We have made a thorough study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>η</mi><mi>η</mi></math> reaction, recently measured by the Beijing Spectrometer III Collaboration, which shows an abnormal strength at high invariant masses in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>η</mi></math> mass distribution. We studied in detail the triangle mechanism and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> excitation modes that have been suggested to explain this abnormal feature, and concluded that they are too small to have any important role in the solution to that problem. We have also studied other possible solutions, evaluating the contribution of excitations of other <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub></math> resonances, and reached the same conclusion. Unexpectedly, the solution to the problem is found considering the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> excitation, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> decaying to two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>, which is tied to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> production, and well under control. At the same time, the consideration of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> excitation solves another nonreported problem, which is the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>η</mi></math> mass distribution that comes when only the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> resonance is allowed to be excited, which produces a large deficiency at low invariant masses compared with experiments.

China

Spain

Jing Song

Yi-Yao Li

Türkiye

Melahat Bayar

Eulogio Oset

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> excitation in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>η</mi><mi>η</mi></math> decay

In this work, we investigate neutron stars (NSs) in the strong field regime within the framework of symmetric teleparallel $\textit{f}$($\textit{Q}$) gravity, considering three representative models: linear, logarithmic, and exponential. While Bayesian studies of NS observations are well established in general relativity and curvature based modified gravity theories, such analyses in $\textit{f}$($\textit{Q}$) gravity remain largely unexplored. For the first time we perform a Bayesian inference analysis by confronting theoretical NS mass-radius predictions with NICER observations of PSR J0030+0451, PSR J0740+6620, PSR J0437+4715, and PSR J0614+3329 in the background of nonmetricity based gravity. The dense matter equation of state is fixed to DDME2 in order to isolate the effects of modified gravity on NS structure. Our results indicate a statistical preference for the exponential $\textit{f}$($\textit{Q}$) model over the linear and logarithmic cases, as supported by the Bayes-factor analysis, and show that its parameters are comparatively well constrained. For this model, we obtain a radius and tidal deformability at $$1.4\,M_\odot $$ of $$R_{1.4} = 11.27^{+0.53}_{-0.36}\,\textrm{km}$$ and $$\varLambda _{1.4} = 156.95^{+84.02}_{-41.73}$$ , respectively, consistent with current observational constraints. The median values of the maximum mass are found to be around $$M_{\max }\approx 2.3M_\odot $$ for all three constrained models. However, the upper parts of the 95% credible regions of the mass-radius relations extend beyond $$2.5M_\odot $$ and approach $$\sim 3M_\odot $$ within the adopted framework. This indicates the possibility of comparatively massive stable compact configurations in the Bayesian constrained parameter space. These results highlight the potential of NSs as powerful probes of symmetric teleparallel gravity in the strong field regime. We note that these results are conditional on the use of a fixed DDME2 equation of state and the coincident-gauge formulation adopted in this work.

India

Sneha Pradhan

N. Patra

Kai Zhou

P. Sahoo

Bayesian inference of neutron star properties in $\textit{f}$($\textit{Q}$) gravity using NICER observations

In this work, Static wormhole models are examined within the framework of curvature-based <math altimg='si17.svg'><mrow><mi mathvariant='italic'>f</mi><mo>(</mo><mi mathvariant='fraktur'>R</mi><mo>,</mo><msub><mi mathvariant='fraktur'>L</mi><mi mathvariant='fraktur'>m</mi></msub><mo>,</mo><mi mathvariant='italic'>T</mi><mo>)</mo></mrow></math> gravity theory. A relationship between the matter energy density and pressure is proposed for the Morris-Thorne wormhole geometry with a constant redshift function. By incorporating a gradient-dependent equation of state ( <math altimg='si18.svg'><mrow><msub><mi>P</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>P</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>&#961;</mi><mo>,</mo><msup><mi>&#961;</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> and <math altimg='si19.svg'><mrow><msub><mi>P</mi><mi>t</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>P</mi><mi>t</mi></msub><mrow><mo>(</mo><msub><mi>P</mi><mi>r</mi></msub><mo>,</mo><msubsup><mi>P</mi><mi>r</mi><mo>&#8242;</mo></msubsup><mo>)</mo></mrow></mrow></math>), we derive exact wormhole solutions for two representative cases. Our analysis shows that exact wormhole models can admit null energy condition violations localized at the throat, while preserving a non-negative matter energy density. The stability analysis is performed via the Tolman&#8211;Oppenheimer-Volkoff equation under hydrostatic equilibrium, demonstrating that the balance among anisotropic and hydrostatic forces sustains the wormhole&#8217;s stable configuration. For positive and negative values of <italic>&#950;</italic>, the energy flux attains a pronounced negative magnitude, inducing an outward flux that supports the stability of the wormhole throat. The geometric characteristics of the wormhole are examined through embedding diagrams, and the total exotic matter required to maintain the configuration is evaluated using the volume integral quantifier. Simultaneously, the effective potential demonstrates enhanced photon confinement and increased stability of particle orbits.

Sweeti Kiroriwal

Azerbaijan

Oman

S.K. Maurya

Jitendra Kumar

Wormholes generated by a density-gradient dependent equation of state in <math altimg='si17.svg'><mrow><mi mathvariant='italic'>f</mi><mo>(</mo><mi mathvariant='fraktur'>R</mi><mo>,</mo><msub><mi mathvariant='fraktur'>L</mi><mi mathvariant='fraktur'>m</mi></msub><mo>,</mo><mi mathvariant='italic'>T</mi><mo>)</mo></mrow></math> gravity

In view of the recent theoretical developments in the fixed center approximation for the scattering of a particle with a a two-body cluster, implementing elastic unitarity on the standard fixed center formalism, and the imminent availability of ALICE data on the correlation function of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mtext> </mtext><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> system, we update the results of a previous work for this correlation function and the low-energy scattering observables. The new results show appreciable changes in some observables and should provide valuable input for comparison with the forthcoming experimental data. Such a comparison is expected to yield relevant information on the nature of the axial-vector meson states.

P. Encarnación

A. Feijoo

E. Oset

Scattering observables and correlation function for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> <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> revisited

We suggest a new duality between a pair of 3d $$ \mathcal{N} $$ = 5 SCFTs, one of ABJ type and one based on the exceptional superalgebra $\textit{F}$ (4). Our main evidence for the proposed duality is the matching of the superconformal index. In addition to the intrinsic interest in dualities between strongly coupled field theories, the result can also be useful in the classification of 3d $$ \mathcal{N} $$ = 5 SCFTs.

Israel

Ki-Hong Lee

Belal Nazzal

Gabi Zafrir

A note on dualities of F(4) type 3d $$ \mathcal{N} $$ = 5 SCFTs

We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $\textit{f}$($\textit{R}$) model $$f(R)=R+\alpha R^2$$ . We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $$\alpha $$ . For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. We then use these results to infer the expected trend in the PBH formation threshold $$\delta _c$$ , rather than a direct quantitative determination. Within this perturbative framework, the quadratic correction modifies the dust collapse dynamics at first order, while the flat radiation-dominated background does not receive a nontrivial correction at the same order. As result, any modification of PBH formation in the radiation era must arise from nonlinear or non-perturbative effects. The perturbative analysis therefore provides qualitative insight into how curvature corrections influence collapse, particularly in high-curvature regimes. To access this regime we reformulate the theory in the Einstein frame, where the model becomes GR plus the scalaron field $$\phi $$ with the Starobinsky potential. We provide the complete ODE system governing both the cosmological background and the evolution of an overdense closed FLRW patch. This system can be numerically integrated to obtain the critical overdensity $$\delta _c(k)$$ for PBH formation near the end of inflation.

Egypt

G. Nashed

Saudi Arabia

A. Eid

Primordial black hole formation in $$f(R)=R+\alpha R^2$$ gravity: perturbative and non-perturbative analysis

We employ the island formula to investigate the entanglement entropy of the Hawking radiation in an asymptotically AdS black hole background within the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity. Through an analysis based on the Euclidean action, we find that the area term of the generalized entropy must be modified, which in turn leads to a modification of the island formula. Using the modified formula to compute the radiation entropy for an eternal asymptotically AdS black hole reveals that, the result diverges as the cutoff surface is moved outward, indicating the breakdown of the <italic>s</italic>-wave approximation. A possible reason is that we have neglected the gravitational back-reaction. For a collapsing asymptotically AdS black hole, the radiation entropy is dominated by the area term, with a correction proportional to the logarithm of the event horizon area, which is consistent with the predictions of quantum gravity. Both the radiation entropy and the Page time are ultimately influenced by the choice of the <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> model, implying that the information regarding the underlying gravitational model is encoded in the final radiation.

Yipeng Liu

Wei Xu

Baocheng Zhang

Radiation entropy in asymptotically AdS black holes within <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity

We study the natural scheme-independent quantity obtained from the three-sphere partition function of a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional quantum field theory by removing all local counterterm ambiguities. At conformal fixed points this quantity equals the standard <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-theorem invariant. Conformal perturbation theory shows that it locally decreases at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msup><mi>g</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> under any relevant scalar deformation of a three-dimensional Conformal Field Theory. However, an exact analysis of the free massive scalar on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mn>3</mn></msup></math> shows that this sphere-free-energy interpolant is not monotone along the full renormalization-group flow: it dips below its infrared value and then returns to it. Thus the natural counterterm-subtracted quantity built from sphere thermodynamics is not, by itself, a monotone <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-function. We trace the obstruction to the second-order differential operator required to eliminate the local ambiguities.

Italy

Giacomo Santoni

Francesco Scardino

Scheme independent 3-sphere free energy is not a monotone <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-function

We constrain the Hu–Sawicki and Starobinsky $\textit{f}$($\textit{R}$) gravity models utilizing current electromagnetic (PantheonPlus + cosmic chronometers [PP+CC], Planck, and DESI2) datasets and simulate standard siren (SS) catalogs based on the resulting best-fit parameters. We demonstrate that the simulated SS data provide complementary sensitivity to the modified gravitational wave propagation friction term, thereby enhancing the discriminating power between $\textit{f}$($\textit{R}$) gravity and the $$\varLambda $$ CDM model. However, we note that standard sirens do not offer a viable resolution to the Hubble tension in this analysis, as the inferred constraints are predominantly driven by the fiducial cosmologies adopted in the simulations. Regarding the specific models, we find that for the Hu–Sawicki scenario, several data combinations favor $$F_{RR0}<0$$ , implying potential theoretical instabilities. And, for the Starobinsky model, while electromagnetic-only constraints are nearly symmetric between the two parameter branches ( $$b<0$$ and $$b>0$$ ), the inclusion of SS constraints introduces mild asymmetries, revealing the sensitivity of SS observables to the curvature dependence of the theory. Future truly independent standard siren observations would be crucial for a definitive assessment of $\textit{f}$($\textit{R}$) gravity as an alternative to $$\varLambda $$ CDM.

Yi Zhang

Xuanjun Niu

Xianfu Su

Dong-Ze He

The standard siren tests of viable $\textit{f}$($\textit{R}$) cosmologies

The present study analyzes anisotropic compact objects coupled with the electromagnetic field within the context of <italic>f</italic>( <italic>R, T</italic>) gravity. We obtain two novel solutions of modified field equations for a static charged spacetime. To simplify the system, we employ two different assumptions for the radial metric component and specific anisotropic pressure profiles, and obtain exact analytical solutions. The governing field equations in both models yield differential equations whose general solutions contain undetermined constants. These constants are evaluated through the junction conditions between the interior and the exterior Reissner-Nordstr&#246;m spacetimes across the boundary surface. In this regard, we also impose the condition that the radial pressure drops to zero on the star&#8217;s interface. Furthermore, we examine the fundamental prerequisites that must be fulfilled for physical existence of compact objects. For graphical analysis, we consider the observed data of two stars, LMC X-4 and SMC X-4, together with multiple parametric values. Our findings demonstrate that both resulting solutions satisfy the essential physical requirements under the considered modified gravitational framework for certain values of the charge and model parameter.

Pakistan

Hira Shadab

M. Sharif

Tayyab Naseer

Role of electric charge in the construction of relativistic stellar solutions in <italic>f</italic>( <italic>R, T</italic>) gravity