We present a systematic study of the magnetic dipole and electric quadrupole moments of compact <math altimg='si3.svg'><mrow><mrow><mo>[</mo><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub><mo>]</mo></mrow><mrow><mo>[</mo><msub><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover><mn>3</mn></msub><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover><mo>]</mo></mrow></mrow></math> tetraquark states with quantum numbers <math altimg='si22.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math>, in the diquark&#8211;antidiquark picture and within the light-cone QCD sum rule framework. By performing a flavor decomposition across all admissible <italic>u</italic>/ <italic>d</italic> configurations, we show that the charm-quark contribution to the electromagnetic moments vanishes algebraically at the operator level &#8211; a structural feature of the specific spin organization adopted here, in which the heavy antiquark resides in a pseudoscalar antidiquark, distinct from the dynamical 1/ <italic>m<inf>c</inf></italic> suppression operative in alternative compact constructions and in hadronic molecules. The magnetic moments follow a coherent light-flavor pattern &#8211; positive for <italic>uu</italic>-, negative for <italic>dd</italic>-, and suppressed for mixed-flavor diquarks &#8211; and the quadrupole moments are non-zero throughout, corresponding, in the customary geometrical interpretation, to intrinsically deformed charge distributions. We further identify the dimensionless multipole ratio <math altimg='si39.svg'><mrow><mi mathvariant='script'>D</mi><mo linebreak='goodbreak'>/</mo><mi>&#956;</mi></mrow></math> as a structural observable, independent of the normalization of the interpolating current, which probes the relative geometry of the spin-current and charge distributions complementary to the absolute moments. Taken together, the algebraic decoupling of the charm contribution and the operator-level distinction it implies among different singly-heavy tetraquark architectures constitute methodological signatures that discriminate among the corresponding internal organizations and, to the extent that a physical candidate is dominated by one of them, among compact and molecular interpretations.

Türkiye

Ulaş Özdem

Flavor decomposition of electromagnetic multipole moments in <math altimg='si3.svg'><mrow><mrow><mo>[</mo><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub><mo>]</mo></mrow><mrow><mo>[</mo><msub><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover><mn>3</mn></msub><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover><mo>]</mo></mrow></mrow></math> tetraquarks: Light-quark analogs of <italic>T</italic> <inf><italic>cs</italic>1</inf>(2900) 0 with <math altimg='si22.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math>

We examine whether nonlinear matter dependence in <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math>gravity can account for the observed late-time acceleration of the Universe. For this purpose, we consider <math altimg='si25.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>a</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><msubsup><mi>L</mi><mi>m</mi><mi>n</mi></msubsup><mo linebreak='goodbreak'>+</mo><mi>b</mi></mrow></math> and reconstruct the expansion history using <math altimg='si26.svg'><mrow><mi>H</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>H</mi><mn>0</mn></msub><mtext>exp</mtext><mi>&#8289;</mi><mrow><mo>(</mo><mrow><mi>&#945;</mi><mi>z</mi><mo linebreak='badbreak'>+</mo><mi>&#946;</mi><msup><mrow><mi>z</mi></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></math>. The parameters of the Hubble parametrization are constrained through Bayesian analysis using the joint Cosmic Chronometer and DESI BAO datasets. The reconstructed evolution is consistent with the observational measurements and describes a smooth transition from past deceleration to the present accelerated phase. The model produces positive energy density and negative pressure at late times, leading to a quintessence-like cosmic evolution without entering the phantom regime. Its dynamical behaviour also provides testable departures from the spatially flat <math altimg='si12.svg'><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></math>CDM expansion history. These findings support nonlinear <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math> gravity as a viable framework for describing late-time cosmic acceleration.

India

S.N. Bayaskar

A.D. Vishwakarma

S.A.A. Qadeer

Azerbaijan

J. Praveen

S.C. Darunde

Dark energy in non-linear <math altimg='si23.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math> gravity with exponential parametrization of Hubble parameter

We present a theory-constrained hierarchical Bayesian analysis of primordial black holes (PBHs) generated by inflationary perturbations in <italic>f</italic>( <italic>Q, T</italic>) gravity, and confront the resulting PBH population with the gravitational-wave catalog GWTC-3. In this framework, the parameters ( <italic>&#945;, &#946;, &#955;</italic>) characterize the effective inflationary dynamics, with <italic>&#945;</italic> and <italic>&#946;</italic> specifying the adopted <italic>f</italic>( <italic>Q, T</italic>) gravitational sector and <italic>&#955;</italic> parameterizing the local behavior of the specified inflaton potential near its quasi-inflection-point region. Starting from the modified background dynamics in <italic>f</italic>( <italic>Q, T</italic>) gravity, we compute the curvature power spectrum and determine the resulting PBH mass distribution through gravitational collapse at horizon re-entry. Within the adopted analytic approximation and Gaussian-modulated potential, the inflationary dynamics determine the PBH mass-function parameters through the background evolution and the curvature power spectrum. Using posterior samples of detected binary black-hole events, we construct a theory-constrained hierarchical likelihood and explore the corresponding hyperparameter space with Markov Chain Monte Carlo, obtaining constraints on the effective inflationary parameters of the adopted model. Our analysis demonstrates how gravitational-wave population data can be used to constrain an inflationary modified-gravity model through its predicted PBH population. This provides a statistical framework linking early-Universe modified gravity to late-time compact-binary observations and offers a new observational probe of the inflationary sector of alternative gravity theories.

Iran

S. Davood Sadatian

S. Mohamad Reza Hosseini

Theory-constrained hierarchical inference of primordial black holes in <italic>f</italic>( <italic>Q, T</italic>) gravity with GWTC-3

We study the real-time quantum dynamics of Q-balls in the Friedberg-Lee-Sirlin model within the inhomogeneous Hartree approximation. The mean fields are evolved self-consistently with the leading quantum two-point functions, which are implemented numerically through a stochastic ensemble representation. After introducing a renormalized formulation and a classical-limit scaling, we simulate single-Q-ball configurations in 3 + 1 dimensions and compare their quantum-corrected evolution with the corresponding classical dynamics. We find a clear separation between a classical regime, where quantum fluctuations remain small and the evolution closely follows the classical solution, and a quantum regime, where the fluctuation sector carries a sizable fraction of the Noether charge. We also observe a periodic exchange of Noether charge between the mean fields and the fluctuation modes within the Hartree approximation. We further investigate the stability of quantum-corrected Q-balls and find an intermediate window in which configurations that are classically stable become unstable once Hartree fluctuations are included. Our results provide a first step toward real-time quantum simulations of Q-balls in renormalizable two-field soliton models.

China

Yong-Xiang Su

United Kingdom

Qi-Xin Xie

Shuang-Yong Zhou

Quantum-corrected Q-balls in the Friedberg-Lee-Sirlin model

We introduce a novel method to compute structure constants from Q functions in the scalar sector of planar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills (SYM) and related theories. The method derives from operatorial as well as functional separation of variables, and the structure constants are expressed as determinants of matrices whose entries are integrals over products of Q functions. In this framework, each operator is twisted by an external angle, mirroring the cusped Maldacena-Wilson loop. The structure constants of local single-trace operators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> SYM are recovered in the untwisting limit, where we obtain a one-to-one correspondence between our key building blocks and those of the hexagon formalism. Retaining appropriate twists, our structure constants also perfectly match those of the orbifold points of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> SYM. Our results thus far are valid at leading order in the weak-coupling expansion, but their formulation in terms of Q functions provides a natural starting point for including loop corrections. Many of the methods we develop in this work apply more generally to the computation of correlation functions in integrable models.

Germany

Till Bargheer

Carlos Bercini

France

Brazil

Gabriel Lefundes

Paul Ryan

Structure constants from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> systems and separation of variables

In this work we explore the non-singular bouncing scenarios in the framework of <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity, where the gravitational action depends on the non-metricity scalar ( <italic>Q</italic>) and matter Lagrangian density <math altimg='si10.svg'><mrow><mo>(</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math>. Using the functional form <math altimg='si11.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi></mrow></math>, two different bouncing scenario models are analyzed in a homogeneous, isotropic and flat FLRW universe. The cosmological evolution is analyzed through the behavior of the Hubble parameter, deceleration parameter, energy density, pressure, and equation of state parameter. Both models exhibit a successful bounce characterized by a smooth transition from a contracting universe ( <italic>H</italic>&#8239;&lt;&#8239;0) to an expanding phase ( <italic>H</italic>&#8239;&gt;&#8239;0) without encountering any initial singularity <math altimg='si12.svg'><mrow><mo>(</mo><mi>H</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>)</mo></mrow></math>. The EOS parameter exhibits phantom crossing behavior, while the energy conditions reveal NEC and SEC violation around the bounce, consistent with bouncing cosmology requirements. Stability analysis through metric perturbations and adiabatic index confirms stable late-time cosmic evolution. The study suggests that <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> theory offers a promising geometrical background for understanding non-singular early universe dynamics and bouncing scenarios.

Vinod Kumar Bhardwaj

Saudi Arabia

Meraj Ali Khan

Shyam Das

Saibal Ray

Exploring the scenarios of non-singular bouncing cosmology in <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity

In this work, we examine Big Bang Nucleosynthesis (BBN) within the framework of <italic>f</italic>( <italic>Q, C</italic>) gravity by considering three representative functional forms of the gravitational Lagrangian. The first model is constructed from quadratic contributions involving the nonmetricity scalar <italic>Q</italic> and the boundary term <italic>C</italic>. The second employs a separable form containing the standard linear dependence on <italic>Q</italic> together with a logarithmic correction associated with <italic>C</italic>, whereas the third model introduces a multiplicative coupling between <italic>Q</italic> and <italic>C</italic>. For each scenario, we investigate the background dynamics during the radiation-dominated phase and assess whether the resulting expansion history is compatible with the requirements of successful BBN. We subsequently derive constraints on the corresponding model parameters by confronting the predicted primordial abundances of the principal light elements, with particular emphasis on helium-4 and deuterium. Among the three cases considered, the second model yields the most favorable agreement with the observationally inferred primordial abundances of helium-4 and deuterium, thereby identifying a viable region of its parameter space.

Subhajit Sarkar

Ujjal Debnath

Big Bang nucleosynthesis constraints on f(Q,C) gravity

We present an investigation of the $ K^*(1680) $ state in its strong decays into two-body final states within the flux-tube model and quark pair creation model. Since charge conjugation parity is not conserved in the strange sector, the conventional $ q\bar{q} $ states with $ J^{P(C)}=1^{-(-)} $ can mix with the lowest hybrid states with $ J^{P(C)}=1^{-(+)} $ . Our analysis of the $ K^*(1680) $ two-body strong decays indicates that the decay pattern of $ K^*(1680) $ cannot be explained by the conventional $ q\bar{q} $ scenario. Moreover, there is strong evidence for the $ q\bar{q} $ -hybrid mixing mechanism in the strange sector. The phenomenological consequences of such mixing are also discussed. Our study can provide guidance for future searches for hybrid multiplets in experiments at BESIII, LHCb, and Belle II.

Samee Ullah

Ye Cao

Ming-Xiao Duan

Hai-Bing Fu

Qiang Zhao

Nature of ${K^*(1680)}$ and ${q\bar{q}}$ -hybrid mixing as the $\textit{SU}$(3) partner of ${\eta_{1}(1855)}$ in the strange sector * Supported in part by the National Natural Science Foundation of China (12235018, 12265010, 12505098), and the Project of Guizhou Provincial Department of Science and Technology (MS[2025]219, CXTD[2025]030, ZD[2026]168, QN[2025]178), and the project of Guizhou Normal University (GZNUD[2025]05)

Classical A-polynomials <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">(</mo><mo>ℓ</mo><mo>,</mo><mi>m</mi><mo stretchy="false">)</mo></math> define constraints on coordinates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">C</mi><mo stretchy="false">)</mo></math> [a complexification of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math>] character varieties associated to knot complements <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mn>3</mn></msup><mo>\</mo><mi>K</mi></math>. Quantum A-polynomials <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>A</mi><mo stretchy="false">^</mo></mover><mo stretchy="false">(</mo><mover accent="true"><mo>ℓ</mo><mo stretchy="false">^</mo></mover><mo>,</mo><mover accent="true"><mi>m</mi><mo stretchy="false">^</mo></mover><mo stretchy="false">)</mo></math> are difference operators annihilating Jones polynomials believed to represent wave functions of 3D Chern-Simons theory with gauge group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> on a toroidal pipe surrounding the knot <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> strand—a boundary of the knot complement <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mn>3</mn></msup><mo>\</mo><mi>K</mi></math>. In this note we suggest a construction of classical shaded A-polynomials <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mi>a</mi></msub><mo stretchy="false">(</mo><msub><mo>ℓ</mo><mi>b</mi></msub><mo>,</mo><msub><mi>m</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> associated to Lie groups <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math>, assuming that color <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> adds some extra “depth” and “shade” to the classical notion of A-polynomials. We exploit a formalism of Clebsch-Gordan (CG) chords, where indices <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math> run over <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>N</mi><mo>−</mo><mn>1</mn></math>. CG chords have a natural interpretation in terms of 2D conformal field theories of Wess–Zumino–Witten type, or, alternatively, in terms of quantum group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>U</mi><mi>q</mi></msub><mo stretchy="false">(</mo><msub><mi mathvariant="fraktur">su</mi><mi>N</mi></msub><mo stretchy="false">)</mo></math>. In the case of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="fraktur">s</mi><msub><mi mathvariant="fraktur">u</mi><mn>2</mn></msub></math>, CG chords could be associated to Reeb chords in a knot contact homology (KCH) framework. KCH suggests its own analog of A-polynomials, known as augmentation polynomials, which is allowed to have extra spurious roots in principle. Yet the CG chord formalism could be easily extended to arbitrary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="fraktur">su</mi><mi>N</mi></msub></math> allowing us to generalize the construction of A(ugmentation)-polynomials to arbitrary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="fraktur">su</mi><mi>N</mi></msub></math> and arbitrary representations as well. Here we primarily aim at classical A-polynomials by considering a double scaling limit in which <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><msup><mi>e</mi><mi>ℏ</mi></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ℏ</mi><mo stretchy="false">→</mo><mn>0</mn></math> and the representations are huge: highest weight vector components <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>w</mi><mi>i</mi></msub><mo stretchy="false">→</mo><mi>∞</mi></math> while combinations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ℏ</mi><msub><mi>w</mi><mi>i</mi></msub><mo>∼</mo><msub><mi>m</mi><mi>i</mi></msub></math> remain finite. Still, we expect the presented techniques will be helpful in deriving quantum A-polynomials for arbitrary Lie (super)algebras <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="fraktur">g</mi></math>. Also, we discuss explicit examples of A-polynomials for knots <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mn>3</mn><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mn>4</mn><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mn>5</mn><mn>1</mn></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="fraktur">g</mi><mo>=</mo><mi mathvariant="fraktur">s</mi><msub><mi mathvariant="fraktur">u</mi><mn>3</mn></msub></math>.

Russia

Dmitry Galakhov

Alexei Morozov

Shading A-polynomials via huge representations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>U</mi><mi>q</mi></msub></math>(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="fraktur">su</mi><mi>N</mi></msub></math>)

Recent experimental advances in the baryon sector, including the observation of doubly charmed states, have renewed interest in the production mechanisms of increasingly heavy hadronic systems, calling for precision and uncertainty-controlled descriptions. We present the omg3q1.1 framework for the fragmentation of same-flavor all-heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mn>3</mn><mi>Q</mi></mrow></msub></math> baryons in high-energy hadronic collisions. The construction combines diquark-inspired inputs for constituent-heavy-quark and gluon channels with threshold-aware DGLAP evolution within the HF-NRevo scheme. A replica-based strategy consistently quantifies perturbative missing-higher-order effects and nonperturbative wave-function uncertainties, yielding the first uncertainty-resolved fragmentation-function set for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mn>3</mn><mi>Q</mi></mrow></msub></math> sector. The resulting LHAPDF6 grids are employed to investigate semi-inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mn>3</mn><mi>Q</mi></mrow></msub></math> plus jet production at the HL-LHC and future circular collider within the (sym)JETHAD environment. The omg3q1.1 framework establishes a precision-oriented baseline for rare triply heavy baryons and provides a foundation for future studies of the heavy-flavor baryon landscape.

Spain

Francesco Giovanni Celiberto

Toward precision fragmentation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mn>3</mn><mi>Q</mi></mrow></msub></math> baryons: The omg3q1.1 framework