We point out that the odd-in-velocity contribution to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> radiated angular momentum for two-body scattering is determined by the radiation-reaction (RR) term in the one-loop waveform. This RR term is actually proportional to the tree-level waveform, and this reduces the calculation of the odd-in-velocity contribution to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> angular momentum loss, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></msub></mrow></math>, to two loops, instead of three loops as one would expect by power counting. We exploit this simplification, which follows from unitarity, to obtain a closed-form expression for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></msub></mrow></math> for generic velocities, which resums all fractional post-Newtonian (PN) corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> angular momentum loss starting at 1.5PN.

France

Carlo Heissenberg

Radiation-reaction and angular momentum loss at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>4</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>

The low-energy spectrum relevant to the lattice calculation of the hadronic vacuum polarization contribution to muon anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math> is dominantly given by two-pion states satisfying Lüscher’s finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the volume and Euclidean-time region. Using phenomenological inputs for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> phase shift and the timelike pion form factor, we obtain an estimate for the finite-volume effects on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math>, which is consistent with previous works. Numerical results are given for the “window” observables of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>.

Japan

Sakura Itatani

Hidenori Fukaya

Shoji Hashimoto

Anatomy of finite-volume effects on the hadronic vacuum polarization contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

We present a calculation of the leading two-loop corrections to the axial-vector coupling constant <math altimg='si1.svg'><msub><mrow><mi>g</mi></mrow><mrow><mi>A</mi></mrow></msub></math> in two covariant versions of two-flavor baryon chiral perturbation theory. Taking the low-energy constants from a combined analysis of elastic and inelastic pion-nucleon scattering, we find that these corrections are rather moderate.

Véronique Bernard

Germany

Georgia

Jambul Gegelia

Shayan Ghosh

China

Ulf-G. Meißner

Calculation of the axial-vector coupling constant <italic>g</italic> <inf><italic>A</italic></inf> to two loops in covariant chiral perturbation theory

The novel Branching-Ratio Method (BRM) for the determination of effective value <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> of the weak axial coupling <math altimg='si2.svg'><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow></msub></math> for forbidden non-unique (FNU) <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/electron-capture(EC) decays is introduced. The method offers new possibilities for testing the fitness of nuclear Hamiltonians in modeling the physics of complex <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/EC decays. The constraint of simultaneously reproducing the branching to <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> and EC transitions offers an additional constraint in tackling the problem of <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> determination. In the BRM the ambiguity in the choice of the values of <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> and s-NME (small relativistic vector nuclear matrix element) is lifted when constraints of the branching ratios of <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> and EC decays are applied. As an example, in the present work we apply BRM to the case of second FNU <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/EC decay of 59Ni. This decay is treated with three different nuclear shell-model (NSM) Hamiltonians demonstrating the effects of different nuclear-structure aspects in application of the BRM.

Finland

Aagrah Agnihotri

Romania

Jouni Suhonen

Novel way of evaluating <italic>g</italic> <inf><italic>A</italic></inf> quenching in <italic>&#946;</italic> +/EC decays: Introducing the Branching-Ratio Method (BRM)

In this paper, we consider hard-wall anti–de Sitter/quantum chromodynamics (AdS/QCD) models extended by a string-theory inspired Chern-Simons action in terms of a superconnection involving a bifundamental scalar field which corresponds to the open-string tachyon of brane-antibrane configurations and which is naturally identified with the holographic dual of the quark condensate in chiral symmetry breaking. This realizes both the axial and chiral anomalies of QCD with a Witten-Veneziano mechanism for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mass in addition to current quark masses, but somewhat differently than in the Katz-Schwartz AdS/QCD model used previously by us to evaluate pseudoscalar and axial vector transition form factors and their contribution to the hadronic light-by-light (HLBL) piece of the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>. Compared to the Katz-Schwartz model, we obtain a significantly more realistic description of axial-vector mesons with regard to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo>−</mo><msubsup><mi>f</mi><mn>1</mn><mo>′</mo></msubsup></math> mixing and equivalent photon rates. Moreover, predictions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> branching ratios are found to be in line with a recent phenomenological study. However, pseudoscalar transition form factors compare less well with experiment; in particular the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math> transition form factor turns out to be overestimated at moderate nonzero virtuality. For the combined HLBL contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> from the towers of axial vector mesons and excited pseudoscalars we obtain, however, a result very close to that of the Katz-Schwartz model.

Austria

Josef Leutgeb

Jonas Mager

Anton Rebhan

Superconnections in AdS/QCD and the hadronic light-by-light contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>

We propose a novel method to determine the strong coupling of quantum chromodynamics (QCD) and fix its running behavior at all scales by using the Bjorken sum rules (BSR). The BSR defines an effective coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></mrow></math> which includes the nonperturbative higher-twist corrections and perturbative QCD (pQCD) corrections to the leading-twist part. For the leading-twist part of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>, we adopt the infinite-order scale-setting procedure of the principle of maximum conformality (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>PMC</mi><mi>∞</mi></msub></math>) to deal with its pQCD corrections, which reveals the intrinsic conformality of the series and eliminates conventional renormalization scheme-and-scale ambiguities. Using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>PMC</mi><mi>∞</mi></msub></math> approach, we not only eliminate the first kind of residual scale dependence due to uncalculated higher-order terms, but also resolve the previous “self-consistency problem.” The light-front holographic QCD model is used for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math> in the infrared region, which also reveals a conformal behavior at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo stretchy="false">→</mo><mn>0</mn></math>. As a combination, we obtain a precise <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math> at all scales, which matches well with the known experimental data with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-value <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>98</mn><mo>%</mo></math>, and determines the strong coupling constant at the scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>Z</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi>Z</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>0.122</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>0.0012</mn></mrow><mrow><mo>+</mo><mn>0.0011</mn></mrow></msubsup><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><mi>κ</mi><msubsup><mo stretchy="false">)</mo><mrow><mo>+</mo><mn>0.0007</mn></mrow><mrow><mo>−</mo><mn>0.0046</mn></mrow></msubsup><mo stretchy="false">(</mo><mrow><mi>the</mi><mo>.</mo></mrow><mo stretchy="false">)</mo></math>, where the first error comes from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>κ</mi></math> of LFHQCD model and the second error is from the second kind of residual scale dependence.

Qing Yu

Xing-Gang Wu

Hua Zhou

Jian-Ming Shen

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi>Z</mi></msub><mo stretchy="false">)</mo></math> via a high-precision effective coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>

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.

Pakistan

Azerbaijan

M. Gul

W. Ahmad

M. Nasir

Faisal Javed

Kuwait

Orhan Donmez

Saudi Arabia

Bander Almutairi

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

In previous works, an operator was developed for heterotic compactifications on ℝ × $\textit{G}$ and $\textit{AdS}$ × $\textit{G}$ , which preserves $\textit{N}$ = 1 $\textit{d}$ = 3 supersymmetry and whose kernel is related to the moduli of the compactification. The operator is described in terms of non-physical spurious degrees of freedom, specifically, deformations of a connection on the tangent bundle. In this paper, we eliminate these spurious degrees of freedom by linking deformations of the spin connection to the moduli of the $\textit{G}$ manifold $\textit{Y}$. This results in an operator $$ \overset{\check{} }{D} $$ that captures the physical moduli space of the $\textit{G}$ heterotic string theory. When $\textit{Y}$ = $\textit{X}$ × $\textit{S}$ , with $\textit{X}$ an SU(3) manifold, we show $$ \overset{\check{} }{D} $$ produces results that align with existing literature. This allows us to propose a $\textit{G}$ moduli space metric. We check that this metric reduces to the SU(3) moduli metric constructed in the literature. We then define an adjoint operator $$ {\overset{\check{} }{D}}^{\dagger } $$ . We show the $\textit{G}$ moduli correspond to the intersection of the kernels of $$ \overset{\check{} }{D} $$ and $$ {\overset{\check{} }{D}}^{\dagger } $$ . These kernels reduce to the SU(3) F-terms and D-terms respectively on $\textit{X}$ × $\textit{S}$ . This gives two non-trivial consistency checks of our proposed moduli space metric. Working perturbatively in $\textit{α}$‵, we also demonstrate that the heterotic $\textit{G}$ moduli problem can be characterised in terms of a double extension of ordinary bundles, just like in the SU(3) case.

Australia

Jock McOrist

Martin Sticka

Norway

Eirik Svanes

The physical moduli of heterotic $\textit{G}$

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.

Spain

Giuseppe Luciano

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

The study of modified gravity models has garnered significant attention because of their potential to provide alternative explanations for cosmological phenomena, such as the accelerated expansion of the universe and the nature of dark energy. One such model, the Einstein–Gauss–Bonnet–Myrzakulov <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>F</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mi>G</mi><mo stretchy='false'>)</mo></math> gravity (EGBMG), which incorporates the curvature <italic>R</italic>, torsion <italic>T</italic>, and the Gauss-Bonnet term <italic>G</italic>, offers a promising framework to explore the dynamics of the universe and its evolution. This paper delves into the theoretical and observational implications of the EGBMG model, focusing on its ability to address long-standing challenges in cosmology, including the evolution of dark energy and the transition from early-time inflationary behavior to late-time acceleration. We review recent advancements in the model, including its compatibility with observational data and its ability to provide new insights into cosmic acceleration. Through a combination of theoretical models, dynamical systems analysis, and cosmological diagnostics, we demonstrate the robustness of the EGBMG framework in explaining the large-scale structure of the universe and its accelerated expansion. This paper serves as a step toward further exploring the potential of this model to understand the fundamental forces driving the cosmos and its consistency with modern observational constraints in Weitzenb&#246;ck spacetime.

United States

South Africa

Davood Momeni

Kazakhstan

Ratbay Myrzakulov

Einstein–Gauss–Bonnet–Myrzakulov gravity from <italic>R</italic>&#8239;+&#8239; <italic>F</italic>( <italic>T</italic>, <italic>G</italic>): Numerical insights and torsion&#8211;Gauss&#8211;Bonnet dynamics in Weitzenb&#246;ck spacetime