We report the first lattice QCD study of the $s$-wave scattering of the $\bar{D}$-meson and the nucleon at the physical point, utilizing (2+1)-flavor configurations generated by the HAL QCD collaboration with a pion mass of $m_\pi\simeq 137$ MeV and a lattice spacing of $a\simeq0.084$ fm. By applying the HAL QCD method to the four-point correlation function of the $\bar{D}N$ system, we obtain a leading-order potential of the derivative expansion of the interaction kernel, which is then used to extract the $s$-wave phase shifts of low-energy $\bar{D}N$ scattering. Both the isospin $I=0$ and $I=1$ channels have a short-range repulsive core and a shallow attractive pocket in the intermediate to long-range region, though the $I=0$ channel is more attractive than the $I=1$ channel. We also observe that the $\bar{D}N$ potential exhibits more attraction than the $KN$ potential, which is its analog in the strange sector. In terms of the $s$-wave phase shifts, the $I=0$ channel shows a weak attractive behavior in the low-energy region with a positive scattering length of $0.246 \pm 0.105 (_{-0.051}^{+0.084})$ fm, whereas the $I=1$ channel shows repulsion with a negative scattering length of $-0.086 \pm 0.050 (_{-0.001}^{+0.037})$ fm. No bound states are found in both isospin channels, indicating the absence of a pentaquark state in the $s$-wave $\bar{D}N$ system.

We provide a short review of the progress made in the past decade with functional QCD in the description of the phase structure of QCD. We summarise the most important technical aspects of the framework, discuss strategies for truncations and address the problem of systematic error estimates. We detail efforts to gauge the approach systematically with lattice QCD at zero chemical potential, also including the physics of the Columbia plot at non-physical quark masses. Our main focus is, however, the high density regime of QCD. We address the predictive power of the functional approach for the appearance of new phases beyond the chiral crossover regime for chemical potentials $\mu_B/T\geq 4.5$. The onset of this regime may be signalled by a critical end point of the crossover line but may also involve a moat regime or the emergence of an instability that indicates an inhomogeneous phase. Respective results include estimates for the location of the onset of new phases, and predictions for their experimental signatures.

In this article, we use two different methods for studying the mass spectra of fully-heavy baryons and pentaquarks. In the first section, we use state-of-the-art machine learning methods, such as deep neural networks and the Particle Transformer model architecture, to predict baryon masses directly from their quantum numbers, based on experimental information on hadrons from the Particle Data Group (PDG). We use this data-driven approach for the case of fully heavy baryons, and a large number of exotic pentaquark states, going much beyond the well-known $ P_c^+(4380) $ and $ P_c^+(4457) candidates. Subsequently,we extend the Gürsey-Radicati mass formula to incorporate the contributions of charm and bottom quarks, enabling analytical calculations for both ground and radially excited states of baryons and pentaquarks. The results obtained from both approaches demonstrate strong agreement with experimental data where available and make predictions for a number of unobserved states, including higher radial excitations. By addressing the question through both data-driven prediction and analytical modeling in different frameworks, this study offers complementary insights into the mass spectrum of conventional and exotic hadrons, guiding future experimental searches.

By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge or BRST invariant non-perturbative ansatz of the 1PI Wilson action in quantum electrodynamics. The gauge invariance of the Wilson action is \emph{exactly\/} preserved under the RG flow. We explicitly solve the GFERG equation in the leading and partially the next to leading orders of the large $N_f$ approximation, where $N_f$ is the number of flavors. We obtain gauge invariant critical exponents and the gauge invariant 1PI Wilson action at an infrared (IR) fixed point for~$D<4$, where $D$ is the spacetime dimension.

One of the major open puzzles in the Standard Model of particle physics is the strong CP problem: although Quantum Chromodynamics allows a CP-violating topological $\theta$-term, experiments constrain its value to be extremely small. The Peccei--Quinn mechanism resolves this problem by promoting the $\theta$-angle to a dynamical field-introducing the axion -- whose dynamics relax the effective angle $\theta_\text{eff}$ to a CP-conserving minimum. Here, we investigate the resulting axion physics in a Hamiltonian lattice gauge theory (LGT) by coupling a quantized axion field to the massive Schwinger model with a topological $\theta$-term. Using infinite matrix product state techniques, we compute the ground-state properties of the resulting theory and demonstrate that the axion dynamically relaxes $\theta_\text{eff}$ to the minimum of the vacuum energy. Consequently, the ground-state energy becomes independent of $\theta$, demonstrating the axion-mediated solution to the strong CP problem within a fully dynamical LGT. We further analyze CP restoration and extract the axion mass from the topological susceptibility and excitation spectrum. Our results provide a nonperturbative demonstration of axion dynamics in a quantum LGT amenable to investigation on modern quantum hardware.