In this article, we develop two unique singularity-free solutions that describe anisotropic interior fluid configurations in <math altimg='si6.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity. In this regard, the extended field equations are developed corresponding to a static interior spacetime. This system of equations is facilitated by imposing two novel constraints in order to get a unique solution. We derive two different solutions by choosing specific types of anisotropic pressure. While solving these equations, several constants are involved as a result of performing exact integration. Matching the interior metric to the Schwarzschild exterior metric at the sphere&#8217;s boundary in both scenarios yields these integration constants. Another factor that plays an important role in finding the constants is the zero radial pressure. Afterwards, physical feasibility of both compact models is explored under specific conditions. To do so, the predicted data of two stars, named 4U 1820-30 and Cen X-3 is used along with different values of the model parameter. It is reported that both our astrophysical solutions are aligned with the criteria of physical existence of such models under certain parametric values.

Pakistan

Azerbaijan

Tayyab Naseer

M. Sharif

M. Waqas

Saudi Arabia

Mohamed R. Eid

Abdel-Haleem Abdel-Aty

Astrophysical stellar models in <math altimg='si6.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity under Tolman IV and Kohler-Chao-Tikekar spacetimes

We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, $ a_{\mu} $ . Utilizing a coupled non-perturbative framework combining Schwinger-Dyson and Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing $ a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13} $ , $ a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = $ $ -(2.02 \pm 0.10) \times 10 ^{-13} $ . Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to $ a_{\mu} $ .

Spain

Mexico

Angel S. Miramontes

K. Raya

A. Bashir

P. Roig

G. Paredes-Torres

Radially excited pion: electromagnetic form factor and the box contribution to the muon's $\textit{g}$-2 * A. S. Miramontes acknowledges $\textit{Consejo Nacional de Ciencia, Humanidades y Tecnología}$ (CONAHCyT), Mexico, for the financial support received through the program '$\textit{Postdoctorados Nacionales por México}$', additionally, has been partially funded by the 'PROMETEO' programme of the 'Generalitat Valenciana' grant CIPROM/2022/66, and by the Spanish 'Agencia Estatal de Investigación', MCIN/AEI/10.13039/501100011033, through the grants PID2020-113334GB-I00 and PID2023-151418NB-I00. A. Bashir thanks $\textit{Coordinación de la Investigación Científica}$ of the $\textit{Universidad Michoacana de San Nicolás de Hidalgo}$ Grant No. 4.10., CONAHCyT grant CBF2023-2024-3544 and $\textit{Ayudas Beatriz Galindo}$, Spain. P. Roig acknowledges Conahcyt (México) funding through project CBF2023-2024-3226 as well as Spanish support during his sabbatical year through projects MCIN/AEI/10.13039/501100011033, grant PID2020-114473GB-I00, and Generalitat Valenciana grant PROMETEO/2021/071. G. Paredes-Torres acknowledges CONAHCyT, Mexico, for the financial support provided to him through the program '$\textit{Beca de Posgrado en México}$'. The work of A. Bashir and K. Raya is supported by Spanish Ministry of Science and Innovation (MICINN grant no. PID2022-140440NB-C22) and Junta de Andalucía (grant P18-FR-5057)

In order to reach a precision of 0$\textit{.}$2% on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, ($\textit{g}$ – 2) , such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($\textit{α}$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a (−0.89 ± 0.18)% correction to the leading-order HVP contribution to ($\textit{g}$ – 2) . To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O($\textit{α}$)-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

Germany

Julian Parrino

Volodymyr Biloshytskyi

United States

En-Hung Chao

Harvey Meyer

Vladimir Pascalutsa

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon ($\textit{g}$ − 2) from lattice QCD

We construct a new stellar compact object model in the regime of anisotropic pressure using the framework of gravitational decoupling via minimal geometric deformation, with the particularity that the seed solution used is the known Kohler–Chao–Tikekar cosmological solution. As an extra condition to close the Einstein’s field equations resulting for this construction, we use a generalised complexity factor for self-gravitating spheres to the well-known Wyman IIa solution. The resulting model fulfils the fundamental physical acceptability stellar conditions for a compactness factor of a pulsar SMC X-1. The stability of the model is also investigated.

Ecuador

B. Siza

J. Andrade

D. Santana

Anisotropic extension of the Kohler–Chao–Tikekar cosmological solution with like Wyman IIa complexity factor

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects.

Abeer Albalahi

Z. Yousaf

S. Khan

Akbar Ali

Anisotropic interior models with Kohler–Chao–Tikekar-like complexity factor

We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to <math><msub><mi>K</mi><mi>L</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay can be calculated using lattice quantum chromodynamics. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard model prediction for this second-order weak process depends on an accurate result of this two-photon amplitude. A limiting factor of our proposed method comes from low-energy three-particle <math><mi>π</mi><mi>π</mi><mi>γ</mi></math> states. The contribution from these states will be significantly distorted by the finite volume of our calculation—a distortion for which there is no available correction. However, a simple estimate of the contribution of these three-particle states suggests their contribution to be at most a few percent allowing their neglect in a lattice calculation with a 10% target accuracy.

Norman Christ

Calculating the two-photon exchange contribution to <math><msub><mi>K</mi><mi>L</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay

This paper is devoted to obtaining and studying two interior exact solutions of Einstein’s Field Equations (EFE) for spherical geometry in the context of gravitational decoupling (GD) through minimal geomentric deformation (MGD). We take the well-known Kohler–Chao–Tikekar cosmological solution as a seed in the framework of GD to first obtain an isotropic solution, which is decoupled again in order to obtain a second stellar anisotropic solution. Both resulting models turn out to be physically viable stellar models. Their stability is also being studied.

 Oswaldo-Villacrés

S. Carrera

Gravitational decoupled interior solutions from Kohler–Chao–Tikekar cosmological model

This work is devoted to transforming the known cosmological solution of Kohler–Chao–Tikekar into an anisotropic interior solution using the framework of Gravitational Decoupling by minimal geometric deformation. The resulting interior solution fulfils the fundamental physical acceptability stellar conditions for a specific set of compactness factors. The stability of the model is also investigated.

K. Ortega

W. Klínger

R. Copa

S. Medina

J. Cruz

Anisotropic extension of Kohler–Chao–Tikekar solution by minimal geometric deformation

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor g of the muon to deviate from the value of two predicted by Dirac’s theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon (g − 2). Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at  https://github.com/RJHudspith/KQED  .

United Kingdom

Nils Asmussen

France

Antoine Gérardin

Jeremy Green

Renwick Hudspith

Andreas Nyffeler

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale Λ ~ 400 MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale Λ, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to γ ∗ γ ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ ∗ γ ∗ → e + e  −  cross-section, we predict the expected lattice-QCD integrand resulting from the γ ∗ γ ∗ → π 0 process.

Ireland

Switzerland

Franziska Hagelstein

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization