Heavy meson HQET light-cone distribution amplitudes (LCDAs) are critical for precision predictions of $B$ meson weak decays, but currently are one of dominant theoretical uncertainties that obscure interpretations of $B$ anomalies and CP-violating measurements. Building on the established HQLaMET framework, supplemented by lattice QCD calculations of the OPE moments, we present a precise lattice QCD calculation of HQET LCDAs by employing multi-ensemble simulations for continuum and physical pion mass extrapolation, quantifying comprehensive systematic errors, and validating results through OPE moment cross-validation. Details of the lattice calculations are provided in a companion paper \cite{HeavymesonDA_long_paper}. Our final results for key inverse moments (at $\mu=1$ GeV) are $\lambda_B=0.340(20)$ GeV and $\sigma_B^{(1)}=1.685(63)$, with the total uncertainty reduced by a factor of three relative to the previous analysis. These results can greatly reduce the uncertainty in the $B \to K^*$ form factors in the large-recoil region. This work resolves the long-standing bottleneck in first-principles predictions of heavy meson LCDAs, advancing precision flavor physics to new frontiers.

Trained lattice samplers are usually judged by the ensembles they generate. Here we instead analyze the trained field-space function itself: a flow-matching velocity, a diffusion score, or a normalizing-flow action residual. We project these functions onto operator bases fixed before the fit, chosen from symmetry, exact Gaussian path limits, finite-volume modes, and gauge covariance. For two-dimensional lattice \(\phi^4\), a trained straight-flow teacher is not described by a local force basis alone. After the local transport basis, the residual separates into a zero-mode Binder component and a lowest-shell finite-\(k\) correlator component. The deflated zero-mode polynomial \(P_5(M;t)\) reduces the dominant Binder-tail component, while \(\phi^\perp_{|n|^2=1}\) reduces the finite-\(k\) correlator component; wrong-parity, off-zero-mode, and random controls do not produce the same reductions. The same projection distinguishes other sampler classes. Diffusion follows the force-resolvent ordering predicted by the free theory, reverse-KL normalizing-flow collapse appears as a forbidden odd zero-mode residual, and gauge-equivariant teachers are resolved by Wilson-loop-force tangent directions. The operator basis is model- and symmetry-dependent, but the test is common: project the trained field-space function and retain sectors that lower held-out residuals and pass the available controls.

A strongly coupled confining gauge theory with a non-zero vacuum angle undergoing a deconfinement to confinement phase transition is studied in the holographic gravitational description. A simplified five-dimensional setup is constructed where a bulk scalar models the effect of the vacuum angle, and the suitable boundary conditions on the ultra-violet (UV) and the infra-red (IR) boundaries are identified. The IR boundary condition is motivated by higher dimensional examples where the bulk scalar comes from a Wilson loop on a shrinking cycle. In this five-dimensional dual geometry, and in the limit of small backreaction in the infra-red, the critical temperature for the phase transition is shown to reduce quadratically with the vacuum angle, matching lattice results. The topological susceptibility has a sharp reduction across the critical temperature, also matching lattice results. The rate for the phase transition is estimated as a function of the vacuum angle, and is seen to be enhanced (reduced) when the field theory has a relevant (irrelevant) deformation at high energies. Crucially, for the irrelevant case, the confined phase can get destabilized for a range of parameters. In the context of early universe dynamics, if the vacuum angle is time-dependent, the transition history changes strongly: the deconfined phase can last till much lower temperatures than naively expected, and one can trigger a transition to the confined phase by a change in the vacuum angle, thus providing a controlled way to generate supercooling. As a phenomenological application, the peak frequency and the power of resulting gravitational wave signal from bubble collisions change, affecting their visibility in detectors. Possible generalizations of the scenario are discussed.

The dipolar universality class describes the phase transition in 3D ferromagnets with strong dipolar interactions, as first discussed by Aharony and Fisher in the 1970s. While this universality class has been studied theoretically using renormalization group methods, as well as experimentally, little is known about it from Monte Carlo simulations. In this paper we aim to bridge this gap. We introduce a lattice model that faithfully implements the transverse constraint on the order parameter. We introduce a Markov Chain Monte Carlo algorithm which involves a combination of local Metropolis updates preserving the constraint, and a global update of the zero mode. We perform simulations on cubic lattices up to volume $48\times 48 \times 48$. We observe a continuous phase transition between the disordered and ordered phases. We obtain estimates of universal quantities such as the main critical exponents and the Binder ratio, and compare them with results from other techniques. We also investigate the emergence of rotation invariance at the critical point.

We compare the isospin-one, vector-current hadronic vacuum polarization (HVP) obtained from isospin-symmetric lattice QCD with that obtained from a dispersive representation employing inclusive hadronic $\tau$ decay data corrected for isospin breaking. We consider the subtracted HVP evaluated at squared Euclidean momenta ranging from $0.5$ GeV$^2$ to $12$ GeV$^2$, together with the light-quark-connected HVP contribution to the muon anomalous magnetic moment and the short-, intermediate- and long-distance RBC/UKQCD window components thereof. Dispersive contributions from the region of hadronic invariant masses above the $\tau$ mass are evaluated using perturbative QCD. We also consider dispersive determinations using $\tau$ data only for contributions from two-pion, or two-pion and four-pion, modes, and evaluating the remaining contributions using exclusive-mode $e^+e^-\to\mbox{hadrons}$ cross sections up to about 2 GeV, lessening the dependence on perturbation theory. We find generally good agreement between lattice and $\tau$-based results. However, a comparison of $\tau$-based window-quantity contributions for the two four-pion modes to expectations for those contributions based on the Pais relations and $e^+e^-$ four-pion cross sections, reveals significant differences for the $2\pi^-\pi^+\pi^0$ mode.

We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation -- where the gauge field is exactly integrated out and no truncation of the electric flux is required -- we investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$. These correspond respectively to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling, the $B = 0$ and $B = 2$ channels exhibit predominantly elastic dynamics closely resembling those of the U(1) Schwinger model. In contrast, the mixed $B = 1$ sector shows qualitatively new behavior: meson and baryon wave packets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.

Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.

We perform a comprehensive study of the properties of Dirac eigenvalue spectrum in QCD as a function of temperature on the lattice. In addition to effects due to interplay between interactions and disorder inherently present in a many-body system, the Dirac spectrum also contains crucial information about the effective restoration of different subgroups of almost exact two-flavor chiral symmetry in QCD. We calculate the infrared eigenvalues of the overlap Dirac operator on 2+1 flavor QCD ensembles generated using domain wall fermion discretization, on a large volume lattice. From the normalized level spacing ratios, we identify those eigenvalues that have intermediate level statistics, distinctly different from the majority in the bulk spectrum that follow universal level fluctuations similar to a random matrix of Gaussian unitary type. We provide an explanation of these intermediate level ratios in terms of a specific random matrix model and quantify the correlation between these eigenstates and disorder in the gauge fields manifested in the renormalized Polyakov loop values. Whereas the existence of intermediate eigenmodes is intimately connected to the effective restoration of different subgroups of chiral symmetry close to chiral crossover transition, their origin can be traced to random uncorrelated disorder at higher temperatures when the $U_A(1)$ is effectively restored. We also, for the first time, calculate the Thouless conductance for the Dirac spectrum that quantifies the structural rigidity of the eigenvectors, and use it as a diagnostic tool to understand the restoration of the anomalous $U_A(1)$ subgroup of chiral symmetry and localization driven by disorder.