High Energy Physics - Lattice

We determine the momentum fraction and angular momentum carried by quarks and gluons in the proton in lattice QCD. We use four ensembles simulated with up, down, strange and charm quarks with their masses tuned to their physical values. These ensembles have similar physical volume and different lattice spacings allowing us to take the continuum limit directly at the physical pion mass point. We extract the quark and gluon momentum fractions and total angular momentum in the continuum limit as well as the intrinsic quark spin and orbital angular momentum contributions to the proton spin. We find the total momentum fraction $\langle x_N \rangle= 0.995(60)(29)$ and the total spin $J_N = 0.507(43)(65)$, showing that both the momentum and spin sum rules are satisfied. We compare our results to those extracted from phenomenological analyses.

In this paper we derive the expansion of the generalized domain-wall fermion Dirac operator including electromagnetic corrections up to $\mathcal{O}(e^2)$, which are relevant for lattice computations of radiative corrections to hadronic processes with chiral fermions. In the generalized formulation of the domain-wall fermionic QCD+QED action, physical quark fields are related to the corresponding five-dimensional fields in a way which depends on the (QCD+QED) gauge links, generating extra contact terms when expanding correlation functions with respect to the electric charge. We re-derive the known first-order correction using a background-field approach and, at second order, obtain new local operator insertions (seagull vertices) required for gauge covariant calculations.

Stochastic quantization defines a Euclidean quantum field theory as the equilibrium of a fictitious-time Langevin dynamics, which reaches the Gibbs measure asymptotically. We show that this quantization can be formulated as a finite-time stochastic optimal control problem. A tractable reference process, naturally supplied by the free theory when available, provides an Ornstein--Uhlenbeck dynamics, while the full interaction enters as a reference-corrected terminal cost. The optimal control is a Doob-transform force that steers the path-reweighted terminal ensemble to the target at a prescribed time and for a given noise amplitude. A neural network learns the residual control, realizing this optimal stochastic quantization (OSQ). Because the path weights are exact, imperfect training increases the variance of estimators but does not introduce model bias. On multimodal potentials we recover all modes at finite time and find that the noise amplitude sets a practical diffusion-horizon window. In two-dimensional lattice scalar $\phi^4$ theory we recover observables from hybrid Monte Carlo simulations near the critical point. Quantization is thereby formulated as control rather than equilibration.

We present an algorithm that addresses topological freezing in lattice QCD simulations by combining parallel tempering with collective-variable-based enhanced sampling methods, and apply it to a particularly challenging system with $N_f = 2$ staggered fermions. We find that the algorithm unfreezes the system, which is otherwise completely frozen for approximately 40000 Molecular Dynamics Units with the Rational Hybrid Monte Carlo algorithm.

In these proceedings, we provide a summary of our recent advancements in determining the mass of the lightest gluelump using hyperasymptotic expansions in Quantum Chromodynamics (QCD) \cite{Ayala2025}. This paper details our methodology, our precise determination of leading renormalon normalization constants, and our extraction of the gluelump mass from two independent physical systems, yielding a final combined, renormalization-group-invariant and scheme-independent result of $\Lambda_{B}^{\rm PV} = 2.44(7) r_0^{-1}$.

We present a comprehensive analysis of the angular coefficients of $Z$ and $W$ boson production at hadron colliders in different kinematical ranges, using data from the ATLAS, LHCb, and CMS Collaborations at the LHC, as well as CDF data at the Tevatron. We provide theoretical predictions obtained by consistently combining the resummation of logarithmically enhanced QCD corrections at small transverse momenta $q_T$ up to next-to-next-to-leading logarithmic accuracy (NNLL) with fixed-order calculations at next-to-leading order (NLO), valid at large $q_T$. We quantify the impact of transverse-momentum resummation on the angular coefficients. We find that the inclusion of resummation effects leads to a moderate and systematic improvement in the description of the data in the intermediate $q_T$ region, $q_T \sim 20-50$~GeV, for several angular coefficients, while in the remaining cases it does not degrade the agreement of fixed-order QCD predictions with experimental measurements.

The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

Four-dimensional chiral gauge theory can be formulated as the boundary theory on a five-dimensional manifold in a manner that may be realized on a finite lattice. There are interesting features of these theories which defy a purely four-dimensional conception of universality. We find that QCD when embedded in a chiral gauge theory (the Standard Model) and regulated this way can simultaneously avoid both the $U(1)_A$ problem and the strong $CP$ problem, with a central role played by fermion zeromodes localized far away in the fifth dimension. In this way it differs from conventional lattice QCD formulated as a stand-alone theory, universality being violated by inaccessible light modes in the five-dimensional bulk. Our analysis builds on recent work by others that highlights the role of global $U(1)$ symmetries in five dimensional formulations of four-dimensional chiral gauge theories, and the generic appearance of fermion zeromodes in the bulk.

The role of tetraquark operators in studying the isodoublet strange $\kappa$ and isovector nonstrange $a_0(980)$ scalar mesons in lattice QCD is examined using an ensemble with $m_\pi\approx230$ MeV and spatial extent $L$ such that $m_\pi L\approx4.4$. Hermitian correlation matrices using both single-meson, meson-meson, and tetraquark interpolating operators are used to extract the spectrum of finite-volume stationary states in the appropriate symmetry channels. Hundreds of local and extended tetraquark operators are explored. Determinations of the spectrum in each channel are found to be unreliable without the inclusion of at least one tetraquark operator. For example, the inclusion of tetraquark operators with isospin 1/2 and strangeness 1 quantum numbers reveals the existence of an additional energy level in the $K\eta$ sub-system below the $K\eta$ threshold. The implications of this on parametrizing the scattering $K$-matrix through a well-known quantization condition to extract properties of the $\kappa$ and $a_0(980)$ scalar meson resonances are discussed.

How should one define thermodynamic quantities (internal energy, work, heat, etc.) for quantum systems coupled to their environments strongly? We examine three (classically equivalent) definitions of a quantum system's internal energy under strong-coupling conditions. Each internal-energy definition implies a definition of work and a definition of heat. Our study focuses on quenches, common processes in which the Hamiltonian changes abruptly. In these processes, the first law of thermodynamics holds for each set of definitions by construction. However, we prove that only two sets obey the second law. We illustrate our findings using a simple spin model. Our results guide studies of thermodynamic quantities in strongly coupled quantum systems.

Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge. In particular, autoregressive models and normalizing flows have become prominent due to their appealing ability to yield closed-form probability densities. Moreover, it is well-established that incorporating prior knowledge - such as symmetries - into deep neural networks can substantially improve training performances. In this context, recent advances have focused on developing symmetry-equivariant generative models, achieving remarkable results. Building upon these foundations, this paper introduces Symmetry-Enforcing Stochastic Modulation (SESaMo). Similar to equivariant normalizing flows, SESaMo enables the incorporation of inductive biases (e.g., symmetries) into normalizing flows through a novel technique called stochastic modulation. This approach enhances the flexibility of the generative model, allowing to effectively learn a variety of exact and broken symmetries. Our numerical experiments benchmark SESaMo in different scenarios, including an 8-Gaussian mixture model and physically relevant field theories, such as the $\phi^4$ theory and the Hubbard model.