We consider electric flux tube solutions in SU(3) gauge theory with scalar fields in the fundamental representation. Such solutions can possibly be constructed in two classes, corresponding to the two maximally commuting generators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mn>3</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mn>8</mn></msub></math> of SU(3). We successfully construct the 3-type solution with two scalar fields and show that it is immune to decay through Schwinger pair production of gauge bosons, but we have not been able to construct an 8-type solution.

Jude Pereira

Tanmay Vachaspati

Electric flux tube solutions in SU(3) gauge theory

We test the eigenstate thermalization hypothesis (ETH) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>-dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cutoff, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and nonlocal operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various timescales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and nonlocal operators. We find numerical evidence of the spectral gap and the memory peak in the nonlocal operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.

Diptarka Das

Lukas Ebner

Saurabh V. Kadam

Indrakshi Raychowdhury

Andreas Schäfer

Xiaojun Yao

Eigenstate thermalization in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional SU(2) lattice gauge theory coupled with dynamical fermions

In this work, we scrutinize local gauge-invariant vector operators of dimension four in the adjoint <italic>SU</italic>(2) Higgs model, which are candidates for interpolating fields of the fundamental excitations of the model due to the so-called FMS mechanism. We use the equations of motion and the properties of the BRST operator to derive a Ward identity that allows us to determine whether an operator can create a propagating mode. To corroborate this analysis, we explicitly compute the two-point function of the non-propagating operator at the one-loop level.

Brazil

Giovani Peruzzo

Local gauge-invariant vector operators in the adjoint <italic>SU</italic>(2) Higgs model

We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavor (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math>) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by results obtained for the SU(2) gauge theory with two Dirac fermion flavors (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math>) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterization of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub></math> decreasing significantly as one approaches the continuum limit for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math> theory towards a value consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.170</mn><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo></math>, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math> the anomalous dimension converges more rapidly with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math> to a value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.291</mn><mo stretchy="false">(</mo><mn>9</mn><mo stretchy="false">)</mo></math>. A chiral perturbation theory analysis shows that the infrared behavior of both theories is incompatible with the breaking of chiral symmetry.

Andreas Athenodorou

Ed Bennett

Georg Bergner

Pietro Butti

Julian Lenz

Biagio Lucini

SU(2) gauge theory with one and two adjoint fermions toward the continuum limit

We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional SU(3) Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as 0$\textit{.}$045 fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions.

Spain

Claudio Bonanno

Italy

Germany

Andrea Bulgarelli

United Kingdom

Elia Cellini

Alessandro Nada

Dario Panfalone

Davide Vadacchino

Lorenzo Verzichelli

Scaling flow-based approaches for topology sampling in SU(3) gauge theory

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.

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.

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