We examine the Lüscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total angular momentum $J=11/2$ in both cubic and elongated geometries, and for both rest and moving frames. Then, we introduce a method to transparently cross-check their convergence, using both quantized energy levels in the box and infinite-volume phase shifts for the same potential. We clarify how to incorporate spin-orbit coupling into the formalism and show in detail how the quantization conditions converge order by order in the various irreducible representations. In all, we validated 19 quantization conditions (12 in cubic box, 7 in elongated box). This is a necessary step in applying the method in precision studies of systems in finite volume with half-integer spin, such as meson-baryon scattering.

The real-time evolution of strongly interacting matter remains a frontier of fundamental physics, as classical simulations are hampered by exponential Hilbert space growth and entanglement-driven bottlenecks in tensor networks. This study reports the quantum simulation of hadron dynamics within a $(1+1)$-dimensional SU(2) lattice gauge theory using a 156-qubit IBM superconducting processor. Leveraging a hardware-efficient Loop-String-Hadron (LSH) encoding, we simulate the dynamics of the physical degrees of freedom on a $60$-site lattice in the weak-coupling regime, as a crucial step toward the continuum limit. We successfully observe the light-cone propagation of a confined meson and internal oscillations indicative of early-time hadronic breathing modes. Notably, these high-fidelity results were obtained directly from the quantum data via a differential measurement protocol, together with measurement error mitigation, demonstrating a robust pathway for large-scale simulations even on noisy hardware. To validate the results, we benchmarked the quantum algorithm and outcome from the quantum processor against state-of-the-art approximated classical algorithms using CPU -- based on tensor network methods and Pauli propagation method, respectively. Furthermore, we provide a quantitative comparison demonstrating that as the system approaches the weak-coupling or the continuum limit, the quantum processor maintains a consistent structural robustness where classical tensor networks and Pauli propagation methods encounter an onset of exponential complexity or symmetry violations as an artifact of approximation in the algorithm. These results establish a scalable pathway for simulating non-Abelian dynamics on near-term quantum hardware and mark a critical step toward achieving a practical quantum advantage in high-energy physics.

We study the phase structure of a model containing two flavors of massless staggered fermions interacting through two independent four-fermion couplings, UI and UB, formulated on a three-dimensional Euclidean space-time lattice. At UB = 0, this model is known to exhibit a direct second-order quantum phase transition between a massless fermion (MF) phase and a phase in which fermions acquire masses through the mechanism commonly referred to as symmetric mass generation (SMG). We demonstrate that introducing a small nonzero value of UB qualitatively alters this structure: the single exotic transition at UB = 0 splits into two distinct, conventional transitions, separated by an intermediate phase in which fermion masses arise through the standard mechanism of spontaneous symmetry breaking (SSB). The first of these is a Gross-Neveu transition separating the MF phase from the SSB-induced massive phase, while the second is a three-dimensional XY transition between the SSB phase and the SMG phase. Using the fermion-bag Monte Carlo method, we verify that the critical exponents associated with both transitions are consistent with the literature, thereby yielding a quantitative characterization of the resulting phase structure of the model.

We consider the two- and three-flavor QMD models as renormalizable low-energy models for QCD at finite quark chemical potentials with quarks, mesons, and diquarks as effective degrees of freedom. Using the on-shell scheme the parameters in the scalar sector can be fixed and expressed in terms of observed meson masses and decay constants. The remaining parameters can be varied. In the QMD models, all the symmetries are global, including the $SU(N_c)$ symmetry. The breaking of the global symmetries gives rise to a number of Goldstone bosons depending on the symmetry-breaking pattern, i.e. whether the system is in the 2SC phase or the color-flavor-locked (CFL) phase. This is in contrast to perturbative QCD, where some of the gauge bosons become massive via the Higgs mechanism. We classify the Goldstone bosons and show that their type and number are in accordance with general counting rules. The thermodynamic potential $\Omega$ is calculated in the mean-field approximation, where we include quark loops, while mesons and diquarks are treated at tree level. As important applications, we study the properties of the pion-condensed phase at finite isospin chemical potential, and the 2SC and CFL phases at finite baryon chemical potential. We present a few numerical results focusing on the speed of sound, gaps, and condensates. It is shown that the BCS gaps approaches a constant for large isospin and baryon chemical potentials and that the speed of sound approaches the conformal value from above in the same limit.

The relations between the window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a^{\text{HVP}}_{\mu}$ in spacelike and timelike domains are studied. Two types of window functions (abrupt and smooth) as well as two kinds of kinematic intervals (symmetric and asymmetric with respect to the spacelike/timelike flip) are addressed. It is shown that the window quantities for $a^{\text{HVP}}_{\mu}$ represented in terms of the hadronic vacuum polarization function $\bar\Pi(Q^2)$, the Adler function $D(Q^2)$, and the $R$-ratio of electron-positron annihilation into hadrons are mutually equivalent only if the additional contributions due to the window edge effects are properly taken into account and the explicit expressions for such contributions are derived. The obtained results enable one to evaluate $a^{\text{HVP}}_{\mu}$ by making simultaneous use of the inputs for functions $\bar\Pi(Q^2)$, $D(Q^2)$, and $R(s)$ at various energies and an example of such hybrid assessment is provided. The obtained results also enable one to accurately compare the window quantities for $a^{\text{HVP}}_{\mu}$ based, e.g., on MUonE or lattice data with the ones based on $R$-ratio data, even if the window function covers different kinematic ranges in spacelike and timelike domains.

Nucleon elastic electromagnetic form factors obtained using both the three-body and quark + fully-interacting-diquark pictures of nucleon structure are employed to calculate an array of light-front transverse densities for the proton and neutron and their dressed valence-quark constituents, viz. flavour separations of the proton and neutron results. These two complementary descriptions of nucleon structure deliver mutually compatible predictions, which match expectations based on modern parametrisations of available data, where such are available. Amongst other things, it is found that transverse-plane valence $u$- and $d$-quark Dirac radii are practically indistinguishable; but regarding kindred Pauli radii, the $d$ quark value is roughly 10% greater than that of the $u$-quark. Moreover, magnetically, the valence $d$ quark is far more active than the valence $u$ quark, probably because it has much greater orbital angular momentum. Both pictures of nucleon structure agree in predicting that, in a polarised nucleon, the transverse-plane charge densities are no longer rotationally invariant. Instead, for a $+\hat x$ polarised nucleon, positive charge is displaced in the $+\hat y$ direction, with the opposite effect for negative charge.