We revisit the fundamentals of two different methods for calculating classical observables: the eikonal method, which is a scattering amplitude-based method, and the worldline quantum field theory (WQFT) method. The latter has been considered an extension of the worldline effective field theory. We show that the eikonal and WQFT methods are equivalent and that calculations can be translated freely between them. We also show how the scattering amplitude can serve as the generating function of all the WQFT diagrams. This offers another computational avenue for the WQFT diagrams, which can be useful at higher loop orders. Concretely, we focus on 2-into-2 scattering processes mediated by massless force carriers. On one hand, taking the classical limit of the QFT scattering amplitude leads to the eikonal method. On the other hand, since in the classical limit the scattering particles are almost on-shell throughout the scattering process, the worldline, a first quantized formalism, is the most efficient framework to study the scattering amplitude. This is an alternate but equivalent formalism to the quantum field theoretical (QFT) framework. By taking the classical limit of the scattering amplitude computed in the worldline, we can derive the WQFT rules of Mogull, Plefka and Steinhoff [1]. In WQFT, the Feynman diagrams are reorganized into a new set of diagrams that facilitate the ℏ expansion. Unlike the QFT eikonal method, which identifies the eikonal phase recursively, the worldline-based computation allows to target and systematically extract the classical contributions directly through a specific set of WQFT diagrams. In worldline formalism the perturbative expansion of the scattering amplitude is naturally organized in diagrams which factorize (reducible) and diagrams which are new to that order (irreducible), in a one-to-one map with the structure of the amplitude in the eikonal method. This opened up the possibility to investigate and prove the conjectured exponentiation of the eikonal phase in Du et al.[2].

United States

Siddarth Ajith

China

Yuchen Du

Ravisankar Rajagopal

Diana Vaman

Worldline formalism, eikonal expansion and the classical limit of scattering amplitudes

This paper presents a feasible static and cylinder-like symmetric thin shell wormhole model within the exponential form of <italic>f</italic>( <italic>R, T</italic>) gravity with normalized Ricci scalar relative to the cosmological constant and this gravity model is coherent with local gravity constraints and cosmologically viable. In this study, the cut-and-paste approach joins two identical spacetimes along a hypersurface &#931;. This model assumes isotropic fluid representing the matter sector, with quintessence polytropic energy sustaining matter at the shell. To ensure consistent spacetime matchings, the investigation establishes certain constraints for stable wormhole formations and examines the impact of mass, equation of state parameters, and selected gravitational theory. Stability is ascertained by evaluating the positive value of the potential&#8217;s second derivative at the throat radius.

Azerbaijan

Pakistan

M.Z. Bhatti

A. Adeel

M. Yousaf

Z. Yousaf

A study of stability and quintessence polytropic matter with thin shell wormholes in exponential gravity

We analyze the experimental data of <math altimg='si1.svg'><mrow><mi mathvariant='monospace'>p</mi><mo linebreak='goodbreak'>&#8722;</mo><mi mathvariant='monospace'>p</mi></mrow></math> collisions by the ATLAS and confront it with the AGK model developed by two of the authors, the Kharzeev-Levin (KL) model and the simple exponential behavior for the Koba, Nielsen and Olesen (KNO) scaling function. We show that all three models virtually coincide with all available experimental curves crossed at value <math altimg='si4.svg'><mrow><mi>z</mi><mo linebreak='goodbreak'>=</mo><mi>n</mi><mo linebreak='goodbreak'>/</mo><mo>&#9001;</mo><mi>n</mi><mo>&#9002;</mo></mrow></math> of the KNO scaling parameter in the broad range of the center-of-mass energies. The theoretical results and the experimental data show that the KNO violating terms are highly suppressed in the vicinity of <math altimg='si16.svg'><mrow><mi>z</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math>. The special status of the universal scaling point <math altimg='si16.svg'><mrow><mi>z</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math>, where the KNO scaling is restored for <math altimg='si1.svg'><mrow><mi mathvariant='monospace'>p</mi><mo linebreak='goodbreak'>&#8722;</mo><mi mathvariant='monospace'>p</mi></mrow></math> collisions, suggests that it originates from statistical saturation of the optical theorem. We claim that any unitary model that approximates memoryless distribution in the high energy limit must have the same KNO scaling function <math altimg='si8.svg'><msup><mi>e</mi><mrow><mo>&#8722;</mo><mi>z</mi></mrow></msup></math> in the vicinity of <math altimg='si16.svg'><mrow><mi>z</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> with KNO violating corrections of the order of one over average multiplicity squared. This reflects the maximal entanglement of the final states.

Israel

Mustapha Ouchen

Alex Prygarin

KNO scaling, memorylessness and maximal entanglement at universal fixed point

Recent advances in modeling compact astrophysical objects have focused on incorporating dark energy as a relativistic component within their internal structures, offering novel insights into extreme matter configurations. Theoretical frameworks now explore anisotropic pressure profiles and modified equations of state, enabling predictions about stability and mass-radius relationships under dark energys repulsive influence. Such studies aim to resolve discrepancies in observed compact object populations while probing interactions between high-density matter and cosmological vacuum energy. This study presents a new analytical framework for a two-fluid system consisting of ordinary baryonic matter and dark energy in modified <italic>f</italic>( <italic>Q</italic>) gravity, with <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>=</mo><mi>&#958;</mi><mo linebreak='goodbreak'>+</mo><mi>&#967;</mi><mi>Q</mi></mrow></math>, where <italic>&#958;</italic> and <italic>&#967;</italic> are coupling constants. By utilizing the Durgapal-Lake metric potentials (Durgapal et al., Gen. Relativ. Gravit. 17:671, 1985, Lake K, Phys. Rev.D 67:10 2003) as seed solutions and assuming a linear equation of state for dark energy, the modified gravitational field equations are solved to derive exact interior solutions. The model parameters, including the dark energy coupling constant and constants from the metric ansatz, were determined by smoothly matching the interior geometry with the exterior spacetime at the stellar boundary. Observational data from three compact stars <math altimg='si9.svg'><mrow><mo>(</mo><mi>H</mi><mi>e</mi><mi>r</mi><mi>X</mi><mo linebreak='goodbreak'>&#8722;</mo><mn>1</mn><mo>,</mo></mrow></math> <math altimg='si10.svg'><mrow><mn>4</mn><mi>U</mi><mn>1538</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>52</mn><mo>,</mo></mrow></math> <math altimg='si11.svg'><mrow><mi>S</mi><mi>A</mi><mi>X</mi><mi>J</mi><mn>1808.4</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>3658</mn><mo>)</mo></mrow></math> were used to test the model&#8217;s viability and regularity. The study included a thorough physical analysis, examining energy density gradients, anisotropy, stability, equilibrium conditions using the modified TOV equation. The results align with observational data, indicating that the model offers a physically plausible description of compact stars while maintaining stability and equilibrium under the tested conditions.

M.R. Shahzad

Wajiha Habib

Saudi Arabia

Muneerah Alomar

Mona Bin-Asfour

Possible existence and physical features of mathematical models of dark energy ultra-compact objects in modified symmetric teleparallel gravity

We improve the theoretical predictions for rare <italic>Z</italic>-boson decays, <math altimg='si1.svg'><mrow><mi>Z</mi><mo>&#8594;</mo><mi>V</mi><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> ( <math altimg='si9.svg'><mrow><mi>&#8467;</mi><mo linebreak='goodbreak'>=</mo><mi>e</mi></mrow></math> or <italic>&#956;</italic>), where <italic>V</italic> denotes a heavy vector quarkonium including <italic>J</italic>/&#936;, &#936;(2 <italic>S</italic>), and &#933;( <italic>nS</italic>) with <math altimg='si10.svg'><mrow><mi>n</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math>. These processes are thought to be dominated by the electromagnetic fragmentation transition, i.e., <math altimg='si11.svg'><mrow><mi>Z</mi><mo>&#8594;</mo><msup><mi>&#947;</mi><mo>*</mo></msup><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> followed by <italic>&#947;</italic>*&#8239;&#8594;&#8239; <italic>V</italic>. The present study includes all of the relevant tree-level Feynman diagrams, which contribute to these decays in the standard model. Our analysis shows that, for the charmonium final states, the fragmentation transition almost saturates the whole contribution and the other diagrams can be neglected; while for the bottomonium final states, the inclusion of other diagrams can increase their branching fractions by 4%&#8239;&#8764;&#8239;9%. Further investigation of the differential distributions, especially the angular distributions, indicates that forward-backward asymmetries for final leptons in these processes would be zero in the standard model. Therefore, in future experimental facilities with large number of <italic>Z</italic>-boson events accumulated, studies of these rare <italic>Z</italic> decays may help both to test the standard model and to probe its interesting extensions.

Li Ang

Dao-Neng Gao

Improved analysis of rare <italic>Z</italic>-boson decays into a heavy vector quarkonium plus lepton pair

Phantom divide line transitions are not possible in the context of single scalar field scalar-tensor theories. In this article we study a combined framework of a tachyonic minimally coupled single scalar field theory in the presence of an <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math> correction term and with a rescaled Einstein-Hilbert term of the form <math altimg='si6.svg'><mrow><mo>&#8764;</mo><mi>&#955;</mi><mfrac><mi mathvariant='script'>R</mi><mrow><mn>16</mn><mi>&#960;</mi><mi>G</mi></mrow></mfrac></mrow></math>. Such terms can be part of an <math altimg='si7.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>)</mo></mrow></math> gravity which in the large curvature regime yields such correction terms effectively. Alternatively, such terms can simply be quantum corrections to the scalar field action. We aim to answer two questions, firstly if this framework can lead to phantom divide line transitions and secondly whether the resulting model can be compatible with the ACT data. The model we studied is an inverse square power-law model, well known from tachyon inflation models. As we show, the field equations can be cast in terms of the scalar field solely, however the resulting theory is distinct from a single scalar field theory, because the phantom divide line is crossed during inflation. Thus initially the tachyonic nature of the scalar field generates a phantom equation of state parameter, and during inflation the phantom divide line is crossed, with the effective equation of state parameter at the end of inflation being <math altimg='si8.svg'><mrow><mi>w</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><mn>3</mn></mrow></math> which corresponds to the non-accelerating state of the Universe. The model is proved to be compatible with the ACT data, only when the gravity during inflation is stronger than Einstein-Hilbert gravity, with the effective gravitational constant during inflation being <math altimg='si9.svg'><mfrac><mi>G</mi><mi>&#955;</mi></mfrac></math>. The effective theory is valid only during inflation, thus Big-Bang nucleosynthesis is not affected by the rescaling of the Einstein-Hilbert gravity. The feature of a phantom crossing in <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>&#981;</mi><mo>)</mo></mrow></math> frameworks is new in the literature.

Spain

S.D. Odintsov

Greece

V.K. Oikonomou

<math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected Tachyon Scalar Field Inflation, the ACT Data, and Phantom Transition

In this paper we propose two sets of nonlinear integral equations (NLIE) for describing the thermodynamics in the sine-Gordon model, when higher Lorentz spin conserved charges are also coupled to the Gibbs ensemble. We call them NLIE I and II. The derivation of the equations, is based on <math altimg='si7.svg'><mrow><mi>T</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>Q</mi></mrow></math> relations given by the equivalent thermodynamic Bethe ansatz (TBA) formulation of the problem in the repulsive regime. Though the equations are derived in the repulsive regime at discrete values of the coupling constant, a straightforward analytical continuation ensures their validity within the whole repulsive regime of the theory. For the NLIE I formulation, appropriate analytical continuation makes the penetration into the attractive regime also possible. However, the magnitude of this penetration is restricted by the spin of the largest spin conserved charge contained in the Gibbs ensemble. Within their range of validity, these NLIE formulations provide efficient theoretical frameworks for computing expectation values of conserved charge densities, their associated currents, and vertex operators and their descendants, with respect to the generalized Gibbs ensemble.

Hungary

Árpád Hegedűs

NLIE formulations for the generalized Gibbs ensemble in the sine-Gordon model

In this paper, we develop a method to extract the Bekenstein-Hawking entropy of <italic>D</italic>-dimensional black holes using the entanglement entropy of a lower-dimensional conformal field theory (CFT). This approach relies on two key observations. On the gravitational side, the near-horizon geometry of extremal black holes is AdS <inf>2</inf>, and the Bekenstein-Hawking entropy is entirely determined by this two-dimensional geometry. Moreover, the higher-dimensional spherical part of the black hole metric is absorbed into the <italic>D</italic>-dimensional Newton&#8217;s constant <math altimg='si3.svg'><msubsup><mi>G</mi><mrow><mi>N</mi></mrow><mrow><mo stretchy='true'>(</mo><mi>D</mi><mo stretchy='true'>)</mo></mrow></msubsup></math>, which can be effectively reduced to a two-dimensional Newton&#8217;s constant <math altimg='si4.svg'><msubsup><mi>G</mi><mrow><mi>N</mi></mrow><mrow><mo stretchy='true'>(</mo><mn>2</mn><mo stretchy='true'>)</mo></mrow></msubsup></math>. On the field theory side, the entanglement entropy of two disconnected one-dimensional conformal quantum mechanics (CQM <inf>1</inf>) can be calculated. According to the Ryu-Takayanagi (RT) prescription, this entanglement entropy computes the area of the minimal surface in the AdS <inf>2</inf> geometry. Since the near-horizon region of the black hole and the emergent spacetime derived from the entanglement entropy share the same Penrose diagram&#8212;with both the black hole event horizon and the RT surface corresponding to specific points on this diagram&#8212;the Bekenstein-Hawking entropy can be probed via entanglement entropy when these points coincide. This result explicitly demonstrates that the entanglement across the event horizon is the fundamental origin of the Bekenstein-Hawking entropy.

Shuxuan Ying

Probing black hole entropy via entanglement

The interaction problem between solitons and mean flows including the dispersive shock wave, rarefaction wave, kink and contact dispersive shock wave, is discussed in the framework of the Gardner equation, a generic non-convex mathematical model containing quadratic-cubic nonlinear terms, describing the dynamics of internal waves for an arbitrary vertical stratification of the density field. Based on the augmented solitonic modulation system constructed in a Riemann invariant form, two main interaction regimes are identified: soliton tunneling and soliton trapping. Furthermore, kinks and flat-top solitons caused by the non-convexity, play dual roles as both mean flows and localised waves, imparting polarity reversal to solitons and mean flows. Specially, flat-top solitons formed by the quadratic-cubic nonlinear competition, can be considered as a combination of kinks and antikinks, and induce polarity reversal to solitons and mean flows twice, which is an evidence of elastic collisions between flat-top solitons and bell solitons. In addition, the shape of flat-top solitons is changed after the interaction with mean flows. A full classification of the interaction problem is given for both signs of the cubic nonlinear term in the Gardner equation, and numerical simulations agree with modulation theory predictions.

Jia-Xue Niu

Rui Guo

Jian-Wen Zhang

Soliton–mean flow interaction problem for a non-convex system with quadratic-cubic nonlinearity in the stratified fluid

Thermodynamics stability of various higher (five) dimensional black holes such as Euler-Heisenberg, non-linear electrodynamic, and Yang-Mills massive gravity is being investigated. Thermodynamic topology along with stability within their respective parameter spaces will also be addressed by employing exponential corrected entropy (non-extensive entropy). We manifest first-order phase transitions by finding critical points and topological charges through the <italic>&#981;</italic>-mapping method. Our comprehensive thermodynamic analysis incorporates key variables such as pressure, temperature volume and free energy. We observe notable result is the critical role played by the QED parameter ( <italic>a</italic>) in Euler-Heisenberg black holes, which determines the existence of two distinct topological classes. It is also noted that non-linear electrodynamic fields inspired black holes parameters does not impact on the number of critical points or topological classes. For Yang-Mills black hole in massive gravity, it is found that there exists a unique topological structure with one critical point that depends on corresponding black hole parameter.

Muhammad Usman

Shahid Chaudhary

Abdul Jawad

Uzbekistan

Sanjar Shaymatov

Iran

Saeed Noori Gashti

Mohammad Ali S Afshar

Mohammad Reza Alipour

Jafar Sadeghi

Probing topological thermodynamics of specific black holes inspired by corrected entropy