In this paper, we present a new three-dimensional non-perturbative (NP) function to account for and parameterize the NP contributions in the jet invariant mass spectrum, in addition to the conventional NP mass shift parametrization. By implementing Bayesian analysis on experimental data of the jet invariant mass from exclusive <math altimg='si28.svg'><mrow><mi>W</mi><mo linebreak='goodbreak'>/</mo><mi>Z</mi><mo linebreak='goodbreak'>+</mo></mrow></math>jet events and inclusive jet events in <italic>pp</italic> collisions at RHIC and LHC, where collisional energy increases by a factor of up to 65 from RHIC to LHC, we ensure the analysis covers a wide range of data. For the first time, we simultaneously extract NP contributions from hadronization, initial soft-gluon radiation, and underlying events, based on two different NP prescriptions. We find that the contribution from initial soft-gluon radiation is negligible, and the hadronization effect dominates in the small- <italic>R</italic> region, while underlying events provide the dominant contribution in the large- <italic>R</italic> region. Moreover, when only hadronization effects are considered, our results successfully describe the jet mass data measured in <math altimg='si3.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> collisions, where only hadronization effects are expected to be present. Our work offers quantitative insights into understanding the soft hadronic contribution to jet substructure.

China

Zhan Gao

France

Yu Shi

Bo-Wen Xiao

Han-Zhong Zhang

Extracting essential non-perturbative information in jet invariant mass via the Bayesian analysis

In the standard formulation of relativistic quantum field theory, a <math altimg='si2.svg'><msub><mi mathvariant='double-struck'>Z</mi><mn>2</mn></msub></math>-graded structure is assumed to realize locality and the boson&#8211;fermion dichotomy. While <math altimg='si3.svg'><msubsup><mi mathvariant='double-struck'>Z</mi><mn>2</mn><mi>n</mi></msubsup></math>-graded extensions are known to be allowed at the level of symmetry, their realization in interacting quantum field theories remains unclear.

Japan

Ren Ito

Akio Nago

Shou Tanigawa

On generalized statistics and stability in <math altimg='si1.svg'><msubsup><mi mathvariant='double-struck'>Z</mi><mn>2</mn><mn>2</mn></msubsup></math>-graded classical supersymmetric Yang&#8211;Mills theory

We formulate a covariant fractional quantum framework for collective spontaneous emission in many-body atomic systems embedded within curved spacetime, based on the Riemann-Liouville (RL) formalism. The fractional time derivative introduces intrinsic memory effects and non-Markovian correlations, thereby modifying the dynamical evolution of radiative processes significantly. Starting from a general theoretical formulation, we construct the fractional generalization of collective emission in atomic arrays and extend it to incorporate gravitational contributions arising from spacetime curvature. Resulting dynamics exhibit a pronounced interplay between long-range coherence, fractional temporal evolution, and geometric phase modulation induced by gravity within the framework. In this case, we derive within this framework the fractional emission spectrum and show significant deviations from standard exponential decay, including spectral broadening and anomalous relaxation behavior. A covariant extension in <math altimg='si1.svg'><mi mathvariant='script'>D</mi></math>-dimensional curved spacetime is constructed to guarantee consistency with general relativistic constraints, followed by an eikonal reduction revealing gravitationally induced fractional phase shifts therein. Also, we construct the many-body transition amplitude within the fractional RL framework, providing a unified description of nonlocal quantum dynamics in radiative processes under gravitational influence. In this context, the results emphasize the influence of fractional calculus as an effective tool for describing memory-driven quantum radiation in curved spacetime.

Algeria

Mourad Benzahi

Brazil

Allan R.P. Moreira

Azerbaijan

Abdelmalek Bouzenada

Covariant fractional quantum framework for collective spontaneous emission

We investigate the Wilson line sector contribution to holographic complexity for five-dimensional Einstein-Gauss-Bonnet AdS black holes immersed in a static string cloud, working within the complexity equals action framework. The string cloud induces geometric backreaction on the AdS background, while the Gauss-Bonnet (GB) term captures higher derivative curvature corrections from string theory. Following the probe string formalism established in previous works, we compute the time growth rate of the Nambu-Goto worldsheet action for a moving fundamental string over a range of probe velocities, string cloud densities, and GB coupling strengths. This observable isolates nonlocal contributions from heavy Wilson line operators in the dual boundary theory, rather than evaluating the full gravitational action on the Wheeler-DeWitt patch. Our numerical results reveal a nontrivial competition between spacetime backreaction and curvature corrections, governed primarily by the black hole horizon size and probe kinematics. For large black holes, increasing the string cloud density accelerates the Wilson line complexity growth for slowly moving probes but suppresses it at relativistic velocities, producing a characteristic velocity dependent crossover. Small black holes exhibit no such crossover, with complexity rising monotonically with cloud density for all probe speeds. GB curvature corrections reduce the probe string complexity growth across all parameter choices, with much stronger suppression acting on small black holes due to their enhanced near horizon curvature. Beyond critical values of the GB coupling and cloud density, thermodynamically unstable small black hole solutions disappear, and the single surviving stable black hole recovers the dynamical signatures of large black hole geometries. Geometric analysis shows that slowly moving strings access deeper bulk regions and amplify complexity, while relativistic probes remain confined near the horizon and yield lower complexity growth. This work demonstrates that the horizon scale controls the interplay between background geometric deformations and the Wilson line sector of holographic complexity in strongly coupled conformal theories.

Hu-wei Zhu

Long Guo

Zi-qiang Zhang

Complexity growth of AdS black holes with higher derivative corrections in presence of string cloud

The resonance <italic>X</italic>(6600) is explored as the all-charm tetraquark structure with spin-parities <math altimg='si16.svg'><mrow><msup><mi>J</mi><mtext>PC</mtext></msup><mo linebreak='goodbreak'>=</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math>. It is considered in the diquark-antidiquark picture and modeled as a tensor state <italic>X</italic> composed of the axial-vector diquark <italic>cC&#947;<inf>&#956;</inf>c</italic> and antidiquark <math altimg='si17.svg'><mrow><mover><mrow><mi>c</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><msub><mi>&#947;</mi><mi>&#957;</mi></msub><mi>C</mi><mover><mrow><mi>c</mi></mrow><mo stretchy='true'>&#8254;</mo></mover></mrow></math> with <italic>C</italic> being the charge conjugation matrix. The mass and decay width of <italic>X</italic> are evaluated in the framework of QCD sum rule (SR) methods. The two-point SR approach is applied to find its spectroscopic parameters, while three-point SRs used to calculate partial widths of different decay channels of <italic>X</italic>. We study its leading decays <italic>X</italic>&#8239;&#8594;&#8239; <italic>J</italic>/ <italic>&#968;J</italic>/ <italic>&#968;, X</italic>&#8239;&#8594;&#8239; <italic>&#951;<inf>c</inf>&#951;<inf>c</inf></italic> and <italic>&#967;</italic> <inf><italic>c</italic>1</inf>(1 <italic>P</italic>) <italic>&#951;<inf>c</inf></italic> in which all four <italic>c</italic>-quarks constitute final-state mesons. We consider also the subleading channels <math altimg='si18.svg'><mrow><mi>X</mi><mo>&#8594;</mo><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mo>+</mo></mrow></msubsup><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mo>&#8722;</mo></mrow></msubsup></mrow></math> and <math altimg='si19.svg'><mrow><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mn>0</mn></mrow></msubsup><msubsup><mover><mrow><mi>D</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mn>0</mn></mrow></msubsup></mrow></math> generated by annihilation of <math altimg='si20.svg'><mrow><mover><mrow><mi>c</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>c</mi></mrow></math> quarks in the tetraquark. Comparison of the mass <math altimg='si21.svg'><mrow><mi>m</mi><mo linebreak='goodbreak'>=</mo><mo>(</mo><mn>6609</mn><mo>&#177;</mo><mn>50</mn><mo>)</mo><mspace width='0.33em' /><mtext>MeV</mtext></mrow></math> and width <math altimg='si22.svg'><mrow><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mo>[</mo><mi>X</mi><mo>]</mo><mo>=</mo><mo>(</mo><mn>165</mn><mo>&#177;</mo><mn>23</mn><mo>)</mo><mspace width='0.33em' /><mtext>MeV</mtext></mrow></math> of the tensor diquark-antidiquark state <italic>X</italic> with experimental data allows us to interpret it as an essential component of the resonance <italic>X</italic>(6600). We also provide a lower limit for the mass of the first radial excitation of <italic>X</italic>.

S.S. Agaev

Iran

Türkiye

K. Azizi

H. Sundu

Resonance <italic>X</italic>(6600)

In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by standard Bethe equations. We derive for this model exact representations for a set of elementary blocks of correlation functions, hence generalising to XYZ the results obtained in the XXZ open case in [1]. Our approach is also similar to the approach proposed in the XXZ case [1]: we solve the model by Sklyanin’s version of the quantum Separation of Variables, using Baxter’s Vertex-IRF transformation; in this framework, we identify a basis of local operators with a relatively simple action on the transfer matrix eigenstates; we then use the solution of the quantum inverse problem and our recent formulae on scalar products of separate states [2] to compute some of the corresponding matrix elements, which can therefore be considered as elementary building blocks for the correlation functions. The latter are expressed in terms of multiple sums in the finite chain, and as multiple integrals in the thermodynamic limit. Our results evidence that, once the basis of local operators is properly chosen, the corresponding building blocks for correlation functions have a similar structure in the XXX/XXZ/XYZ open chains, and do not require any insertion of non-local ”tail operators”.

G. Niccoli

V. Terras

On correlation functions of the open XYZ spin 1/2 chain with boundary fields related by a constraint

We construct new multiparticle models of <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets <math altimg='si3.svg'><mrow><mo>(</mo><mn mathvariant='bold'>1</mn><mo>,</mo><mn mathvariant='bold'>4</mn><mo>,</mo><mn mathvariant='bold'>3</mn><mo>)</mo><mspace width='0.16em' /><mrow><mo>&#8835;</mo><mo>+</mo></mrow><mspace width='0.16em' /><mo>(</mo><mn mathvariant='bold'>4</mn><mo>,</mo><mn mathvariant='bold'>4</mn><mo>,</mo><mn mathvariant='bold'>0</mn><mo>)</mo></mrow></math>. These systems are proper deformations of those associated with the standard irreducible <math altimg='si4.svg'><mrow><mi>d</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>, <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> multiplets. In this way we find a deformation of <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric U(2)-spin rational Calogero system invariant under <math altimg='si4.svg'><mrow><mi>d</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> superconformal group OSp(4|2). One more deformed model reproduces <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric U(2)-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U(1) generators. <italic>In Memory of Jerzy Lukierski (1936 &#8211; 2026)</italic>

Russia

Sergey Fedoruk

Evgeny Ivanov

Stepan Sidorov

<math altimg='si1.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mspace width='0.16em' /><mn>4</mn></mrow></math> supersymmetric multiparticle systems based on indecomposable multiplets

We study the classical double copy for static black string solutions in an Anti–de Sitter (AdS) background. By casting the black string metric into Kerr–Schild form over a cylindrical AdS geometry, we construct the corresponding single and zeroth copies. The single copy describes a gauge field satisfying Maxwell-like equations and sourced by an effective line of color charge, while the zeroth copy is given by a scalar field conformally coupled to the AdS background. We also extend the analysis to charged black strings, identifying the associated modifications in the gauge sector. These results show that the classical double copy consistently applies to extended gravitational objects in curved spacetimes.

G. Alencar

C.R. Muniz

M.S. Oliveira

Classical double copy of black strings in an Anti-de Sitter background

The Lorentzian IIB matrix model provides a non-perturbative framework for emergent spacetime from matrix degrees of freedom. We study whether algebraic consistency constrains such structures by imposing restricted off-shell supersymmetry closure, modulo gauge transformations and explicitly identified trivial symmetries, on a CPT-even low-order effective-action ansatz with anisotropic background fields, without imposing their equations of motion.

Tetsuyuki Muramatsu

Off-shell supersymmetry algebra in the Lorentzian IIB matrix model: Algebraic constraints and a <italic>&#954;</italic>-Minkowski-like sector

We focus on the gravitation quasi-normal modes of the Ayón-Beato García (ABG) black hole, which is a regular geometry formulation of Einstein’s equations with non-linear electrodynamics and without singularities. The corresponding geometry has a comparable general framework to the Reissner-Nordström black hole, with the exception that the Reissner-Nordström solution’s center singularity is replaced with a smooth, regular geometry, and <math altimg='si61.svg'><mrow><mi>r</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math> corresponds to the origin in spherical coordinates <cross-ref id='crf0011' refid='bib0001'>[1]</cross-ref>. We use the shadow data of the M87* black hole found by the Event Horizon Telescope to calculate the shadow radius associated with ABG black holes. We have found that the upper bound of the parameter <italic>&#958;</italic> is <math altimg='si62.svg'><mrow><mo>&#8722;</mo><mn>0.22</mn></mrow></math> for lower charge <math altimg='si2.svg'><mi mathvariant='script'>X</mi></math>. We determine that the shadow radius decreases monotonically with the increase of the charge <math altimg='si2.svg'><mi mathvariant='script'>X</mi></math>. Moreover, we present some critical observations regarding the effect of <math altimg='si2.svg'><mi mathvariant='script'>X</mi></math> and <italic>&#958;</italic> parameter on the potential barrier in the black hole geometry. In particular, we establish how these parameters influence the energy dissipating characteristics and the response frequency of the external perturbations. Finally, we compute the quasi-normal mode frequencies of scalar and electromagnetic field perturbations using the sixth order WKB method and provide qualitative visualization of the perturbation decay by time-domain simulations. Our results show that the scalar waves decay faster and then slower with the increase of the charge <math altimg='si2.svg'><mi mathvariant='script'>X</mi></math> and perfect fluid dark matter parameter <italic>&#958;</italic>. Quasi-normal modes stay negative during the whole studied parameter range, which confirms the dynamic stability under scalar and electromagnetic perturbations. Moreover, this study reports a noticeable difference in the sensitivity of the perturbations caused by the scalar and electromagnetic field changes in the parameters.

Pakistan

M.Z. Bhatti

S. Ijaz

Saudi Arabia

Bander Almutairi

Cyprus

Yakup Yildirim

Canada

T. Ganesan

Z. Yousaf

Thermodynamical and perturbative signatures of the regular ABG black hole in a PFDM geometry