark our simulation protocol on a small lattice system of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>×</mo><mn>2</mn></math>, demonstrating the identification of density-induced level crossings in terms of the particle number of the fermion flavors. Classical simulations are used to obtain optimized variational parameters, which are then deployed in inference runs on IBM quantum hardware. We conclude by discussing hardware limitations and prospects for scaling this method to larger systems.

Germany

Emil Otis Rosanowski

Arianna Crippa

Lena Funcke

Cyprus

Paulo Vitor Itaboraí

Karl Jansen

Simran Singh

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> quantum electrodynamics at finite density on a quantum computer

We investigate the electromagnetic and hadronic annihilation decay widths of $\textit{S}$-wave vector quarkonia, namely charmonium ( $$J/\psi (nS)$$ ) and bottomonium ( $$\Upsilon (nS)$$ ) with radial excitations $$n=1$$ –4, within the framework of the instantaneous Bethe–Salpeter (BS) equation. The interaction kernel combines a harmonic confinement potential with one-gluon exchange, using a single unified parameter set for both $$c\bar{c}$$ and $$b\bar{b}$$ systems. The obtained relativistic wave functions are used to compute the decay widths for the processes of $$nJ/\psi \rightarrow 3\gamma $$ , $$nJ/\psi \rightarrow 3g$$ , $$n\Upsilon \rightarrow 3\gamma $$ , and $$n\Upsilon \rightarrow 3g$$ . For the ground state, $$\Gamma _{J/\psi (1S)\rightarrow 3\gamma }=1.004\times 10^{-3}\,\text {keV}$$ agrees well with experiment, while $$\Gamma _{J/\psi (1S)\rightarrow 3g}=59.28\,\text {keV}$$ and $$\Gamma _{\Upsilon (1S)\rightarrow 3g}=43.42\,\text {keV}$$ closely reproduce measured values. The decay widths decrease with radial excitation due to node effects in the wave functions. The ratios $$\Gamma _{3g}/\Gamma _{3\gamma }$$ are found to be $$0.59\times 10^{5}$$ for $$J/\psi $$ and $$0.87\times 10^{6}$$ for $$\Upsilon $$ , consistent with the expected scaling $$\Gamma (3g)/\Gamma (3\gamma )\propto (\alpha _s/\alpha _{\textrm{em}})^3$$ . These results demonstrate that the Bethe–Salpeter approach with a unified parameter set provides a reliable relativistic framework for quarkonium annihilation processes.

Ethiopia

Hluf Negash

Gebretsadik Seyoum

Goitom Tekle

Mekonnen Gebremikael

Three-photon and three-gluon annihilation decays of vector Quarkonia in a unified instantaneous Bethe–Salpeter framework

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)