In this work, we investigate the cosmological consequences of an effective ΛCDM model emerging from the more general <italic>f</italic>( <italic>Q, T</italic>) gravity theory under the special equation-of-state condition <math altimg='si20.svg'><mrow><mi>&#961;</mi><mo linebreak='goodbreak'>+</mo><mi>p</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Under this limit, the field equations yield the constraint <math altimg='si21.svg'><mrow><mi>F</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>C</mi></mrow></math>, implying that the function <math altimg='si22.svg'><mrow><mi>F</mi><mo linebreak='goodbreak'>=</mo><msub><mi>f</mi><mi>Q</mi></msub></mrow></math> becomes purely dependent on the non-metricity scalar <italic>Q</italic>, and the background evolution mimics that of the standard &#923;CDM model. We derive the resulting functional forms of <italic>f</italic>( <italic>Q</italic>), obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we perform a background-level parameter estimation for <italic>H</italic> <inf>0</inf> and &#937; <inf><italic>m</italic></inf>, and evaluate the derived parameter <italic>S</italic> <inf>8</inf> (anchored to the Planck baseline <italic>&#963;</italic> <inf>8</inf>) using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A dual-pipeline analysis is carried out using conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling alongside a machine-learning based Artificial Neural Network (ANN) emulator deployed as a complementary consistency check. We demonstrate that the ANN approach successfully emulates the continuous parameter space with high computational efficiency, yielding results in close agreement with the standard MCMC likelihood framework. Because the background evolution strictly mimics the standard &#923;CDM paradigm, the model successfully reproduces recent observational trends and recovers standard parameter constraints without dynamically resolving the baseline <italic>H</italic> <inf>0</inf> and <italic>S</italic> <inf>8</inf> tensions. Our results indicate that effective &#923;CDM scenarios derived from <italic>f</italic>( <italic>Q, T</italic>) gravity provide a viable and consistent with recent observational data.

India

Anil Kumar Yadav

S.H. Shekh

Kazakhstan

N. Myrzakulov

Anirudh Pradhan

Saudi Arabia

Nafis Ahmad

A.M. Alshehri

Effective ΛCDM model emerging from <italic>f</italic>( <italic>Q, T</italic>) under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints

Understanding near-threshold strong interactions is essential for disentangling hadronic molecules and compact multiquark states in heavy-flavor spectroscopy. In this context, the doubly charmed tetraquark candidate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> serves as a critical benchmark because it lies very close to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo>−</mo><mi>D</mi></math> thresholds. Motivated by the interaction ambiguity reported recently [<a href="http://dx.doi.org/10.1103/kd4s-9rzr">Phys. Rev. D 113, L031505 (2026)</a>], we evaluate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo>−</mo><mi>D</mi></math> scattering lengths and femtoscopic correlation functions for the molecular and molecule-compact admixture assignments of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>. We show that, although these scenarios yield similar invariant-mass line shapes, their corresponding femtoscopic correlation functions differ markedly and remain clearly distinguishable for typical particle-emitting sources created at the LHC. Our results indicate that femtoscopy can serve as a sensitive and complementary probe of the near-threshold dynamics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, providing vital theoretical references for future LHC femtoscopy measurements.

China

Duo-Lun Ge

Zhi-Wei Liu

Li-Sheng Geng

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> correlation functions in deciphering the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>

We study self-dual instantons of topological charge $$ Q=\frac{r}{N} $$ , ∀$\textit{r}$ ∈ $\textit{ℕ}$, in $\textit{SU}$ ($\textit{N}$) Yang-Mills theory on $$ {\mathbbm{T}}^4 $$ with ’t Hooft twists, by embedding them into worldvolume theories of $\textit{D}$-branes. To study their moduli, we construct the wrapped intersecting brane configurations dual to general constant field strength instanton backgrounds. We show that, locally, the moduli space is identified with the Higgs branch of an $$ \mathcal{N} $$ =2 supersymmetric theory. This parameterization of the moduli space is equivalent to one recently found in field theory, but is obtained with significantly less effort and has manifest hyper-Kähler structure. Our hope is that combining different perspectives on instantons on the twisted torus will help understand the still unknown global structure of the moduli space for general solutions with $$ Q=\frac{r}{N} $$ as well as the nature of instantons with all moduli turned on — when some $\textit{Q}$<1 and all $\textit{Q}$≥1 instantons become space-time dependent. For integer $\textit{Q}$, these are expected to match the ADHM solution in an appropriately taken infinite volume limit.

Canada

Erich Poppitz

$\textit{D}$-branes and fractional instantons on a twisted $$ {\mathbbm{T}}^4 $$ : the moduli space as an $$ \mathcal{N} $$ = 2 supersymmetric Higgs branch

Motivated by the recent observation of the pseudoscalar toponium $${\eta }_{t}$$ at the LHC and by the ongoing interest in its properties, we phenomenologically investigate the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ process, one of the characteristic decays of toponium $${\eta }_{t}$$ . The branching ratio for the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ decay is estimated with two scenarios of the decay constant $$f_{{\eta }_{t}}$$ . It is found that tens of dilepton events from the cascade decays, $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ $${\rightarrow }$$ $${\ell }^{-}\bar{\nu }_{\ell }{\ell }^{{\prime }+}{\nu }_{{\ell }^{\prime }}$$ with $${\ell }$$ , $${\ell }^{\prime }$$ $$=$$ $\textit{e}$ and $${\mu }$$ , could be experimentally observed, when considering the realistic identification efficiency of the charged lepton and assuming more than $$3{\times }10^{7}$$ $${\eta }_{t}$$ events available at the future HL-LHC. We propose searching for $${\eta }_{t}$$ via the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ $${\rightarrow }$$ $${\ell }^{-}\bar{\nu }_{\ell }{\ell }^{{\prime }+}{\nu }_{{\ell }^{\prime }}$$ channel, which features no $\textit{b}$-jets and clean dilepton signatures, thus offering a complementary and potentially more sensitive probe.

Yueling Yang

Bingbing Yang

Junfeng Sun

Prospects for observing the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ decay at the HL-LHC

The doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was reported by the LHCb experiment in 2022 and a lot of theoretical studies have been conducted. The small binding energy measured from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> threshold indicates that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> molecule. On the other hand, the superflavor symmetry, which relates heavy antiquarks to heavy diquarks, provides a useful framework for predicting the existence of partner exotic hadrons associated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. By replacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> within this symmetry, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> are expected to form partner structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. In this paper, we investigate bound and resonant states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> based on the one boson exchange potential, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> are considered as bosons. The cutoff parameter and the coupling constants for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> are taken to be the same as those for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> due to superflavor symmetry. We also discuss the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant, which is uncertain, dependence of these mass spectra. A lot of bound and resonant states with some quantum numbers are obtained for each <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant, but these mass spectra depend on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant significantly.

Japan

Manato Sakai

Yasuhiro Yamaguchi

Possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></mrow></math> molecules as superflavor partners of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>

We perform a data-driven study of the doubly charmed tetraquark candidate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. An ensemble of deep neural network classifiers, trained on synthetic amplitudes with controlled analytic structures, identifies a dominant pole topology characterized by an isolated pole on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>b</mi><mi>t</mi><mo stretchy="false">]</mo></math> Riemann sheet which is robust against left-hand cut effects. A subsequent pole parameter extraction was performed via the uniformized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">S</mi></math>-matrix and a complementary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">K</mi></math>-matrix parametrization, which respectively provides a model-independent baseline and dynamical insight on the pole position and trajectory of the resonant state. Using this two-pronged approach, we submit that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is a shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> bound state in the second Riemann sheet of the complex plane.

Philippines

Julius B. Pagayon

Klarence Tomas R. Cervantes

Denny Lane B. Sombillo

Deep learning topological inference-guided <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> pole parameter extraction

We perform three T-dualities on classical $$ \mathcal{N} $$ = 1 scale-separated AdS solutions of massive type IIA supergravity. These solutions arose from a compactification on a toroidal $\textit{G}$ -holonomy space with smeared O2 and O6/D6 sources. The T-dual backgrounds are classical $$ \mathcal{N} $$ = 1 AdS solutions of type IIB supergravity with O5/D5 and O9/D9 sources (type I) compactified on a space with $\textit{G}$ -structure and non-vanishing Ricci scalar. We generalize the original solutions in IIA in the T-dual picture and present on the type IIB side fully classical solutions with parametric control, scale separation, and integer conformal dimensions for the dual operators in the corresponding CFT. We also obtain strongly coupled solutions with the same properties. These are S-dual to parametrically controlled classical solutions of the heterotic SO(32) string theory.

United States

Zheng Miao

Spain

Muthusamy Rajaguru

George Tringas

Timm Wrase

T-dualities and scale-separated AdS3 in type I

In this paper, we investigate the dynamical constraints imposed on the UV theory when it develops an emergent symmetry in the infrared with mixed ’t Hooft anomalies. We demonstrate that, under certain conditions, the UV theory must contain non-genuine operators. Our primary examples illustrating this phenomenon are 2D gauged linear sigma models and 3D Chern-Simons-matter theories. Through this analysis, we establish connections between different classes of topological quantum field theories and propose a correspondence between quantum cohomologies of distinct target spaces.

Wei Gu

Denmark

Du Pei

Xingyang Yu

On mixed ’t Hooft anomalies of emergent symmetries

The non-resonant production of a Higgs boson pair in association with a top-antitop quark pair $$ \left( pp\to t\overline{t} hh\right) $$ has only recently begun to be explored at the Large Hadron Collider (LHC) and provides a unique and largely uncharted probe of the top-Higgs sector, offering complementary sensitivity to the Higgs self-coupling and higher-dimensional interactions beyond the Standard Model. In this work, we present a detailed study of this process within the framework of Higgs Effective Field Theory (HEFT) at the High-Luminosity LHC (HL-LHC). A comparative analysis is performed using a traditional cut-based approach in the single-lepton channel and a multivariate parametric boosted decision tree method in both single-lepton and dilepton final states. We derive one- and two-parameter limits at 95% confidence level on the HEFT couplings $\textit{δκ}$ , $\textit{c}$ , $\textit{c}$ , $\textit{c}$ , and $\textit{c}$ . The projected bound on $\textit{δκ}$ is weaker than current experimental constraints from dedicated Higgs-pair measurement; however, this coupling plays a critical role in shaping the multidimensional allowed parameter space. For the remaining HEFT couplings, where no direct experimental limits currently exist, our results provide the first sensitivity projections in the $$ t\overline{t} hh $$ channel. Overall, this study demonstrates the strong potential of the $$ t\overline{t} hh $$ production process to probe extended Higgs and top-quark interactions beyond the Standard Model through the exploitation of the $$ t\overline{t} hh $$ data at the HL-LHC.

Brazil

Ricardo D’Elia Matheus

Oscar Éboli

Rafiqul Rahaman

France

Aurore Navarro

Exploring Higgs EFT in $$ t\overline{t} hh $$ at high luminosity LHC

In this work, we first present a systematic investigation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math>-type charmed-strange molecular tetraquark candidates composed of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> meson and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-doublet anticharmed meson using the one-boson-exchange model, which exhibit exotic flavor content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mi>q</mi><mi>q</mi></math>. Our results suggest that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>−</mo></msup><mo>,</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mo>*</mo></msubsup></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo>,</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> represent the most promising candidates of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math>-type charmed-strange molecular tetraquarks, while the coupled <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo>/</mo><msup><mi>K</mi><mo>*</mo></msup><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo>/</mo><msup><mi>K</mi><mo>*</mo></msup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mo>*</mo></msubsup></math> system with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and the coupled <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mo>*</mo></msubsup><mo>/</mo><msup><mi>K</mi><mo>*</mo></msup><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo>/</mo><msup><mi>K</mi><mo>*</mo></msup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mo>*</mo></msubsup></math> system with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> can only be regarded as the possible candidates of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math>-type charmed-strange molecular tetraquarks. We further extend our analysis to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msub><mi>D</mi><mn>1</mn></msub><mo>/</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup></math> systems, where our results suggest a series of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math>-type charmed-strange molecular tetraquark candidates. These findings provide a comprehensive picture of the molecular spectrum in the charmed-strange tetraquark sector composed of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave kaons and (anti)charmed mesons in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-doublet and can be tested in future experimental studies.

Fu-Lai Wang

Si-Qiang Luo

Xiang Liu

Predicting charmed-strange molecular tetraquarks with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-doublet charmed or anticharmed meson