A modified gravitational model whose action is given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field, and its kinetic term is investigated as an extension of the gravitational sector including an additional dynamical degree of freedom. Within this framework, the causal structure of rotating cosmological solutions is analyzed by considering Gödel and Gödel-type spacetimes as background geometries used as theoretical probes of the model consistency. Different matter sources are examined, including a perfect fluid and scalar-field configurations. It is found that the standard Gödel metric is not compatible with the scalar sector of the theory unless the model reduces to the General Relativity limit. In contrast, Gödel-type geometries admit a wider class of solutions whose causal properties depend on the model parameters and on the matter content. In particular, perfect-fluid sources may lead to either causal or noncausal configurations, whereas scalar-field configurations constrain the geometry to the causal limit, preventing the formation of closed timelike curves, highlighting that the scalar field plays a nontrivial dynamical role distinct from that of a cosmological constant.

Brazil

L. Evangelista

M. Silva

J. Moretti

A. Santos

Causality and its violation in $$f(R,\mathcal {L}_m,\phi ,g^{\mu \nu }\nabla _\mu \phi \nabla _\nu \phi )$$ gravity

In this paper we consider the localization of the gravitino field on a codimension-one thick brane within the framework of $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) gravity. First, setting $$F(\phi ) = \phi $$ , we derive the potential functions for various parameters. Under appropriate coupling parameters, we can find the localized zero mode and some resonance states. Furthermore, we use these resonance states as initial data to investigate the evolution of the gravitino resonances. It can be observed that various parameters on the brane affect the evolution duration. We focus on comparing the localization behavior of the gravitino field on the brane for the cases with $$k=0$$ and $$k\ne 0$$ .

China

Xiang-Nan Zhou

Miao Wang

Zhi-Chao Duan

Localization of gravitino field on $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) brane

The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term while the boundary term do not contribute to the dynamics. The advantage of the proposition is that the stellar structure equations are up to order two, thus the theory is not haunted by ghosts. We obtain explicitly the defining equations for the thermodynamical variables and the geometry for the pure quadratic case, since the linear case amounts to general relativity. In trying to establish the vacuum geometry associated with the theory it turns out that two possible metrics emerge through the vanishing of the energy-momentum tensor. Next, we analyse the isotropy equation and make the observation that it is autonomous. It is rare that this happens in astrophysical modelling. This behaviour prompted the use of dynamical systems to understand the stability properties of fixed points or invariant submanifolds. It was necessary to choose a gauge in order to split the autonomous equation into a system from which we could plot a phase portrait and deduce the stability of solution trajectories. We find that the invariant submanifolds were generally stable with nearby paths approaching them.

South Africa

Sudan Hansraj

United Kingdom

Christian Boehmer

Ndumiso Buthelezi

Dynamical systems approach to stellar modelling in $\textit{f}$($\textit{G}$, $\textit{B}$) gravity

<p>We study finite-volume (FV) corrections to determinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math>-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> in the isospin limit with subpercent precision, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>g</mi><mi>A</mi><mi>QCD</mi></msubsup><mo>=</mo><mn>1.2674</mn><mrow><mo>(</mo><mn>96</mn><mo>)</mo></mrow></mrow></math>.</p>

United States

Zack Hall

Dimitra A. Pefkou

Aaron S. Meyer

Thomas R. Richardson

Raúl A. Briceño

M.A. Clark

Switzerland

Martin Hoferichter

Emanuele Mereghetti

Henry Monge-Camacho

Colin Morningstar

Amy Nicholson

Pavlos Vranas

André Walker-Loud

Signs of nonmonotonic finite-volume corrections to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math>

The Standard Model prediction of the muon $$g-2$$ increasingly depends on lattice QCD computations of the hadronic vacuum polarization (HVP), where the isospin-breaking (IB) effects remain a significant source of uncertainty. To complement the lattice QCD evaluations, the data-driven approach to HVP has been used to assess some of the electromagnetic IB effects, in particular from the channels with a photon in the final state, e.g., $$e^+e^-\rightarrow \pi ^0 \gamma $$ . Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $$\pi ^+ \pi ^-$$ , $$\pi ^+ \pi ^- \pi ^0$$ , etc. We identify these leading corrections by performing a field-theoretic calculation in a vector-meson dominance model, thereby reconciling the timelike and spacelike approaches to electromagnetic effects. Although these virtual corrections are more difficult to extract in a systematic manner, addressing them is essential for the data-driven method to consistently complement the lattice QCD program.

Germany

France

Volodymyr Biloshytskyi

Dominik Erb

Harvey Meyer

Julian Parrino

Vladimir Pascalutsa

Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $$(g-2)_\mu $$

In this work, we investigate the internal structure and physical features of compact stars in the background of modified gravity, specifically within <italic>f</italic>( <italic>R, G</italic>) gravity, where <italic>R</italic> represents the Ricci scalar and <italic>G</italic> denotes the Gauss&#8211;Bonnet invariant. The interior spacetime of the stellar configuration is described by the Kohler&#8211;Chao metric, which provides a suitable geometric representation for dense compact objects. Our analysis considers ten well-known compact star candidates, namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. To incorporate higher-curvature effects, the functional form of <italic>f</italic>( <italic>R, G</italic>) is decomposed into two independent contributions, <italic>f</italic> <inf>1</inf>( <italic>R</italic>) and <italic>f</italic> <inf>2</inf>( <italic>G</italic>), representing the Ricci scalar and Gauss&#8211;Bonnet sectors, respectively. For the <italic>R</italic>-dependent part, we adopt the Hu&#8211;Sawicki type model, while three different models, namely logarithmic and power-law models, are considered for the Gauss&#8211;Bonnet contribution. This reconstruction gives three distinct modified gravity models used to study the different features of compact stellar configurations. Using these models, we study the physical viability of the stellar structures by examining anisotropic pressure content, equilibrium scenario through the Tolman&#8211;Oppenheimer&#8211;Volkoff equation, energy conditions, and stability conditions. The obtained results demonstrate that the energy density, radial pressure, tangential pressure, and anisotropy remain well-behaved throughout the stellar interior for all considered stars. The analysis indicates that the proposed <italic>f</italic>( <italic>R, G</italic>) models together with the Kohler&#8211;Chao interior solution provide physically consistent and stable configurations for compact stars within the modified gravity framework.

Saudi Arabia

Ahdab K. Althukair

Azerbaijan

Pakistan

M. Ilyas

Greece

Russia

Euaggelos E. Zotos

Kohler-Chao interior solutions for compact stellar objects in <italic>f</italic>( <italic>R, G</italic>) gravity

We examine the cosmological viability of two classes of nonminimally coupled <math altimg='si77.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math> gravity models, where the nonmetricity scalar <math altimg='si78.svg'><mi>Q</mi></math> induces an effective coupling between geometry and matter, with the aim of testing deviations from standard cosmology at the background level. The models considered include a linear, and an exponential nonminimal coupling. We constrain the background expansion histories using Type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, and Big Bang nucleosynthesis data, employing a combined <math altimg='si79.svg'><mrow><mi>&#967;</mi><mi>&#178;</mi></mrow></math> minimization technique to estimate cosmological and coupling parameters. We find that both models provide a stable description of the observed expansion history, yielding consistent values of the matter density parameter <math altimg='si9.svg'><msub><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mrow><mi>m</mi><mn>0</mn></mrow></msub></math> and the Hubble constant <math altimg='si7.svg'><msub><mi>H</mi><mn>0</mn></msub></math>&#8203; across datasets. In the linear model, the coupling parameters are constrained to positive values, while the deviation parameter remains compatible with zero, indicating behavior close to minimal coupling. The exponential model exhibits no statistically significant departure from minimal coupling, with background observations strongly constraining deviations from &#923;CDM. Overall, our results indicate that nonminimally coupled <math altimg='si77.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math> gravity models are consistent with current cosmological observations, with the data favoring parameter regions close to the &#923;CDM limit and showing no statistically significant evidence for deviations from standard cosmology at the background level.

Syria

Yahia Al-Omar

Nonminimally coupled <italic>f</italic>(Q) gravity under observational scrutiny

We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions $\textit{F}$ and $\textit{F}$ at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

Edoardo Spezzano

Tomas Ježo

Australia

Michael Klasen

Peter Risse

Ingo Schienbein

Heavy-quark contributions to the DIS structure functions $\textit{F}$ 4 and $\textit{F}$ 5 at NLO in the ACOT scheme

Gauss–Bonnet inflation typically affects the dynamics over an extended portion of the trajectory, making it difficult to isolate a controlled imprint at CMB scales. We consider a trajectory-selective coupling $$\mu (\phi ,X)$$ that gates the Gauss–Bonnet sector in phase space, enabling the higher-curvature contribution to be localized within a finite e-fold window while remaining negligible elsewhere. We identify stable inflationary solutions consistent with this localization and enforce standard ghost and gradient stability conditions for both scalar and tensor perturbations. For these viable backgrounds we compute pivot-scale observables and examine their dependence on the overall Gauss–Bonnet strength and on the kinetic gating. The framework offers a controlled route for realizing localized higher-curvature effects with predictable consequences for CMB-scale measurements.

Iran

Ali Seidabadi

Sara Saghafi

Kourosh Nozari

Beyond $$f(\phi ){\mathcal {G}}$$ : Gauss–Bonnet inflation with $$\mu (\phi ,X)$$

<p>We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> quarks. The analysis uses gluon configurations from the MILC Collaboration with vacuum polarization contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math> quarks (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math>), and lattice spacings down to 0.032 fm. We find that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></msub><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>5</mn><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>4.1923</mn><mo stretchy="false">(</mo><mn>63</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mrow><mn>0.9813</mn><mo stretchy="false">(</mo><mn>34</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>83.39</mn><mo stretchy="false">(</mo><mn>26</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite-lattice-spacing errors that shows why the highly improved staggered quark discretization of the quark action is particularly useful for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-quark simulations even for lattices where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><msub><mi>m</mi><mi>b</mi></msub><mo>≈</mo><mn>1</mn></math>. We also calculate QED and isospin corrections to the (fictitious) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>s</mi></msub></math>-meson mass, which is used to tune <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-quark masses in lattice simulations.</p>

Brian Colquhoun

Christine T.H. Davies

Daniel Hatton

G. Peter Lepage

New high-precision <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> masses from pseudoscalar-pseudoscalar correlators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math> lattice QCD