Polarization is a prominent feature of gravitational wave observations and can be used to distinguish between different modified gravity theories. Compared to General Relativity, $\textit{f}$($\textit{R}$) gravity exhibits an additional polarization originating from a scalar field, which is a combination of the longitudinal and breathing modes. When the scalar mass of $\textit{f}$($\textit{R}$) is zero, the mixed mode will reduce to a pure breathing mode with the disappearance of the longitudinal mode. However, this reducing seems to be disallowed because a positive scalar mass is often required to maintain the stability of the cosmological perturbation. In fact, the massless scalar case can provide a stable perturbation, but more detailed constraints need to be considered. For the completeness of the polarization analysis, we explore the possibility that there are stable massless scalar polarizations in viable dark energy $\textit{f}$($\textit{R}$) models. We find that the existence of stable massless scalar polarization depends on the structure of $\textit{f}$($\textit{R}$) model and can be used to distinguish different models in $\textit{f}$($\textit{R}$) gravity.

China

Xin-Dong Du

Peng-Cheng Li

Stable massless scalar polarization of $\textit{f}$($\textit{R}$) gravity

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

We have addressed here the problem of calculating the correlation function of a stable particle with a resonance, in particular one resonance that qualifies as a molecular state of two components. The formalism used requires us to evaluate the scattering matrix of the stable particle with the molecule, a nuclear problem which we address by means of the fixed center approximation. We have applied the method to the interaction of a proton with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> resonance, presently under investigation by the ALICE collaboration, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> is taken as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>−</mo><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mi>K</mi></math> molecule. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> interaction develops a resonance state below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> threshold, which leads to a depletion in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> correlation function for small values of the proton momentum. The discussion presented shows that these type of studies can provide much information on the nature of some resonances and the existence of three-body bound states involving mesons and baryons.

Spain

P. Encarnación

A. Feijoo

E. Oset

Correlation function for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></mrow></math> interaction

In this article, we explore an anisotropic model to describe the Buchdahl compact star with a spherically symmetric matter distribution within the framework of modified <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> gravity. To achieve this, we consider the Starobinsky model <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, where <italic>&#945;</italic> is a model parameter. To solve the Einstein Field equations, we adopt the embedded class-I geometry that satisfies the Karmarkar condition. Our analysis includes the generalized Darmois-Israel junction conditions, which are crucial for seamlessly matching the star's interior to the Schwarzschild exterior metric at the boundary in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> gravity. These conditions have been employed to calculate the constant parameters by analyzing observational data from multiple compact stars, including <italic>Cen X-3, PSR J1903+327, Vela X-1</italic>, and <italic>PSR J1614-2230</italic>. This novel approach enables us to conduct a detailed analysis of Buchdahl compact star models and assess their physical viability. We also perform various physical tests, including equilibrium conditions and stability to evaluate the models' validity. The analysis of mass and radius reveals that the <math altimg='si3.svg'><mi>M</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mi>R</mi></math> relationship is based on the Buchdahl limit and is sensitive to variations in the parameter <italic>&#945;</italic>. With <math altimg='si4.svg'><mi>&#945;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math> representing General Relativity, the maximum mass and radius for different <italic>&#945;</italic> values were calculated and compared with observational data from the five aforementioned neutron stars. The range of maximum mass and radii are: <math altimg='si5.svg'><mo stretchy='false'>[</mo><mn>2.51</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>2.54</mn><mspace width='0.25em' /><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub><mo stretchy='false'>]</mo></math> and <math altimg='si6.svg'><mn>8.71</mn><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mn>9.33</mn><mspace width='0.25em' /><mtext>km</mtext></math>. The obtained values of radii align well with observed neutron star radii in X-ray binaries from spectroscopic studies, confirming the validity of the model.

India

Rajesh Kumar

Oman

S.K. Maurya

Y. Sekhmani

Saudi Arabia

Akram Ali

Uzbekistan

Farruh Atamurotov

Anisotropic compact stars in quadratic <italic>f</italic>( <italic>R</italic>) gravity and influence of quadratic parameter on properties of compact stars

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> decays from a data sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>27.12</mn><mo>±</mo><mn>0.14</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>8</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></mrow></math> events collected by the BESIII detector at the BEPCII collider, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math> radiative decays to multiple light hadrons below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.8</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>—<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>η</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mn>2</mn><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math>—are observed for the first time, each with a significance greater than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>. The corresponding branching fractions are measured. Furthermore, intermediate states are investigated, leading to the first observation of the decay process of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> with a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.1</mn><mi>σ</mi></math>. This observation represents the first instance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math> radiative decay to a tensor state.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

G. Chelkov

C. Chen

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

Observation of Charmonium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> Radiative Decays to Multiple Light Hadrons and the Tensor State <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math>

We show that <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> cosmology with a non-trivial connection, namely the Connection II of the literature, is dynamically equivalent with a quintom-like model. In particular, we show that the scalar field arising from the non-linear <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> form, and the scalar field associated to the non-trivial connection, are combined to provide one canonical and one phantom field in the minisuperspace Lagrangian. Hence, the combination of two well-behaved fields appears effectively as a phantom field. This is fundamentally different from the usual approach in phantom and quintom cosmology, in which the phantom field is introduced ad hoc, and thus it may open a new way to handle the phantom fields, namely as effective realizations of the connection-related canonical fields.

Greece

Cyprus

Spyros Basilakos

Chile

South Africa

Andronikos Paliathanasis

Emmanuel N. Saridakis

Equivalence of <italic>f</italic>( <italic>Q</italic>) cosmology with quintom-like scenario: The phantom field as effective realization of the non-trivial connection

In this paper, we evaluate the complexity of the non static cylindrical geometry with anisotropic matter configuration in the framework of modified Gauss–Bonnet theory. In this perspective, we calculate modified field equations, the $\textit{C}$ energy formula and the mass function that help to understand the astrophysical structures in this modified gravity. Furthermore, we use the Weyl tensor and obtain different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $$Y_{TF}$$ is referred to as the complexity factor. This parameter measures the system’s complexity due to non-uniform energy density and non-isotropic pressure. We select the identical complexity factor for the structure as used in the non-static scenario, while considering the analogous criterion for the most elementary pattern of development. This technique involves formulating structural scalars that illustrate the fundamental features of the system. A fluid distribution that satisfies the vanishing complexity requirement and evolves homologously is characterized as isotropic, geodesic, homogeneous, and shear-free. In the dissipative scenario, the fluid remains geodesic while exhibiting shear, resulting in an extensive array of solutions.

M. Gul

W. Ahmad

M. Nasir

Kuwait

Orhan Donmez

Bander Almutairi

Study of complexity factor and stability of dynamical systems in $$f(\mathcal {G})$$ gravity

We study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave single charmed baryons of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mn mathvariant="bold">3</mn><mo stretchy="false">¯</mo></mover><mi mathvariant="bold">F</mi></msub></math> within the framework of heavy quark effective theory. We systematically calculate their strong and radiative decay properties using the light-cone sum rule method. Besides the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2595</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2625</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2790</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2815</mn><mo stretchy="false">)</mo></math>, our results suggest the existence of two additional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> baryons and two additional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> baryons. Their masses, mass splittings within the same multiplets, and decay properties are summarized in for future experimental searches.

Xuan Luo

Yi-Jie Wang

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave single charmed baryons of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mn mathvariant="bold">3</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi mathvariant="bold">F</mi></mrow></msub></mrow></math>

This work presents a novel characterization of complexity for gravitationally bound astrophysical configurations arising from two factors: (i) inhomogeneity and (ii) anisotropy in the complex arrangement of stellar structures. For this purpose, we employ the non-metricity-motivated gravitational model with a linear choice of coincident gauge $$f(\mathbb {Q})$$ gravity, given by $$f(\mathbb {Q}) = \beta _0 \mathbb {Q} + \beta _1$$ , where $$\beta _0$$ and $$\beta _1$$ are model parameters. Our analysis begins by postulating that a fluid distribution exhibiting density uniformity and pressure isotropy is characterized by a minimal (or zero) gravitational complexity factor. The novelty of this study lies in its ability to study the effect of non-metricity on the intricate mechanism of dense-matter static stars while also considering the effectiveness of the complexity factor in determining fluctuations in the Tolman mass for both complex and non-complex compact structures within a non-metricity framework. The variation in the Tolman gravitational mass is caused by a suggested formulation of anisotropic pressure and density non-uniformity. It is observed that in Einstein’s gravitational model, a stellar system that features both can exhibit zero complexity ( $$Y_{TF}=0$$ ) if their contributions cancel out. On the other hand, the linear $$f(\mathbb {Q})$$ model compels the gravitational configuration to maintain $$Y_{TF}\ne 0$$ due to non-metricity contributions, even when the fluid exhibits density uniformity and pressure anisotropy. Furthermore, we discuss the construction of anisotropic self-gravitating polytropes by coupling the $$Y_{TF}=0$$ condition with a polytropic EoS. This underscores the importance of the zero-complexity criterion in modeling astrophysical compact systems.

Abeer Albalahi

Akbar Ali

M. Bhatti

Gravitational complexity factor of anisotropic polytropes in coincident gauge $$f(\mathbb {Q})$$ gravity

In this work, we present a $\textit{f}$($\textit{G}$, $\textit{T}$) gravity-based reconstruction of Barrow Holographic Dark Energy (BHDE). This approach extends the conventional HDE model by replacing the standard Bekenstein–Hawking entropy with Barrow entropy, which encapsulates quantum gravitational corrections to the geometry of black hole horizons. We explore the cosmological dynamics of a spatially flat Friedmann–Robertson–Walker background filled with a pressureless dust fluid, considering both conserved and non-conserved energy–momentum tensor models. To this end, we employ the Hubble horizon as the infrared cutoff and adopt a power-law ansatz for the scale factor. We then investigate the evolution of key cosmological parameters, including the equation-of-state parameter $$ \omega _{GT} ,$$ the deceleration parameter $\textit{q}$, and the squared sound speed $$ v_s^2 .$$ Furthermore, we explore the dynamical behavior in the $$ \omega _{GT} $$ - $$ \omega '_{GT} $$ phase space. In the case of conserved energy–momentum tensor, our findings indicate that the BHDE model evolves from a quintessence-like regime into the phantom domain. This transition supports the current accelerated expansion of the Universe and offers an improvement over the original HDE model, which does not adequately account for the observed phenomenology. The corresponding $$ \omega _{GT} $$ - $$ \omega '_{GT} $$ trajectory lies within the freezing region of the phase space. On the other hand, within the non-conserved framework, the BHDE model exhibits phantom-like behavior in the early Universe, subsequently evolving toward either a cosmological constant-like state or a quintessence-like regime. Notably, unlike the conserved scenario, the squared sound speed $$ v_s^2 $$ asymptotically attains positive values in the far future, signifying a stable configuration. Moreover, the trajectory in the $$ \omega _{GT} $$ - $$ \omega '_{GT} $$ phase space displays a thawing behavior. Finally, we evaluate the observational viability of our results and compare them with predictions from alternative reconstructed dark energy models.

Giuseppe Luciano

Quantum entropy-driven modifications to holographic dark energy in $\textit{f}$($\textit{G}$, $\textit{T}$) gravity