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)

The Belle Collaboration has recently reported a measurement of the branching fraction for the semileptonic decay $ B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell $ , with $ \ell=e $ or $\textit{μ}$. Using the newly available data across the full $ \pi\pi $ invariant-mass spectrum, we determine the non-resonant $ B\to\pi\pi $ transition form factors. We obtain a non-resonant branching fraction $ {\cal B}_N(B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell)=(3.5\pm 1.4^{+4.3}_{-2.4})\times 10^{-5} $ . This result indicates that the non-resonant contribution can be comparable in magnitude to the resonant components and should not be treated as a negligible background in precision measurements. Our findings highlight the importance of dedicated experimental efforts at Belle II and LHCb to further probe the non-resonant contribution.

Yan-Li Wang

Xiao-Yu Hao

Yu-Kuo Hsiao

Semileptonic ${B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell}$ decay over the full ${\pi\pi}$ invariant mass spectrum * Supported in part by the National Natural Science Foundation of China (12575101, 12175128)

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 present the first computation of the full one-loop electroweak radiative corrections to the process $ \mu^- \mu^+ \to W^\pm W^\mp \to hh $ within the Standard Model (SM). Building upon this, we investigate neutral scalar pair production via vector boson fusion at multi–TeV muon colliders in the framework of the Two-Higgs-Doublet Model (2HDM). In our phenomenological analysis, we introduce an enhancement factor, defined as the ratio of the cross section for SM-like Higgs pair production in the 2HDM to the corresponding SM prediction. This factor is systematically evaluated across the allowed regions of parameter space in both Type-X and Type-Y 2HDMs. Our results indicate that, within the viable Type-X parameter space, this factor can reach a value of 3, whereas it remains between 0.91 and 0.95 across the allowed parameter space of the Type-Y scenario. We observe that the enhancement factor exhibits distinct behaviors in the Type-X and Type-Y 2HDMs. This feature provides a promising opportunity to discriminate between the two scenarios through precision measurements of double Higgs production at future multi–TeV colliders. Furthermore, we perform a detailed scan of the cross sections for both CP-odd and CP-even Higgs pair production over the viable parameter spaces of the Type-X and Type-Y 2HDMs. In the Type-Y scenario, at a center-of-mass (CoM) energy $ \sqrt{s} = 10\; \text{TeV} $ and an integrated luminosity of $ {\cal{L}} = 10000\; \text{fb}^{-1} $ , both CP-odd and CP-even Higgs pair production in the $ t\bar{t}b\bar{b} $ final state, with subsequent top-quark decays into leptons and bottom quarks, can be probed with a statistical significance exceeding the $ 2\sigma $ level at several viable parameter points.

Vietnam

Khiem Hong Phan

Quang Hoang-Minh Pham

Neutral scalar pair production via $\textit{W}$-boson fusion at multi–TeV muon colliders * This work is supported by the Vietnam National Foundation for Science Technology Development (NAFOSTED) (103.01-2023.16)

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 investigate the discovery potential of the $T_{bc}$ state with $J^P = 0^+$ in proton-proton ( $pp$ ) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~{\rm{TeV}}$ . The study focuses on the decay channel $T_{bc} \to B^- D^+$ . A phenomenological approach is employed to construct the background model based on the associated production of $\textit{B}$ and $\textit{D}$ mesons, incorporating previously published LHCb results. Background processes are simulated using ${\mathtt{MadGraph5\_aMC@NLO}}$ and ${\mathtt{Pythia8.3}}$ . We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton scattering cross section ( $\sigma_{{\rm{eff}}}$ ) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. In particular, we consider three representative $T_{bc}$ production cross section scenarios: an optimistic estimate of $103~{\rm{nb}}$ , an intermediate value of $18~{\rm{nb}}$ obtained by scaling from the $T_{cc}^+$ production cross section, and a conservative lower bound of $0.3~{\rm{nb}}$ . We find that a $5\sigma$ observation is achievable for a production cross section of $103~{\rm{nb}}$ , which is expected to be within reach during Run4. In contrast, the more realistic cross section estimate of $18~{\rm{nb}}$ requires the full Run5 dataset ( $300~{\rm{fb}}^{-1}$ ) under the most favorable parameter choices. For the conservative scenario, no significant signal would be observable even with $300~{\rm{fb}}^{-1}$ . In addition, we estimate the minimum observable $\sigma(T_{bc}) \times {\cal{B}}(T_{bc} \to $ $ B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

Mingjie Feng

Yiming Li

France

Hua-Sheng Shao

Prospects for discovering strongly decaying doubly heavy T$_{bc}$ tetraquark states at LHCb * Mingjie Feng and Yiming Li is Supported by the National Natural Science Foundation of China (NSFC) (2175245, 12188102, W2443008). Hua-Sheng Shao is Supported by the European Research Council (101041109, 'BOSON') and the French National Research Agency (grant ANR-20-CE31-0015, 'PrecisOnium')

In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an $\textit{SU}$(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$ . Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$ . In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$ ( $\text{MeV}$ ).

Na Li

Ye Xing

Jing-Rui Shi

Analysis of molecular state $\textit{η$_{c}$D}$ $^{*}$ and $\textit{J}$/$\textit{ψD}$ $^{*}$ in the effective Lagrangian approach * Supported by the National Natural Science Foundation of China (NSFC) (12005294)

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)