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.

China

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)

The femtoscopic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> correlations are investigated to predict the signature of the not-yet-established <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3960</mn><mo stretchy="false">)</mo></math> state reported by the LHCb Collaboration in three scenarios: resonant, virtual, or bound. In the last two scenarios, it might also be identified as the state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3930</mn><mo stretchy="false">)</mo></math>. The formalism employed to generate this structure dynamically is based on the Bethe-Salpeter equation with a general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave potential. We investigate how the relevant properties and observables characterizing this state—such as the pole position, scattering length, and effective range—might be affected by variations in the model parameters. The amplitudes encoding the distinct interpretations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3960</mn><mo stretchy="false">)</mo></math> state are then used as input to calculate the femtoscopic correlation function of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> pair, which is analyzed and discussed.

Hao-Nan Liu

Zhi-Wei Liu

Brazil

Luciano Abreu

Li-Sheng Geng

Traces of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3960</mn><mo stretchy="false">)</mo></mrow></math> state in the femtoscopic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> correlations

We present the first rainbow-ladder Dyson-Schwinger equations study of the pion’s chiral-odd, twist-3 parton distribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>e</mi><mi mathvariant="normal">q</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>. By deriving a novel Dyson–Schwinger equation for the pion’s quark–quark correlation matrix, we simultaneously extract from it both the unpolarized twist-2 parton distribution function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi mathvariant="normal">q</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> and the twist-3 distribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>e</mi><mi mathvariant="normal">q</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>. Our results show that chiral symmetry strongly suppresses the twist-2 component of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>e</mi><mi mathvariant="normal">q</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, leaving the genuine twist-3 quark-gluon component dominant and featuring a node. We therefore argue that the genuine twist-3 term can make a substantial contribution to hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, producing a nonmonotonic structure that is a clear imprint of intrinsic quark-gluon correlations. We point out that the existence of a humplike feature is compatible with, although not uniquely indicated by, recent proton extractions and awaits more precise determination.

Chao Shi

Liming Lu

United States

Ian C. Cloët

Wenbao Jia

Peter C. Tandy

Imprint of intrinsic quark-gluon correlations: A nonmonotonic feature in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>

X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of general relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modified gravity theories and non-vacuum general relativity solutions. In this work, we test a specific non-circular metric constructed based on a locality principle, where the deviation from the Kerr spacetime is driven by the local spacetime curvature. To accurately model the reflection spectrum in this background, we implement a relativistic ray-tracing code in horizon-penetrating (ingoing Kerr) coordinates, which are favored for their ability to avoid introducing curvature singularities at the horizon in non-circular spacetimes. We apply this model to the high-quality $\textit{NuSTAR}$ spectrum of the Galactic black hole binary EXO 1846-031. Our spectral analysis reveals a source with a high inclination angle ( $$\iota \approx 76^{\circ }$$ ) and a near-extremal spin parameter ( $$a_* \approx 0.98$$ ). While we identify a global minimum in the parameter space suggesting a non-zero deformation ( $$\ell _{\textrm{NP}} \approx 0.12$$ ), the 99% confidence interval fully encompasses the Kerr limit ( $$\ell _{\textrm{NP}}=0$$ ). We conclude that the current X-ray reflection data for EXO 1846-031 are consistent with the Kerr hypothesis. This work demonstrates the feasibility of using X-ray reflection spectroscopy to constrain non-circular metrics and establishes a framework for future tests.

Leda Gao

Germany

Swarnim Shashank

Uzbekistan

Cosimo Bambi

Testing non-circular black hole spacetime with X-ray reflection

Recent studies have shown that hadronic multiplicity in deep inelastic scattering can be associated with entanglement entropy. However, such definitions are intrinsically longitudinal and do not capture the full phase–space structure of the proton. In this work, we investigate the proton Wehrl entropy constructed from the gluon Husimi distribution, which provides a positive phase-space description within the present definitions and model calculations. Within this framework, we employ a gluon light-front spectator model based on soft-wall anti–de Sitter (AdS)/QCD-inspired wave functions, with free parameters constrained by global fits obtained by the NNPDF collaboration, allowing us to compute both parton distribution functions and Wigner distributions. The Husimi distribution is obtained via Gaussian smearing of the Wigner distribution with width given by the saturation scale in the Golec-Biernat-Wüsthoff model. We show that from a normalized Husimi distribution one can decompose the Wehrl entropy into an entanglement entropy term and a residual term associated with transverse degrees of freedom. Numerical results for the proton entanglement entropy are shown and compared with data obtained by the CMS collaboration, while the Wehrl entropy is presented for different values of the virtuality.

Gabriel Rabelo-Soares

Reinaldo Francener

Gabriel S. Ramos

Giorgio Torrieri

QCD Wehrl and entanglement entropies in a gluon spectator model at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>

Assuming <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo></math> is a tetraquark state, the decay width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mn>2</mn><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> is calculated in a covariant quark model, with the diquark-antidiquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>c</mi><mi>c</mi><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">]</mo></math> picture. Two possible structures, vector-vector and axial-vector–axial-vector coupling, are investigated. The result indicates that the axial-vector–axial-vector coupling is consistent with the experiments. Additionally, as another application of the covariant quark model, the decay width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mn>2</mn><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> is predicted to be 66–88 keV.

Duo-Duo Lu

Shao-Zhou Jiang

Investigating the internal structure of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo></mrow></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> decay channel

Black holes in dense astrophysical environments, such as globular clusters or in the vicinity of other massive objects, may possess accelerations. Such acceleration would modulate the characteristics of the quasi-periodic oscillations (QPOs) observed in X-ray black hole binaries. In this paper, we explore the influence of spin-aligned acceleration of a black hole on QPOs observed in X-ray binaries. For this purpose, we compute the fundamental frequencies arising from the motion of test particles around an accelerating (spin-aligned) black hole and apply the relativistic precession, parametric resonance, and forced resonance models to establish their correspondence with several observed QPOs of X-ray binaries (GRO J1655-40, XTE J1550-564, XTE J1859+226, GRS 1915+105, H1743-322, M82 X-1, and Sgr A $$^{*}$$ ). We then employ the Bayesian Markov-Chain Monte Carlo method to constrain the black hole parameters. Our results show no evidence for spin-aligned acceleration in any of the analyzed sources, suggesting that most of these X-ray binaries reside in isolated environments and therefore experience only small perturbations to the background spacetime geometries.

Azerbaijan

Hamza Rehman

Saddam Hussain

Pakistan

G. Abbas

Tao Zhu

Exploring the accelerating black holes from the observations of quasi-periodic oscillations in X-ray binaries

Recent evidence suggests that, at small Bjorken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, QCD evolution drives the proton into a state of maximal entanglement. If the evolution kernel is assumed to be conformally invariant—as is the case for the Balitsky-Fadin-Kuraev-Lipatov equation—we can describe it by a conformal field theory. Moreover, the central charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math> of the corresponding conformal field theory emerges as the key parameter governing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> dependence of both the entanglement entropy and the structure function. Here we apply the exact Bethe ansatz methods to the quantum spin chain dual to Lipatov’s high energy effective action to extract the central charge of the theory, and find that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo>=</mo><mn>1</mn></math>. This implies the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mi>x</mi><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math> small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> behavior for the structure function—the prediction that can be tested at the forthcoming Electron-Ion Collider.

Sebastian Grieninger

Kun Hao

Dmitri E. Kharzeev

Vladimir Korepin

Small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math> behavior in QCD from maximal entanglement and conformal invariance

We investigate the radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>X</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> within the framework of nonrelativistic effective field theory (NREFT). The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> is treated as an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mtext>−</mtext><mi>D</mi></mrow></math> mixed state of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>3</mn><mrow><msub><mrow><mmultiscripts><mrow><mi>D</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub></mrow><mo stretchy="false">)</mo></math>, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> is interpreted as a weakly bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> molecule with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. The decay process was assumed to occur via the intermediate meson loops involving the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</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>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msubsup></math> mesons. Our calculated results indicate that the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>X</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> is dominated by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msubsup></math> meson loops. The partial decay width is predicted to be 0.2–1.5 keV for a binding energy range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ε</mi><mi>X</mi></msub><mo>=</mo><mn>0</mn><mi>–</mi><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, corresponding to a branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. The decay width is found to be insensitive to the full width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mn>1</mn><mo>′</mo></msubsup></math> meson. Our study suggests that the radiative decay of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> is a promising channel to search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> state, which is crucial for testing heavy quark symmetries and understanding the exotic hadron spectrum in the bottom sector.

Yuan-Jun Gao

Gang Li

Shi-Dong Liu

Qi Wu

Hunting for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub></math> via radiative transition of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math>

Structure Functions for small DIS (deep inelastic scattering) $\textit{x}$ for integrable models are investigated, in particular, for the $\textit{O}$($\textit{N}$) $\textit{σ}$-model and SU($\textit{N}$) chiral Gross-Neveu model, which are asymptotically free. We get the universal behavior $\textit{x}$ ln $\textit{x}$ at small Bjorken variable $\textit{x}$ and confirm a Balog Weisz conjecture. For the second group of models, the Sine-Gordon, sinh-Gordon and $\textit{Z}$($\textit{N}$), we find power behavior $\textit{x}$ . The special behavior of the structure function for the Sine-Gordon model is probably crucial for future investigation in 4D QCD.

Armenia

Hrachya Babujian

Angela Foerster

Michael Karowski

Structure functions for small DIS $\textit{x}$