This article explores how modifications to gravity influence the structure of the brane, with the goal of identifying the gravitational model that most closely reflects the one governing our physical universe. To achieve this, we consider a generalization of standard General Relativity. The stability of the model is evaluated through probabilistic measurements, revealing minimum points that represent the most probable and stable configurations of the brane for different values of the gravitational terms. Furthermore, the location of fermions on the brane is affected by gravitational variations, with the presence of resonance modes and the possibility of leakage of massive fermions into the bulk. Numerical analyses are presented, showing that the increase in the influence of gravitational terms increases the certainty of the location of massless fermions on the brane. All these results provide important insights for understanding the dynamics of the braneworld universe.

China

Brazil

A.R.P. Moreira

Mexico

Shi-Hai Dong

Braneworld- <italic>f</italic>( <italic>R</italic>, <italic>T</italic>, <italic>G</italic>)

We present an analytic reconstruction of one-loop amplitudes for the process $$ 0\to \overline{q} qt\overline{t}H $$ . Our calculation is a novel use of analytic reconstruction, retaining explicit covariance in the massive spin states through the massive spinor-helicity formalism. The analytic reconstruction relies on embedding the massive five-point kinematics in a fully massless eight-point phase space while still building a minimal ansatz directly in the five-point phase space. In order to obtain compact analytic expressions it is necessary to identify suitable partial fraction decompositions and extract common numerator factors, which we achieve through careful inspection of limits in which pairs of denominators vanish. We find that the resulting amplitudes are more numerically efficient than ones computed using automatic methods but that the gains are not as significant as in the massless case, at least at present. The method opens the door to applications at two-loop order, where numerical efficiency and improvements in the reconstruction methodology are more crucial, especially with regards to the number of free parameters in the ansatz.

United States

John Campbell

United Kingdom

Giuseppe Laurentis

R. Ellis

Analytic reconstruction with massive particles: one-loop amplitudes for $$ 0\to \overline{q} qt\overline{t}H $$

In recent years, the holographic duality between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed conformal field theory (CFT) and Anti-de Sitter (AdS) spacetime with finite radial cutoff has received significant attention. The study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math> deformation within the framework of de Sitter (dS)/CFT duality has also progressed. This paper shows that the trace flow equation in dS spacetime can be analytically extended from its AdS counterpart through double Wick rotations. Meanwhile, we generalize the replica method in both AdS and dS holography to derive a general expression for the entanglement entropy of arbitrary single spatial intervals within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed framework. For both finite size and finite temperature systems, we obtain the analytical expression for the entanglement entropy after <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math> deformation. Finally, in dS/dS holography and half-dS holography, we find that the dual field theory exhibits nonlocality by analyzing the strong subadditivity and boosted strong subadditivity of entanglement entropy.

Jing-Cheng Chang

Germany

Song He

Yu-Xiao Liu

Long Zhao

Holographic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math> deformation of the entanglement entropy in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">A</mi><mo stretchy="false">)</mo><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>

This study explores wormhole solutions within two distinct modified gravity theories, namely <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity and <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, incorporating Bose-Einstein condensate (BEC) dark matter to analyze their geometric properties. The primary objective is to comprehensively compare wormhole characteristics in these frameworks under the influence of BEC matter. The derived shape functions satisfy all fundamental traversability conditions. Furthermore, we examine the energy conditions, revealing that the NEC holds in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity but is violated in <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, highlighting the contrasting nature of wormhole solutions in these theories. Additionally, we investigate the effects of anisotropy, active gravitational mass, and surface diagram of wormhole geometries. Our findings confirm the existence of physically viable and stable wormhole models within these modified gravity theories.

India

Chaitra Chooda Chalavadi

H. Aruna Kumara

V. Venkatesha

Probing the geometries of wormholes: A comparative study of <italic>f</italic>( <italic>R</italic>, <italic>T</italic>) and <italic>f</italic>( <italic>Q</italic>, <italic>T</italic>) theories in the presence of BEC matter

The current paper reports an investigation of a warm inflationary scenario in the context of $\textit{f}$($\textit{T}$) gravity for a spatially flat FLRW universe. In our model, inflation is driven purely by the torsional sector of $\textit{f}$($\textit{T}$) gravity, without introducing any additional scalar fields. We focus on the high dissipative regime ( $$R \gg 1$$ ), reconstruct the Hubble parameter as a function of the e-folding number $\textit{N}$, and derive the slow-roll parameters $$\varepsilon _1(N)$$ and $$\varepsilon _2(N)$$ . The study has encapsulated the dynamics of inflation and its duration under strong dissipation. The dissipative coefficient $$\Gamma $$ is modeled with a temperature-dependent power-law form, linking the inflationary dynamics to thermal corrections and the particle content of the early universe. The analysis has affirmed that the torsion-induced energy density $$\rho _T$$ successfully transitions to radiation energy density $$\rho _{rad}$$ , facilitating a graceful exit from inflation. Finally, we have validated our model by comparing the scalar spectral index and tensor-to-scalar ratio with Planck 2018 results, demonstrating consistency within observational bounds. Additionally, it is verified that the thermal domination condition $$T_{*}/H > 1$$ and the torsion dominance condition $$\rho _T/\rho _{rad} > 1$$ are satisfied.

Moli Ghosh

Türkiye

Can Aktaş

Surajit Chattopadhyay

Reconstructing $\textit{f}$($\textit{T}$) gravity and exploring the torsion driven warm inflationary cosmology

We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $\textit{W}$ boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or $\textit{Z}$-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external $\textit{W}$ boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator $\textit{ϵ}$ for sectors where these analytic structures appear, and are $\textit{ϵ}$-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions.

Italy

Matteo Becchetti

Dhimiter Canko

Vsevolod Chestnov

Tiziano Peraro

Mattia Pozzoli

Switzerland

Simone Zoia

Two-loop Feynman integrals for leading colour $$ t\overline{t}W $$ production at hadron colliders

We discuss prompt production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mesons in proton-proton collisions at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mrow><mn>68.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> energy within the nonrelativistic quantum chromodynamics <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>k</mi><mi>t</mi></msub></math>-factorization approach using different unintegrated gluon distribution functions (UGDFs). We include both direct color-singlet production (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mi>g</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>g</mi></math>) as well as a feed-down from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ψ</mi><mo>′</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>X</mi></math> decays. The production of the decaying mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mi>c</mi></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ψ</mi><mo>′</mo></msup></math> is also calculated within the nonrelativistic quantum chromodynamics <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>k</mi><mi>t</mi></msub></math>-factorization approach. Differential distributions in the rapidity and transverse momentum of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> are calculated and compared with experimental data of LHCb collaboration. The LHCb fixed target data allow us to test UGDFs in a new range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>.

Poland

Anna Cisek

Antoni Szczurek

Prompt inclusive production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ψ</mi><mo>′</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mi>c</mi></msub></math> mesons at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>68.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> energy within the NRQCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>k</mi><mi>t</mi></msub></math>-factorization approach

In this study, we explore the realization of spherically symmetric solutions in the context of modified teleparallel gravity, particularly in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> theory, where <math altimg='si2.svg'><mi mathvariant='script'>T</mi></math> denotes the torsion scalar. Traditional mimetic gravity and its extension using two scalar fields fail to reproduce general spherically symmetric spacetimes within <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> gravity due to the requirement of a constant torsion scalar or a linear form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math>, which restricts the theory to the teleparallel equivalent of general relativity (TEGR). To address this limitation, we propose a four-scalar field model that extends the two-scalar framework, allowing the construction of arbitrary spherically symmetric spacetimes. We show that this model eliminates ghost degrees of freedom through suitable constraints enforced by Lagrange multipliers. As a test of our procedure, we consider a specific form of a spherically symmetric spacetime and derive the associated four scalars, analyzing their behavior. Within the framework of a quadratic correction term, <math altimg='si3.svg'><mi mathvariant='script'>T</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mfrac><mrow><mi>&#945;</mi></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi mathvariant='script'>T</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, our method demonstrates the ability to reconstruct physically relevant solutions with non-ghost scalar fields. These results underscore the broader applicability of scalar field models in constructing viable geometries within modified gravity theories, extending beyond the scope of standard formulations.

Egypt

South Africa

G.G.L. Nashed

Saudi Arabia

A. Eid

Four-scalar model and spherically symmetric solution in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> theory

In this Letter, we demonstrate that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-odd and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-even correlations, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> representing time reversal, when satisfying specific conditions, result, respectively, in cosine and sine strong phase dependencies of the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. Additionally, we identify pairs of these <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation observables in hadron decays depend on precisely the same strong phases within the helicity amplitude scheme. This complementarity could reduce the strong phase reliance in the study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation while also mitigating the risk of suppressed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation due to exceptionally small strong phases. Moreover, our proposal holds broad application prospects in further investigating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in baryon decays, which has recently been discovered in the LHCb experiment.

Jian-Peng Wang

Qin Qin

Fu-Sheng Yu

Complementary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation induced by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-odd and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-even correlations

Our paper examines effect of the recently developed <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory on a structure of dense objects containing dense matter distribution. For this purpose, we consider viable solutions to study the interior region of considered compact stars. With the Darmois constraints we evaluate unidentified constants of metric coefficients. Additionally, assume a precise <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory model to reduce complication of the system and obtain explicit equation of matter contents that further used to investigate various physical parameters in the interior of considered compact objects. The equilibrium state for dense compact stars is determined by the TOV equations. The stability state for the compact stars is determined by the causality method. We finalize that the anisotropic spheres in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory background are feasibly stable.

Azerbaijan

M. Zeeshan Gul

Pakistan

M. Sharif

Adeeba Arooj

Faisal Javed

Analysis of physical aspects in the interior of static spherical spacetime admitting Durgapal-IV spacetime in <italic>f</italic>( <italic>Q</italic>,T) theory