We investigate the direct $\rm CP $ violation in the decay $ D^\pm \to \pi^\pm \pi^+ \pi^- $ incorporating the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism. The integrated mixing intensities $ \overline \xi_{fa} $ and $ \overline \xi_{af} $ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $ \pi^+\pi^- $ pair lies near the $ f_0(980) $ resonance, this isospin-breaking mechanism can enhance the $\rm CP $ asymmetry. The enhancement is particularly pronounced when the $ f_0(980) $ carries a significant $ n\bar{n} $ quark component and the $ f_0(980) $ and $ \sigma(600) $ mixing angle is approximately $ 26^\circ $ . After accounting for non-factorizable effects, we find these corrections tend to partially cancel the leading-order contributions, resulting in a suppression of the $\rm CP $ violations relative to the naive factorization predictions. It is emphasized that the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism should be taken into account in both theoretical and experimental studies of $\rm CP $ violation in $\textit{B}$ or $\textit{D}$ meson decays.

China

Shi-Ji Cao

Jing-Juan Qi

Yi-Fan Zhao

Chao Wang

Zhen-Yang Wang

Xin-Heng Guo

Direct CP violation in ${ {\boldsymbol D}^{\bf\pm }\to {\boldsymbol\pi}^{\bf\pm} {\boldsymbol\pi}^{\bf +} {\boldsymbol\pi}^{\bf -}} $ with ${{\boldsymbol a}_{\bf 0}^{\bf 0}{\bf (980)-}{\boldsymbol f}_{\bf 0}{\bf (980)}} $ mixing * Supported by the National Natural Science Foundation of China (12405115, 12105149, 11805153, 12275024), and the High-Level Scientific Research Fund of Ningbo University (GJPY2026032)

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal {L}_{m},\Phi ,X)$$ class, an extension of $$f(R,\mathcal {L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi $$ , and its kinetic invariant $$X = g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi $$ . Working with the explicit model $$f = R + \mathcal {L}_{m} + (\lambda /2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi (x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$ , respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi \psi }<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal {L}_{m},\Phi ,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Türkiye

İzzet Sakallı

Are Petrov type-N and D spacetimes admitting CTCs valid in $$f(R,\mathcal {L}_m,\Phi ,X)$$ gravity?

In the present work, we studied the $$T_{\bar{c}\bar{s}1}^f(2750)$$ state production through the meson loop mechanism in the $$B^+$$ meson decays, where $$T_{\bar{c}\bar{s}1}^f(2750)$$ is considered as a $$\bar{D}K^*$$ molecular state with $$J^P=1^+$$ . By employing the effective Lagrangian approach, we estimated the branching ratio of the $$B^+ \rightarrow D^+ T_{\bar{c}\bar{s}1}^{f}(2750)$$ and $$B^+ \rightarrow D^{*+} T_{\bar{c}\bar{s}1}^f(2750)$$ processes and found them to be on the order of $$10^{-5}\sim 10^{-4}$$ . The fit fraction of $$T_{\bar{c}\bar{s}1}^f(2750)$$ in different processes was also estimated. We propose to search for $$T_{\bar{c}\bar{s}1}^f(2750)$$ in the $$B^+ \rightarrow D^{*+}\bar{D}^{*-}K^+$$ process, which should be accessible to the Belle II and LHCb Collaborations.

Zhuo Yu

Qi Wu

Zi-Li Yue

Dian-Yong Chen

$$T_{\bar{c}\bar{s}1}^f(2750)$$ production in the $$B^+$$ decays processes

We consider four-derivative superinvariants of five-dimensional $$ \mathcal{N} $$ = 2 supergravity coupled to $\textit{n}$ ≤ 2 vector multiplets, which we obtain from both the superconformal tensor calculus approach and dimensional reduction. For the minimal case, with no vector multiplets, it is known that there is a unique four-derivative superinvariant. However, for the case of one vector multiplet, after field redefinitions, we find that there are three independent superinvariants, one of which is a vector superinvariant that does not contain any curvatures and takes the form of a supersymmetrization of $\textit{F}$ . Similarly, for the two vector multiplet case, corresponding to the STU model, we find three gravitational superinvariants and two $\textit{F}$ -type vector superinvariants. Moreover, we find that these vector superinvariants do not affect the two- and three-charge static BPS black hole solutions. We further consider the rigid limit to $$ \mathcal{N} $$ = 2 super-Yang-Mills and use this to conjecture a family of vector superinvariants for five-dimensional $$ \mathcal{N} $$ = 2 supergravity coupled to an arbitrary number of vector multiplets.

United States

Yide Cai

Sabarenath Jayaprakash

James Liu

Yi Pang

Robert Saskowski

New $\textit{F}$ 4 invariants in five-dimensional supergravity

<p>Recent measurements of charmed-baryon semileptonic decays signal large tensions between experiment and theory, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> analyses and lattice-quantum chromodynamics simulations. Possible sources of the discrepancy include the experimental normalization mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math>. Using lattice-quantum chromodynamics inputs in an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> analysis including first-order symmetry breaking, we predict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.6</mn><mo>±</mo><mn>0.3</mn><mo stretchy="false">)</mo><mo>%</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.1</mn><mo>±</mo><mn>0.1</mn><mo stretchy="false">)</mo><mo>%</mo></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>+</mo></msup><mo>=</mo><mo stretchy="false">(</mo><msup><mi>e</mi><mo>+</mo></msup><mo>,</mo><msup><mi>μ</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>. These ratios provide normalization-independent tests and may help clarify the origin of the present tension.</p>

Chao-Qiang Geng

Chia-Wei Liu

Sheng-Lin Liu

Puzzles in charmed baryon semileptonic decays with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> flavor symmetry and lattice inputs

We investigate thick-brane configurations in five-dimensional $$f(T,T_G)$$ modified teleparallel gravity. In five dimensions, the torsional Gauss–Bonnet invariant $$T_G$$ contributes dynamically, leading to genuinely new effects even at linear order. Within a warped geometry supported by a scalar field, we construct explicit solutions and show that the $$T_G$$ sector significantly modifies the brane structure. In particular, the coupling parameter controls the deformation of the warp factor and energy density; for sufficiently negative values it can induce a genuine two-peak internal structure. We further analyze the localization of spin-1/2 fermions via a Yukawa coupling. For odd Yukawa functions the system admits a normalizable chiral zero mode, while the opposite chirality remains delocalized. The massive Kaluza–Klein spectrum is strongly affected by the torsional Gauss–Bonnet term, which modifies the effective potentials and leads to the appearance of resonant quasi-localized states. Our results show that $$f(T,T_G)$$ gravity provides a richer framework for braneworld models, where torsional higher-order corrections play a key role in shaping both geometry and field localization.

Brazil

A. Moreira

F. Belchior

Mexico

Shi-Hai Dong

Greece

Chile

E. Saridakis

Thick branes and fermion localization in five-dimensional $$f(T,T_G)$$ gravity

We present a rigorous theoretical and observational analysis of the Hybrid <italic>f</italic>( <italic>Q</italic>) class of models by including the late-time modifying 1/ <italic>Q</italic> term. After deriving strict viability conditions from the analytical expansion history, we show that preserving early-universe structure formation dictates that the linear coupling be exactly unity. This fixes the background of the Hybrid model into a geometric degeneracy with &#923;CDM which is confirmed explicitly through MCMC analysis with the latest background-only probes. The physical novelty of this model is manifest in the perturbation sector, where the geometric coupling breaks the background degeneracy and induces a late-time suppression of the effective gravitational constant <italic>G<inf>eff</inf></italic>&#8239;&lt;&#8239; <italic>G<inf>N</inf></italic>. Consequently, the inclusion of RSD data reveals an amplitude compensation mechanism, by which the matching of the signature <italic>f&#963;</italic> <inf>8</inf> of the data causes the clustering amplitude <italic>&#963;</italic> <inf>8</inf> to inflate under weaker gravity. Statistical model comparison through AIC/DIC demonstrates that incorporating growth data yields a moderate to weak preference for the Hybrid model keeping the background cosmology intact. This provides a physically bounded alternative to &#923;CDM with a falsifiable signature in the large scale structure, directly testable by the next generation of galaxy surveys.

Ameya Kolhatkar

P.K. Sahoo

Beyond the cosmological constant: Breaking the geometric degeneracy of <italic>f</italic>( <italic>Q</italic>) cosmology via redshift-space distortions

Egypt

Tahia Dabash

Moataz Emam

Germany

Lukas Schöppner

Reply to “Comment on: Symmetry and conserved quantities in $\textit{f}$($\textit{R}$)-gravity: Mei vs. Noether approaches”

In this work, two analytical solutions are proposed to characterize compact star configurations containing an effective negative-pressure fluid in the <italic>f</italic>( <italic>R, T</italic>) gravity paradigm that admit spherically symmetric geometry. We derive a system of modified field equations by taking into account a static interior spacetime, which consists of both negative-pressure fluid and ordinary matter sources. In order to investigate the interactions between the fluid components, we solve the field equations using two different equations of state. As the gravitational equations still contain more unknowns, we further use the Finch-Skea and Tolman IV spacetimes which lead us to two distinct models. The junction conditions are also applied to compute the constants associated with these solutions. Afterwards, our developed models&#8217; feasibility is explored by contrasting them with the observed characteristics of two particular stars, SAX J1808.4&#8211;3658 and Her X-1. Under certain parametric values, our results demonstrate that both the developed fluid configurations are physically realistic in this minimally coupled gravity framework.

Azerbaijan

Pakistan

M. Sharif

Tayyab Naseer

Aqsa Bashir

Examining the behavior of exotic compact stars within the <italic>f</italic>( <italic>R, T</italic>) gravity under Finch-Skea and Tolman IV spacetimes