We set the scale of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang-Mills theories for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, 5, 8 and in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit via gradient flow, as a first step towards the computation of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>-parameter using step scaling. We adopt twisted boundary conditions to achieve large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>0.025</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> for all the explored values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> twisted volume reduction.

Claudio Bonanno

Jorge Luis Dasilva Golán

Margarita García Pérez

Massimo D’Elia

Andrea Giorgieri

Scale setting of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang–Mills theory, topology and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume independence

We present an application of physics-informed neural networks (PINNs) to the study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> lattice gauge theories. Our method enables the learning of eigenfunctions and eigenvalues at arbitrary gauge couplings, smoothly moving from the analytically known strong-coupling regime toward weaker couplings. By encoding the Schrödinger equation and the symmetries of the eigenstates directly into the loss function, the network performs an unsupervised exploration of the spectrum. We validate the approach on the single-plaquette U(1) and SU(2) pure-gauge theories, showing that the PINNs successfully reproduce the hierarchy of energy levels and their corresponding wave functions.

Switzerland

Simone Romiti

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> lattice gauge theories with physics-informed neural networks

We study the decays of $\textit{B}$ mesons into light pseudoscalar mesons under the SU(3) flavour symmetry. Assuming exact SU(3) symmetry at the level of the amplitudes leads to a simple parametrisation. Using the available experimental data and accounting for mixing effects in the $$ {B}_s^0 $$ branching ratios, we find that the data cannot be described with this assumption. We improve this parametrisation by including $\textit{factorizable}$ SU(3) -breaking effects. This new approach allows for an excellent description of the data, with a fit $\textit{p}$ value of 32$\textit{.}$3%. We provide posterior predictions for all observables and identify several decay channels that would significantly impact our analysis. Finally, we briefly compare our results with the predictions of QCD factorisation, paving the way to a more detailed analysis which could provide insights into QCD effects at low energy scales.

Netherlands

M. Marcos

France

M. Reboud

K. Vos

Detailed SU(3) flavour symmetry analysis of charmless two-body $\textit{B}$-meson decays including factorizable corrections

Using the topological-diagram approach based on SU(3) flavor symmetry, we investigate two-body $$ {\Lambda}_c^{+}\to \textbf{B}S $$ decays, where denotes the final-state baryon and $\textit{S}$ refers to a light scalar meson, such as $\textit{f}$ /$\textit{f}$ (980), $\textit{a}$ /$\textit{a}$ (980), $\textit{σ}$ /$\textit{f}$ (500), or $$ \kappa /{K}_0^{\ast }(700) $$ . Our analysis indicates that interpreting the light scalar mesons as tetraquark states provides a more consistent description of the currently available experimental data. In particular, this framework naturally accommodates the experimentally observed branching fraction $$ \mathcal{B}\left({\Lambda}_c^{+}\to \Lambda {a}_0^{+}\right) $$ , which exceeds predictions based solely on long-distance effects by an order of magnitude. Within the tetraquark scenario, we predict $$ \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{f}_0\right)=\left(4.9\pm 1.9\right)\times {10}^{-2} $$ and $$ \mathcal{B}\left({\Lambda}_c^{+}\to p{f}_0\right)=\left(3.6\pm 1.4\right)\times {10}^{-3} $$ . Owing to $\textit{f}$ − $\textit{σ}$ mixing, $$ \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{\sigma}_0\right) $$ and $$ \mathcal{B}\left({\Lambda}_c^{+}\to p{\sigma}_0\right) $$ are suppressed to the levels of 1 × 10 and 5 × 10 , respectively. These modes therefore provide sensitive probes of the internal structure of the light scalar mesons. More generally, the remaining branching ratios of $$ {\Lambda}_c^{+}\to \textbf{B}S $$ are found to be comparable to those of $$ {\Lambda}_c^{+}\to \textbf{B}M $$ , where $\textit{M}$ denotes a pseudoscalar meson. Their predicted sizes suggest that these decay modes should be accessible to ongoing and near-future experimental studies at BESIII, Belle II, and LHCb.

China

Y. Wang

Y. Hsiao

Charmed $$ {\Lambda}_c^{+} $$ baryon decays into light scalar mesons in the topological SU(3) $\textit{f}$ framework

We attempt to describe the moduli space of boundary states in the SU(2) WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to marginal deformations, our solutions exhibit a $\textit{g}$-function different from that of the background (typically lower). Thus, our method effectively combines features of both marginal and relevant deformations. After partially fixing an SU(2) symmetry of the equations of motion, we find families of solutions parameterized by the coefficient of the marginal field associated with the $\textit{J}$ current, and we identify them as Cardy boundary states with varying angle $\textit{θ}$. However, it turns out that these solutions become inconsistent once the marginal parameter exceeds a certain value, implying that they cover only a part of the moduli space. Finally, we also compare the relation between the marginal parameter and the angle $\textit{θ}$ for different solutions and we find evidence suggesting that this relation is universal for certain classes of solutions.

Czechia

Matěj Kudrna

Marginal deformations of SU(2) $\textit{k}$ WZW model boundary states in open string field theory

We present a high-precision study of the topological susceptibility in SU(3) pure gauge theory in four space-time dimensions. The result is based on ensembles at seven lattice spacings and in seven physical volumes to facilitate a controlled continuum and infinite-volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support the idea that both strategies yield a universal continuum limit; we find <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>top</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0.4775</mn><mo stretchy="false">(</mo><mn>14</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>11</mn><mo stretchy="false">)</mo></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mi>top</mi><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><mo>=</mo><mn>198.1</mn><mo stretchy="false">(</mo><mn>0.7</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2.7</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our Appendix data suggest that the excess kurtosis <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>4</mn></msup><mo stretchy="false">⟩</mo><mo>/</mo><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>2</mn></msup><msup><mo stretchy="false">⟩</mo><mn>2</mn></msup><mo>−</mo><mn>3</mn></math> decreases <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∝</mo><msup><mi>L</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> for large box sizes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>.

Germany

Stephan Dürr

Gianluca Fuwa

Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory

We present a neural network wave function framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of SU(2) equivariant neural networks alongside an SU(2) invariant, physics-inspired ansatz, we learn a parametrization of the ground state wave function of SU(2) lattice gauge theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

Thomas Spriggs

Eliska Greplova

Juan Carrasquilla

Jannes Nys

Accurate Ground States of SU(2) Lattice Gauge Theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math>

We identify a local, gauge-invariant mechanism that generates a finite spectral scale in pure SU(3) Yang–Mills theory on a punctured three-ball. Fixing a <math altimg='si2.svg'><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub></math> center sector isolates a single gauge-invariant holonomy angle whose Berry shift produces a quantum rotor with strictly nonzero level spacing. Gauss law is enforced by a covariant Dirichlet Helmholtz projector built from the Dirichlet inverse of the covariant scalar Laplacian with relative boundary conditions. The slow holonomy mode is chosen variationally as the minimizer of transverse electric energy under the holonomy constraint, yielding an inertia <italic>independent of the gauge representative</italic> with linear domain-size scaling and a controlled commutator-dominated regime. We prove projector stability and derive an adiabatic variational upper bound on the first positive Yang&#8211;Mills eigenvalue, with error controlled by the transverse vector gap of the covariant Laplacian on divergence-free one-forms. A femtometer-scale benchmark at realistic coupling gives an upper bound at a hadronic (&#8239;&#8764;&#8239;1&#8201;GeV) scale. In Wilczek&#8217;s sense this realizes &#8220;mass without mass&#8221;: no explicit mass term or Higgs field is introduced, and the nonzero level spacing is fixed by gauge invariance, topology, and the chosen center sector. The present results are derived on a finite domain; interpreting the length <italic>R</italic> in Minkowski space requires an additional physical input (e.g. as a local confinement length), which we make explicit.

United States

Egypt

Ahmed Farag Ali

Mass without mass from a berry–shifted SU(3) holonomy rotor

We propose a novel method to identify the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>. The two poles owe their origin to different quark flavor irreducible representations in the meson-baryon coupled-channel interactions, thus they should be individually manifested in reactions that provide good flavor eigenstate sources. Hadronic decays of charmonia into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi mathvariant="normal">Σ</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo><mi mathvariant="normal">Σ</mi><mi>π</mi></math> are such reactions, and the flavor octet and singlet poles can be approximately singled out in these two decay modes. This SU(3) flavor filter works even considering the flavor symmetry breaking. With the huge charmonium data sets collected, it is therefore promising to solve the long-standing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> puzzle employing the proposed flavor filter.

Ying-Bo He

Xiao-Hai Liu

Li-Sheng Geng

Feng-Kun Guo

Ju-Jun Xie

Identifying the two-pole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></mrow></math> using an SU(3) flavor filter

Standard Model extensions that yield observable neutrino magnetic moments typically also induce large neutrino masses, incompatible with experimental limits. This tension motivates the search for mechanisms that naturally decouple magnetic moments from mass generation without requiring fine-tuning. In this letter, we propose a novel mechanism for generating Dirac and Majorana neutrino magnetic moment, in which the associated mass contribution is forbidden by $$SU(2)_L$$ invariance. By carefully selecting the $$SU(2)_L$$ representations connecting the neutrino to the loop diagram, we ensure that only the effective dipole operator involving the non-Abelian part of the photon – the neutral $$SU(2)_L$$ gauge boson – is generated. Crucially, the corresponding mass diagram, obtained by removing the external gauge boson leg, vanishes. We provide explicit UV completions that implement this mechanism and yield neutrino magnetic moments within the sensitivity of current and future experiments.

Julie Pagès

Anil Thapa

Decoupling neutrino magnetic moment from mass with $$SU(2)_L$$ invariance