Flagship neutrino oscillation experiments depend on precise and accurate theoretical knowledge of neutrino-nucleon cross sections across a variety of energies and interaction mechanisms. Key ingredients to the amplitudes that make up these cross sections are parameterized form factors. The axial form factor describing a weak interaction with a nucleon is part of one of the primary neutrino-nucleon interaction mechanisms, quasielastic scattering, yet this form factor is uncertain and its precision is limited by the availability of data for a neutrino scattering with nucleons or small nuclear targets. Lattice Quantum Chromodynamics (LQCD) now offers another approach for obtaining mathematically rigorous constraints of the axial form factor from theoretical calculations with complete systematic error budgets. In this work, strategies for averaging LQCD results are explored, including both a random sampling of form factor values across momentum transfers as well as an averaging strategy based on analytic calculations of form factor derivatives. Fits to z expansion parameterizations are reported and compared against neutrino-hydrogen and neutrino-deuterium scattering data.

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical $O(2)$ nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature $T_c=2.2017(2)$ with the critical exponent $\nu = 0.663(33)$ for the 3D $O(2)$ model. In addition, we also study the Berezinskii-Kosterlitz-Thouless (BKT) criticality of the 2D classical $O(2)$ model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, $T_{\mathrm{BKT}}=0.8928(2)$.

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

We study the impact of background electric fields on a hot plasma of charged particles -- a setting relevant for the early stages of heavy-ion collisions as well as laser pulse experiments. Historically, the electric susceptibility -- encoding the behavior of the hot medium for weak fields -- has been defined within two different formalisms, leading to two distinct results at nonzero temperature. With the help of an exact fermion propagator in a homogeneous electric background field at nonzero temperature and finite volume on the one hand, and an improved perturbative result on the other, we identify the origin of this disagreement. The equilibrium conditions for the system are discussed and the role of the thermodynamic ensemble used to describe the system is highlighted. Finally, we construct the electric susceptibility in a simplified hadron resonance gas model, relevant for the strongly interacting medium in the low-temperature regime.

Using continuum Schwinger function methods, a coherent set of predictions for proton, $\Lambda$ and $\Sigma^0$ distribution functions (DFs) has been made available -- both helicity dependent and unpolarised. The results and comparisons between them reveal impacts of diquark correlations and SU$(3)$-flavour symmetry breaking, some of which are highlighted in this contribution. For instance: in-proton ratios of helicity-dependent/unpolarised valence-quark DFs are presented; it is highlighted that, were it not for the presence of axialvector diquarks in the $\Sigma^0$, the valence strange quark would carry none of the $\Sigma^0$ spin; and the sign and size of polarised gluon DFs is discussed -- at a scale typical of modern measurements, gluon partons carry roughly 40% of each octet baryon's spin.

Within the method of parity-projected QCD sum rules, we study the mass spectra of light hybrid baryons with $I(J^{P})=1/2(1/2^{\pm}), 3/2(1/2^{\pm}), 1/2(3/2^{\pm}), 3/2(3/2^{\pm})$ by constructing the local $qqqg$ interpolating currents. We calculate the correlation functions up to dimension eight condensates at the leading order of $\alpha_{s}$. The stable QCD Lapalce sum rules can be established for the positive-parity $N_{1/2^+}, \Delta_{3/2^+}, \Delta_{1/2^+}$ and negative-parity $N_{1/2^-}, N_{3/2^-}, \Delta_{1/2^-}$ channels to extract their mass spectra. The lowest-lying hybrid baryons are predicted to be the positive-parity $N_{1/2^+}$ state around 2.01 GeV. These hybrid baryons mainly decay into conventional baryon plus meson final states. We propose to search for the light hybrid baryons through the $\Upsilon/\psi(3686)$ decays via the three-gluon emission mechanism in BESIII and BelleII experiments. Hopefully our studies of the light hybrid baryons will be useful for understanding the excited baryon spectrum and the behavior of gluonic degrees of freedom in QCD.