We argue that the claim of the absence of charge-conjugation-parity (CP) violating effects due to a topological term in quantum chromodynamics (QCD) is based upon a misunderstanding, and the standard results in the field are correct.

We formulate QCD discretized on the four dimensional 16-cell honeycomb. The advantage is a higher degree of rotational symmetry as compared to a traditional cubic lattice leading to much smaller cut-off effects. We demonstrate in quenched QCD, through both gluonic and fermionic observables, that the scaling properties are indeed superior to the cubic lattice and much larger lattice spacings are sufficient for controlled continuum extrapolations. Chiral and topological properties also show remarkable improvement.

We investigate the combination of a two-level sampling algorithm with distillation techniques to compute disconnected fermionic correlation functions. The method relies on a factorization of the quark propagator into domain-local contributions that depend only on the gauge fields within overlapping temporal regions, enabling independent submeasurements of each term through a two-level sampling strategy. The two-level estimators exhibit the expected $1/N_1^2$ scaling of the variance, up to exponential boundary effects, and achieve an exponential reduction of statistical errors at nearly the same computational cost as standard sampling. The method is tested on pure gauge ensembles, providing a controlled benchmark for its forthcoming application to dynamical QCD studies of glueball and isosinglet meson correlation functions.

I review recent results on phase structure and equation of state of strong interaction matter from lattice QCD. Particular emphasis is given to the axes where direct simulations are possible and results are obtained with sufficient control over systematic effects. I also discuss the status of approaching the region of non-zero baryochemical potentials using indirect methods.

We review the recent progress achieved, using Resonance Chiral Theory, in the hadronic contributions to the muon anomalous magnetic moment. These include the hadronic vacuum polarization, either using $e^+e^-$ or $\tau$ decays into hadron final states as input; and the hadronic light-by-light part, where in addition to previous results on the lightest pseudoscalar and tensor-poles contributions, we first present the evaluation of the pseudoscalar box using this formalism. We also discuss the scalar, axial-pole and other subleading pieces. The results obtained are consistent with the White Paper 2 values, with comparable precision.

The quark-mass dependence of the $N^*(920)$ pole is analyzed using $K$-matrix method, with the $\pi N$ scattering amplitude calculated up to $O(p^3)$ order in chiral perturbation theory. As the quark mass increases, the $N^*(920)$ pole gradually approaches the real axis in the complex $w$-plane (where $w=\sqrt{s}$). Eventually, in the $O(p^2)$ case, it crosses the $u$-cut on the real axis and enters the adjacent Riemann sheet when the pion mass reaches $526~{\rm MeV}$. At order $O(p^3)$, the rate at which it approaches the real axis slows down; however, we argue that it will ultimately cross the $u$-cut and enter the adjacent Riemann sheet as well. Additionally, the trajectory of the \(N^*(920)\) pole is in qualitative agreement with the results from the linear $\sigma$ model calculation.

We revisit the U(1) quantum link model in a ladder geometry, finding, by finite-size scaling, that the critical exponent $\nu=1$ and the central charge $c=1/2$ are consistent with the Ising universality class for all phase transitions observed. A blind application of the Harris criterion would suggest that this criticality is lost in the presence of the disorder. It turns out not to be the case. For the disorder affecting ladder's rung hoppings only, we have found that the transitions survive disappearing only for quite strong disorder. The disorder in the ladder's legs destroys the nonzero mass phase criticality, while the symmetry-protected topological phase for zero mass survives a small disorder. The observed robustness against disorder is explained qualitatively using field-theoretic arguments.

We investigate the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory (LGT) model with hard-core bosons at half-filling, extending previous studies by including second nearest-neighbor (2NN) interactions. Using matrix product state techniques within the density matrix renormalization group, we compute charge gap, static structure factor, and pair-pair correlation functions for various interaction strengths and field parameters. We analyze two representative neatest-neighbor interaction strengths ($V_1$) that correspond to the Luttinger liquid (LL) and Mott insulator (MI) phases in the absence of the 2NN interactions. We introduce the 2NN coupling $V_2$ and investigate its impact on the system. Our results reveal very rich behavior. As the 2NN repulsion increases, in the case of small $V_1$, we observe a direct transition from the LL phase to a charge-ordered insulator (COI) phase, whereas for large $V_1$, we observe a transition from the MI phase (previously found with only $V_1$ included), going through an intermediate LL region, and finally reaching the COI regime. Additionally, the inclusion of 2NN interactions enhances charge order and suppresses pair coherence, evidenced by sharp peaks in the structure factor and rapid decay in pair-pair correlators. Our work extends the well-studied phase structure of 1D $\mathbb{Z}_2$ LGT models and demonstrates the interplay between gauge fields, confinement, and extended interactions.

To investigate the three-dimensional quantum electrodynamics in the radial quantization on the lattice, the lattice action is constructed and the free limit is studied on $S^2 \times \mathbb{R}$. With the overlap fermion, it is numerically verified that the important symmetries of the theory can be realized on the lattice. The analytic correlators are derived and compared to the lattice results, which agree including the overall normalization. The $O(a^2)$-scaling is confirmed toward the analytic value in the continuum limit, and the number of reproduced excited states is estimated heuristically for the first few refinement levels. Our study helps us identify the features of the theory that we can study on the icosahedral lattice without fine-tuning.

The low-energy $J/\psi N$ scattering is important for various reasons: it is related to the hidden-charm $P_c$ pentaquark states, provides insights into the role of gluons in nucleon structures, and is relevant to the $J/\psi$ properties in nuclear medium. The scattering can happen through two distinct mechanisms: the coupled-channel mechanism via open-charm meson-baryon intermediate states, and the soft-gluon exchange mechanism. We investigate the $J/\psi N$ $S$-wave scattering length through both mechanisms, and find that the soft-gluon exchange mechanism leads to a scattering length at least one order of magnitude larger than that from the coupled-channel mechanism and thus is the predominant one. The findings can be verified by lattice calculations and will enhance our understanding of the scattering processes breaking the Okubo-Zweig-Iizuka rule.

We perform large scale quantum Monte Carlo simulations of the Hubbard model at half filling with a single Dirac cone close to the critical point, which separates a Dirac semi-metal from an antiferromagnetically ordered phase where SU(2) spin rotational symmetry is spontaneously broken. We discuss the implementation of a single Dirac cone in the SLAC formulation for eight Dirac components and the influence of dynamically induced long-range super-exchange interactions. The finite size behavior of dimensionless ratios and the finite size scaling properties of the Hubbard model with a single Dirac cone are shown to be superior compared to the honeycomb lattice. We extract the critical exponent believed to belong to the chiral Heisenberg Gross-Neveu-Yukawa universality class: The critical exponent ${\nu = 1.02(3)}$ coincides for the two lattice types once honeycomb lattices of linear dimension ${L\ge 15}$ are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be ${\eta_{\phi}=0.73(1)}$ and ${\eta_{\psi}=0.09(1)}$, they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation.

We perform an in-depth comparative analysis of unintegrated parton distribution function (UPDF) models for isolated prompt diphoton production in proton-proton collisions at $\sqrt{s}=13$~TeV within the $k_t$-factorization framework. Predictions are obtained with three UPDF approaches: Parton Branching (PB), NLO-MRW, and Modified KMRW (MKMRW). Tree-level $q + \bar q\!\to\!\gamma +\gamma$, $q + \bar q\!\to\!\gamma + \gamma + g$, and $q + g\!\to\!\gamma +\gamma + q$ subprocesses are generated with \textsc{KaTie} using off-shell initial states; the loop-induced $g + g\!\to\!\gamma + \gamma$ channel is evaluated independently. We compare differential cross sections with ATLAS measurements across a broad set of observables, including the photon transverse momenta, diphoton invariant mass and transverse momentum, the Collins-Soper angle, acoplanarity, $\phi^*_\eta$, and a transverse thrust-related variable. This comparative study quantifies the impact of the UPDF choice on the diphoton spectra. We find that the PB model provides the most consistent agreement over all distributions, whereas NLO-MRW tends to overshoot in regions correlated with larger factorization scales and MKMRW generally undershoots due to stronger Sudakov suppression. With standard scale variations, our results indicate that $k_t$-factorization with PB UPDFs can accurately describe diphoton production, while fixed-order collinear predictions typically require higher-order corrections together with parton-shower effects to achieve a comparable description.