A crucial step in extracting physical predictions from lattice quantum chromodynamics (QCD) simulations is the scale setting, i.e., the determination of the lattice spacing (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi></math>) in physical units. Herein, the relative scale setting for different <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math>’s is discussed, using the Landau gauge gluon propagator computed with large statistical ensembles. After setting the relative scales, finite size effects are observed in the ultraviolet regime and handled in an effective description, inspired in perturbation theory. The new devised procedure is efficient in handling the finite size effects, linking the lattice simulations with continuum perturbation theory for the high momenta regime. Furthermore, the procedure can be extended to handle other Green’s functions computed within lattice QCD simulations.

Orlando Oliveira

Paulo J. Silva

Using the Landau gauge gluon propagator to set the lattice physical scales and understanding the finite size effects

We compute the phase of the Euclidean gravity partition function on manifolds of the form $\textit{S}$ × $\textit{M}$ . We find that the total phase is equal to the phase in pure gravity on $\textit{S}$ times an extra phase that arises from negative mass squared fields that we obtain when we perform a Kaluza-Klein reduction to $\textit{S}$ . The latter can be matched to the phase expected for physical negative modes seen by a static path observer in $\textit{dS}$ . In the case of $\textit{S}$ × $\textit{S}$ the answer can be interpreted in terms of a computation in the static patch of $\textit{dS}$ or $\textit{dS}$ . We also provide the phase when we have a product of many spheres. We clarify the procedure for determining the precise phase factor. We discuss some aspects of the interpretation of this phase.

United States

Victor Ivo

Juan Maldacena

Zimo Sun

Physical instabilities and the phase of the Euclidean path integral

Guided by the flipping principle, we propose a novel extension of the Standard Model based on a double right-handed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge symmetry. In this framework, all left-handed fermions are neutral, while right-handed fermions of the third generation carry charges distinct from those of the first two generations. This structure provides an explanation for the observed Standard Model fermion mass hierarchy; the heavy masses of the third generation are generated at tree level, while the lighter masses of the first and second generations arise radiatively at the one-loop level. For the active neutrino sector, the tiny masses are generated through a combination of tree-level and two-loop seesaw mechanisms. Crucially, this approach successfully reproduces the observed neutrino mass hierarchy, with the atmospheric mass-squared difference generated at tree level and the solar neutrino mass squared difference emerging at the two-loop level. These hierarchical patterns stem from the interplay between gauge invariance and a residual parity symmetry that survives the spontaneous breaking of the extended gauge group. The same residual symmetry stabilizes a viable scalar singlet dark matter candidate, which we show can reproduce the observed relic abundance while remaining consistent with current direct detection bounds. After addressing constraints from electroweak precision tests and flavor-changing neutral currents, we explore the discovery prospects for the new neutral bosons at existing and future colliders, including the LEP, LHC, and a future ILC.

Duong Van Loi

A.E. Cárcamo Hernández

N.T. Duy

D.T. Binh

Cao H. Nam

Physical implications of a double right-handed gauge symmetry

We revisit the renormalization of the gauge coupling in massless QED coupled to a scaleless quadratic theory of gravity. We compare two alternative prescriptions for the running of the electric charge: (i) the conventional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> running in minimal subtraction, and (ii) a physical running extracted from the logarithmic dependence of amplitudes on a hard scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> (e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>p</mi><mn>2</mn></msup></math> or a Mandelstam invariant) after removing IR effects. At one loop, using dimensional regularization with an IR mass regulator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math>, we compute the photon vacuum polarization. We find a clean separation between UV and soft logarithms: the former is gauge and process independent and fixes the beta function, whereas the latter encodes nonlocal, IR-dominated contributions that may depend on gauge parameters and must not be interpreted as UV running. In the quadratic-gravity sector, the photon self-energy is UV finite—the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ln</mi><msup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> pieces cancel—leaving only <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><msup><mi>m</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> soft (IR) logs, which do not contribute to the running of the coupling once IR effects are consistently removed. Consequently, quadratic gravity does not modify the one-loop UV coefficient and thus does not alter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math>. Therefore, the physical running coincides with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> running in QED at one loop. Our analysis clarifies how to extract a gauge and process independent running in the presence of gravitational interactions and why soft logs from quadratic gravity should not contribute to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math>.

M. Gomes

A.C. Lehum

A.J. da Silva

Physical running of the electric charge in a dimensionless theory of gravity

We develop a fully consistent anisotropic extension of the Imran class ICG (Isotropic Compact Gravastar) model within general relativity. A geometry-coupled anisotropy is introduced at the exact equation level, ensuring regularity at the center, smooth matching to the exterior Schwarzschild spacetime, and the absence of thin shells. A controlled option enforces vanishing anisotropy at both the center and the surface. The resulting equilibrium configurations satisfy energy conditions, causality, compactness bounds, and stability diagnostics. The admissible mass–radius domain overlaps that of neutron star like compact objects, and the isotropic ICG solution is recovered smoothly in the zero-anisotropy limit. These results provide a robust anisotropic gravastar background for future rotational and tidal analyses.

China

M. Sakib

Wenxin Wang

Xiande Wu

Bangladesh

M. Hafez

M. Kauser

Relativistic formulation and physical viability of anisotropic analytic gravastars

We present the first principle calculation of charmed baryon decay constants employing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor gauge ensembles with lattice spacings ranging from 0.05 to 0.1 fm and pion masses between 136 and 310 MeV. Under SU(3) flavor symmetry, we construct the charmed baryon interpolating operators and compute the corresponding hadronic matrix elements to extract the bare decay constants for each ensemble. The nonperturbative renormalization is performed via the symmetric momentum-subtraction (SMOM) scheme. After performing systematic chiral and continuum extrapolations, we obtain the decay constants with a precision of 8%–16% from first principles. We further determine several ratios of decay constants among different charmed baryons, for which renormalization factors and part of the systematic uncertainties largely cancel, providing a cleaner probe of SU(3) flavor symmetry breaking. These ratios offer a quantitative, first-principles characterization of the SU(3)-breaking pattern in the charmed baryon sector.

Lei-Yi Li

Jie Ran

Mengchu Cai

Hao-Fei Gao

Yu Gu

Xue-Ying Han

Jun Hua

Jin-Xin Tan

Guang-Yu Wang

Wei Wang

Fanrong Xu

Yi-Bo Yang

Qi-An Zhang

Lattice QCD calculation of charmed baryon decay constants in the continuum limit and at physical mass

In addition to the well-known quantum chromodynamical theta angle, we show that the Standard Model has another theta angle which is invariant under arbitrary chiral rotations of quarks and leptons. The new theta angle can be identified with the quantum electrodynamical theta angle, which should be viewed as an independent parameter of the Standard Model, and may be observable in spacetime with non-simply connected features, either beyond the visible universe or in an effective background from a laboratory setup.

James Brister

Bingwei Long

Longjie Ran

Muhammad Shahzad

Zheng Sun

Yingpei Zou

Physical remnant of electroweak theta angles

We investigate S-wave kaon-nucleon (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mi>N</mi></mrow></math>) interactions with strangeness <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>+</mo><mn>1</mn></math> in lattice QCD using the time-dependent HAL QCD method. Employing the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor gauge configuration with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>137</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>K</mi></msub><mo>≈</mo><mn>502</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, we calculate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mi>N</mi></mrow></math> potentials at the leading order in the derivative expansion. The potentials in both isospin channels (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>) exhibit repulsion at short distances, while only the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> potential has a small attractive pocket at intermediate distances. The phase shifts computed from these potentials show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Θ</mi><mo>+</mo></msup><mo stretchy="false">(</mo><mn>1540</mn><mo stretchy="false">)</mo></math> pentaquark in the S-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mi>N</mi></mrow></math> systems. The scattering lengths result in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>I</mi><mo>=</mo><mn>1</mn></mrow></msubsup><mo>=</mo><mo>−</mo><mn>0.226</mn><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><msubsup><mrow><mo stretchy="false">(</mo></mrow><mrow><mo>−</mo><mn>0</mn></mrow><mrow><mo>+</mo><mn>5</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mn>0</mn><mrow><mi>I</mi><mo>=</mo><mn>0</mn></mrow></msubsup><mo>=</mo><mo>+</mo><mn>0.028</mn><mo stretchy="false">(</mo><mn>61</mn><mo stretchy="false">)</mo><msubsup><mo stretchy="false">(</mo><mrow><mo>−</mo><mn>26</mn></mrow><mrow><mo>+</mo><mn>3</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. Our results of the S-wave cross sections for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math> are consistent with some of the experimental data within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>–</mi><mn>3</mn><mi>σ</mi></math>, while they deviate from others. The results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>, combined with recent studies on chiral perturbation theory, suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.

Kotaro Murakami

Sinya Aoki

Takumi Doi

Yan Lyu

Wren Yamada

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi></mrow></math>-wave kaon-nucleon interactions from lattice QCD at the physical point

Recent advances in modeling compact astrophysical objects have focused on incorporating dark energy as a relativistic component within their internal structures, offering novel insights into extreme matter configurations. Theoretical frameworks now explore anisotropic pressure profiles and modified equations of state, enabling predictions about stability and mass-radius relationships under dark energys repulsive influence. Such studies aim to resolve discrepancies in observed compact object populations while probing interactions between high-density matter and cosmological vacuum energy. This study presents a new analytical framework for a two-fluid system consisting of ordinary baryonic matter and dark energy in modified <italic>f</italic>( <italic>Q</italic>) gravity, with <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>=</mo><mi>&#958;</mi><mo linebreak='goodbreak'>+</mo><mi>&#967;</mi><mi>Q</mi></mrow></math>, where <italic>&#958;</italic> and <italic>&#967;</italic> are coupling constants. By utilizing the Durgapal-Lake metric potentials (Durgapal et al., Gen. Relativ. Gravit. 17:671, 1985, Lake K, Phys. Rev.D 67:10 2003) as seed solutions and assuming a linear equation of state for dark energy, the modified gravitational field equations are solved to derive exact interior solutions. The model parameters, including the dark energy coupling constant and constants from the metric ansatz, were determined by smoothly matching the interior geometry with the exterior spacetime at the stellar boundary. Observational data from three compact stars <math altimg='si9.svg'><mrow><mo>(</mo><mi>H</mi><mi>e</mi><mi>r</mi><mi>X</mi><mo linebreak='goodbreak'>&#8722;</mo><mn>1</mn><mo>,</mo></mrow></math> <math altimg='si10.svg'><mrow><mn>4</mn><mi>U</mi><mn>1538</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>52</mn><mo>,</mo></mrow></math> <math altimg='si11.svg'><mrow><mi>S</mi><mi>A</mi><mi>X</mi><mi>J</mi><mn>1808.4</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>3658</mn><mo>)</mo></mrow></math> were used to test the model&#8217;s viability and regularity. The study included a thorough physical analysis, examining energy density gradients, anisotropy, stability, equilibrium conditions using the modified TOV equation. The results align with observational data, indicating that the model offers a physically plausible description of compact stars while maintaining stability and equilibrium under the tested conditions.

Pakistan

Azerbaijan

M.R. Shahzad

Wajiha Habib

Saudi Arabia

Muneerah Alomar

Mona Bin-Asfour

Possible existence and physical features of mathematical models of dark energy ultra-compact objects in modified symmetric teleparallel gravity

The Collins-Soper (CS) kernel governs the rapidity evolution of transverse-momentum-dependent (TMD) parton distributions, a cornerstone for QCD factorization and linking nucleon structure data across scales. Its nonperturbative behavior at large transverse separations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math>) remains weakly constrained due to phenomenological model dependencies. We present a first-principles determination of the CS kernel at the continuum limit and physical pion mass from lattice QCD in the large-momentum effective theory framework. Using (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor configurations (lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.052</mn><mo>,</mo><mn>0.105</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, and pion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mo stretchy="false">(</mo><mn>136</mn><mo>,</mo><mn>230</mn><mo>,</mo><mn>300</mn><mo>,</mo><mn>320</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>), we simulating the nonlocal equal-time correlation function and extract the quasi-TMD wave functions. Taking into account systematic improvements including hypercubic smearing, nonperturbative renormalization, and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math>-unexpanded matching kernel, we obtain the CS kernel at the continuum, chiral, and infinite-momentum limits. Our results are determined up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, with controllable uncertainties, and agree with perturbative QCD at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math> and global TMD phenomenological extractions. We conduct a global analysis integrated with phenomenological fits and demonstrate the impact of our results on such fits. This work yields the most precise nonperturbative constraint on the CS kernel’s long-distance behavior from lattice QCD, which not only bridges lattice QCD, perturbation theory, and nucleon structure experiments for TMD studies, but also boosts the utility of our constraint for future global TMD analyses.

Zhi-Chao Gong

Xiangdong Ji

Xiangyu Jiang

Hang Liu

Andreas Schäfer

Yushan Su

Han-Zhang Wang

Jun Zeng

Jian-Hui Zhang

Jia-Lu Zhang

Lattice QCD determination of the Collins-Soper kernel in the continuum and physical mass limits