In this work, the phase function method (PFM) is applied for the first time to explicitly construct scattering wavefunctions for the $\alpha\alpha$ system using interaction parameters optimized from earlier phase shift analysis. While previous investigations employing PFM and related approaches have primarily focused on the reproduction of scattering phase shifts or cross sections, the present study advances the method to directly reconstruct physically meaningful radial scattering wavefunctions for the $\ell = 0$, 2, and 4 partial waves without solving the Schrödinger equation. The computed wavefunctions exhibit well-behaved near-origin and asymptotic characteristics and show excellent agreement with the established resonating-group method results of Hiura \textit{et al.}. This agreement confirms the numerical robustness and accuracy of the proposed framework. The present results establish PFM as an efficient, unified, and computationally attractive tool for scattering wavefunction reconstruction in cluster--cluster systems, opening new possibilities for its application to more complex nuclear scattering problems.

The theory of nuclear excitations involving nucleon resonances is revisited and significantly extended to asymmetric nuclear matter and higher P- and S-wave $N^*$ resonances. Excited states of are described as superpositions of particle-hole configurations including $NN^{'-1}$ and $N^*N^{-1}$ configurations. Configuration mixing is taken into account on the one-loop level by solving the generalized $N^*RPA$ Dyson equation. The underlying coupled channels formalism is derived and response functions is discussed. Applications of the approach are illustrated for charge-exchange modes of asymmetric nuclear matter and finite nuclei. The spectral gross structures of corresponding excitations in finite nuclei are investigated in local density approximation. Applications of the approach to resonance studies by high-energy heavy ion reactions are recapitulated.

Radiative strength functions (RSFs) model the bulk electromagnetic response of highly-excited nuclei and are critical inputs for statistical reaction codes. In this paper, we present a definition of the RSF that is consistent with Hauser-Feshbach reaction codes and that can be efficiently computed with the shell model using the Lanczos strength-function (LSF) method. We introduce a variant of the shell model LSF method that exploits the energy-localized Brink-Axel hypothesis, which makes it possible to compute both electric and magnetic RSFs across all energies relevant to capture reactions. We verify agreement with the conventional definition of RSFs with benchmark calculations of $^{24}$Mg, then present novel results for $^{56}$Fe. For $^{56}$Fe we find that: (i) the M1 RSF shape evolves smoothly with excitation energy, consistent with the energy-localized Brinkl-Axel hypothesis, (ii) both M1 and E1 transitions contribute significantly to the radiative strength below the photo-absorption threshold, and (iii) within the sdpf model space, the strength below 3 MeV observed in Oslo-type experiments cannot be fully reproduced. These results pave the way for a coherent microscopic description of the RSFs and further motivate the use of energy-dependent RSFs in modern reaction codes.

Dissipative processes are pivotal for understanding the hydrodynamic evolution of hot and dense QCD matter created in relativistic nuclear collisions. The interplay of multiple conserved charges -- net baryon, strangeness, and electric charge -- is of particular interest. We simulate the longitudinal hydrodynamic evolution with the three diffusion currents in a hydrodynamic model with a lattice-QCD-based equation of state, NEOS-4D, and estimate rapidity distributions including diffusive corrections to the phase-space distribution in the presence of multiple charges, which ensure charge conservation at particlization. We determine the response of particle yields at midrapidity to changes in the diagonal and off-diagonal conductivities. Inversely, we find that most components of the conductivity matrix can be constrained experimentally using identified particle multiplicities at different collision energies.

The primordial 7Li abundance predicted by standard Big Bang Nucleosynthesis (BBN) exceeds that inferred from old, metal-poor stars by a factor of about 3-4. In standard BBN, most primordial 7Li is produced as 7Be in the early Universe and later converted by electron capture. Additional production or destruction channels of 7Be, such as proton capture or antineutrino capture during BBN, may therefore affect the final lithium yield. We quantify the depletion of 7Be due to in-situ electron capture, including the associated antineutrino channel, positron decay from nuclear excited states, and proton capture through the radiative 7Be(p,gamma)8B reaction. We also investigate stimulated emission induced by the dense photon background during the nuclear statistical equilibrium epoch, as well as a three-body Auger-like variant transferring the capture energy to a continuum electron. Decay rates are computed using first-order perturbation theory, modelling weak interactions with a Fermi contact term and factorising hadronic and leptonic currents. Thermally averaged rates are obtained by folding cross-sections with Maxwell-Boltzmann distributions and accounting for particle densities in the temperature range 10-100 keV. We find that the electron-capture rate decreases rapidly with temperature and is significantly enhanced by the inclusion of the antineutrino channel. Stimulated emission and plasma screening increase the radiative proton-capture rate by only 1-3 percent at temperatures around 87 keV. The Auger-like channel contributes at the level of a few thousandths of a percent and becomes negligible at lower temperatures. Overall, our total rate revises previous estimates by nearly an order of magnitude. Electron capture, proton capture, and positron decay provide corrections to the dominant depletion channel 7Be(n,p)7Li.

In the present work, we have generalized the projected shell model (PSM) approach to include the quasiparticle excitations from two major oscillator shells, and have also extended the basis space to five-quasiparticle configurations for odd-mass nuclei. The magnetic and antimagnetic rotational structures observed in odd-neutron Pd- and Cd-isotopes have been investigated as a first major application of the new development. It is shown that PSM approach provides a reasonable description of the observed properties of magnetic and antimagnetic rotational bands.

The validation of numerical methods is a prerequisite for reliable few-body calculations, particularly when moving beyond standard partial-wave decompositions. In this work, we present a precision benchmark for the two-boson bound-state problem, solving it using two complementary formulations: the standard one-dimensional partial-wave Lippmann--Schwinger equation and a two-dimensional formulation based directly on vector variables. While the partial-wave approach is computationally efficient for low-energy bound states, the vector-variable formulation becomes essential for scattering applications at higher energies where the partial-wave expansion converges slowly. We demonstrate the high-precision numerical equivalence of both methods using rank-one separable Yamaguchi potentials and non-separable Malfliet--Tjon interactions. Furthermore, for the Yamaguchi potential, we derive exact analytical expressions quantifying the systematic errors introduced by finite momentum- and coordinate-space cut-offs. These analytical bounds provide a rigorous tool for disentangling discretization errors from truncation effects in few-body codes. The results establish a reliable reference standard for validating the vector-variable approaches essential for future three- and four-body calculations.

The trace anomaly of dense matter, $\Delta \equiv 1/3 - P/\varepsilon$, defined in terms of the ratio of pressure $P$ to energy density $\varepsilon$, quantifies deviations from conformal symmetry and plays a central role in both the hydrodynamic response and gravitational equilibrium. While $\Delta(\varepsilon)$ has recently been inferred from neutron star observations, we report the first Bayesian extraction of the trace anomaly from collective flow observables in intermediate-energy heavy-ion collisions. By employing transport-model simulations that explicitly decouple the cold-matter mean-field potential from thermal effects, we directly constrain the cold dense-matter equation of state (EOS). Remarkably, the trace anomaly inferred from laboratory flow data agrees quantitatively, within $68\%$ credible intervals, with independent astrophysical posterior bands. This nontrivial agreement demonstrates that heavy-ion collisions and neutron star observations probe the same universal macroscopic properties of dense matter, establishing the trace anomaly as a composition-insensitive descriptor of dense matter across widely different physical environments.

The inner crust of neutron stars hosts a rich variety of nuclear phenomena and provides a unique environment for exploring microscopic nuclear properties relevant to diverse astrophysical observations. Particularly magnetars, which possess extremely strong magnetic-fields, have attracted increasing attention in connection with nuclear spin dynamics and unconventional pairing correlations. This work is dedicated to develop a comprehensive theoretical framework to describe the structures and properties of two-dimensional (rod-phase) matter in the neutron star inner crust, incorporating band-structure effects, neutron spin-triplet pairing, and strong magnetic-fields on an equal footing. The main results of this study can be summarized as follows. In the first place, the magnetic-fields of the order of $10^{16}\,$G are found to substantially enhance the neutron effective mass by a factor of approximately $1.5$, indicating a significant modification of entrainment properties in strongly magnetized crustal matter. In the second place, while the overall behavior of pairing phase transitions is qualitatively similar to that observed in one-dimensional systems studied previously, the present two-dimensional calculations reveal a nontrivial role of the spin-orbit interaction in inducing spin-polarization under magnetic fields. In the third place, concerning spin-triplet superfluidity, the rank-0 component is shown to emerge as a consequence of magnetic-field-induced spin-polarization, irrespective of the presence of spin-triplet pairing interactions, whereas the rank-2 component appears only when the corresponding interaction channel is included.

This work investigates one- and two-neutron transfer in the $^{96}\text{Zr} + {}^{40}\text{Ca}$ reaction at sub-barrier energies using a microscopic framework based on time-dependent covariant density functional theory (TD-CDFT). Pairing correlations are incorporated via the time-dependent BCS approximation, which is shown to significantly enhance pair transfer, as evidenced by an increased two-neutron transfer probability. The oblate deformation of $^{96}$Zr causes the transfer probabilities to vary by orders of magnitude with orientation; a direct comparison with experiment is enabled by averaging results over thirteen systematically chosen orientations. While the orientation-averaged one-neutron transfer probabilities agree well with data, the two-neutron channel is suppressed below the Coulomb barrier. This suppression is attributed to missing quantum fluctuations in the semiclassical TD-CDFT approach. To test this, we employ the generalized time-dependent generator coordinate method (TDGCM), which confirms that quantum fluctuations are essential for an accurate description of sub-barrier two-neutron transfer dynamics.

We theoretically investigate a quartet superfluid state in fermionic matter by using the quartet Bardeen-Cooper-Schrieffer (BCS) variational theory and the Green's function method. We demonstrate that the quartet BCS theory with the multiple-infinite-product ansatz successfully reproduces an exact four-body result in a one-dimensional four-component Fermi gas at the dilute limit, in contrast to the single-infinite-product ansatz. To see the validity of the quartet BCS state, we derive the self-consistent equation for the quartet superfluid order parameter within the generalized imaginary-time Nambu-Gor'kov formalism, which is found to be consistent with the quartet BCS variational equation. Moreover, by numerically computing the momentum-resolved single-particle spectral function in a one-dimensional system, we discuss how the single-particle spectra evolve with increasing the strength of the four-body cluster formation. We show that a coherent BCS-like quasiparticle branch on the weak-coupling side evolves into a strongly damped, continuum-dominated spectrum in the strong-coupling side, while nonzero quartet superfluid order parameter persists throughout the crossover regime. Our results would be useful for understanding beyond-BCS pairing effects and four-body cluster formations in fermionic systems in an interdisciplinary way.

We discuss how to generate entangled Bell states of two nucleons using unpolarized nucleon-nucleon scattering or the exclusive deuteron breakup reaction. We follow the the approach of Z. X. Shen et al., arXiv:2510.24325v1 [nucl-th], where Bell states were identified in unpolarized proton-proton elastic scattering. We confirm these results and show that, in the unpolarized proton-deuteron breakup reaction, it is also possible to generate proton-proton entangled Bell states in kinematically complete proton-proton quasi-free scattering (QFS) and final-state interaction (FSI) configurations. We also discuss an experimental setup that, by exploiting such entangled states, could enable the teleportation of quantum mechanical states in a three-proton system. Such an experiment requires triple coincidences among the outgoing nucleons, which precludes the use of entangled Bell states generated with extremely polarized incoming particles. Since counting rates for unpolarized reactions are much higher than for polarized ones, the present results open a pathway toward searching for signatures of quantum state teleportation in hadronic systems.

We construct posterior distributions of the equation of state (EoS) for matter beyond the inner crust of neutron stars by incorporating finite nuclei (FN) constraints within relativistic mean field models. These constraints are implemented in three complementary ways: (i) through theoretical bounds on the EoS, (ii) implicitly via nuclear matter parameters, and (iii) explicitly by enforcing consistency with experimental binding energies and charge radii of selected nuclei. The resulting low-density nucleonic EoSs are subsequently matched to a model-agnostic speed-of-sound parametrization, constrained by astrophysical observations, including NICER mass-radius measurements, tidal deformability limits from GW170817, and lower bounds on the maximum neutron-star mass inferred from radio pulsar observations. We find that the admissible range of the transition density is strongly sensitive to the choice of the low-density EoS. In particular, the inclusion of explicit FN constraints significantly reduces the allowed parameter space of the nucleonic EoS at low densities, narrowing the transition-density range by nearly a factor of two. Consequently, neutron-star properties inferred from EoSs with explicit FN constraints differ substantially, with especially pronounced effects for low-mass neutron stars and their correlations with nuclear matter parameters. A quantitative comparison, using metrics based on Mahalanobis distance, shows consistency of the explicit constraints with PSRs J0740+6620, J0030+0451, and J0437-4715, but suggest a possible tension with PSR J0614-3329. These findings underscore the critical importance of a consistent treatment of finite-nuclei properties for reliably inferring the behavior of high-density matter and the presence of possible phase transitions from astrophysical observations.

Studying Nambu solutions of the rainbow-ladder gap equation in QCD at zero temperature and chemical potential, we prove that the mass function emerges continuously from zero as the interaction strength is increased past the critical point for all positive, asymptotically perturbative kernels almost everywhere continuous in $L^1$ using the Krasnosel'skii-Guo Cone Compression Theorem. We prove that the coupled system of equations must have a positive, continuous Nambu solution with decreasing mass function for all current quark masses for a class of models which includes the physical point of a popular model of QCD by using a hybrid Krasnosel'skii-Schauder Fixed Point Theorem.

We explore the connection between the four-dimensional Minkowski-space Bethe-Salpeter equation and its light-front projection, emphasizing the implications for bound-state dynamics. Our approach incorporates dressed particles, such as quarks, via the integral representation of the corresponding propagator. We analyze the light-front dynamics of the valence component of the physical state using a hierarchical set of Green's functions, which reveals its coupling to higher Fock components when dressed particles are considered. We also present the light-front Faddeev-Bethe-Salpeter equations for three-body systems with dressed constituents. Furthermore, we discuss formal developments that are central to connecting the three-dimensional light-front dynamics onto the null-plane and the four-dimensional Minkowski-space framework, based on the Nakanishi integral representation. Selected applications to hadron structure are also reviewed.

Bilinear Euclidean quark and gluon correlators with Wilson links have been used widely for applications of large-momentum effective field theories to computing non-perturbative collinear and soft parton physics. Due to color confinement, these correlators decay exponentially at large spatial distances, a behavior crucial for computing momentum-space Fourier transformations with controlled errors from lattice QCD data. Using heavy-quark effective theory reduction, dispersive analysis, Lorentz symmetry, and heavy-flavor spectra, we determine the leading and next-to-leading asymptotic behaviors and relate the expansion parameters to binding energies of heavy-flavor hadrons. We demonstrate the results through two-loop calculations in $\phi^3$ theory and from the perspective of locality and analyticity. We also study the impact of the asymptotic analysis on realistic lattice QCD data and demonstrate reliable error estimates.

We study open charm hadrons production in pp and Au+Au collisions at $\sqrt{s_{\mathrm{NN}}} = 200$~GeV using an improved a multi-phase transport (AMPT) model. Specifically, we show the transverse-momentum spectra and nuclear modification factors $R_{\mathrm{AA}}$ of $D^{0}$ mesons and $\Lambda_{c}^{+}$ baryons, as well as the $\Lambda_{c}^{+}/D^{0}$ ratio in pp and Au+Au collisions. The results obtained from the AMPT model simulations are compared with the STAR experimental data and found to be consistent. We further investigate the $\Lambda_{c}^{+}/D^{0}$ ratio by evaluating contributions from coalescence, fragmentation, and the combined coalescence+fragmentation mechanisms, and we find that fragmentation alone underestimates the pronounced enhancement in Au+Au relative to pp at low and intermediate $p_{\mathrm{T}}$, whereas the coalescence+fragmentation mechanism reproduces the observed trend significantly better. These results indicate that coalescence plays a key role in charm baryon productions and helps constrain the relative importance of different hadronization mechanisms in the ultra-relativistic nuclear collisions.

Precision measurements of four neutrino oscillation parameters, $\theta_{12}$, $\theta_{13}$, $\Delta m^2_{21}$, and |$\Delta m^2_{31}$|, face significant interference from a previously overlooked correlated background. Recent findings from the SNO+ and JUNO experiments reveal that cascade decays of $^{214}$Bi-$^{214}$Po in liquid scintillator detectors can mimic inverse beta decay signals from reactor and geoneutrinos, with a misidentification probability on the order of $10^{-4}$ when hydrogen neutron capture is used, a rate ten times higher than Geant4 simulations predicted. This work identifies the $^5$Li resonance in $\alpha$-$p$ elastic scattering as the underlying cause. For alpha energies above 5~MeV, the cross section is hundreds of times larger than that of Rutherford scattering. After correctly incorporating the differential cross section into Geant4, the misidentification probability is recalculated as 1.9$\times$10$^{-4}$. The simulated shape of the long tail in the alpha deposited energy also differs from the extrapolation models currently used by SNO+ and JUNO. These results will assist both experiments in more accurately estimating this novel background, thereby refining measurements of neutrino oscillation parameters and the geoneutrino flux. Additionally, the study implies an overlooked background with a rate of 0.5 events per detector per day in the Daya Bay $\theta_{13}$ analysis using hydrogen neutron capture, leading to an increase of $\sin^22\theta_{13}$ by approximately 0.012. Consequently, the Particle Data Group's reported $\sin^2\theta_{13}$ value shall increase by about 0.006~(1$\sigma$).

Quantum chromodynamics (QCD) with a general number of colors, $\Nc$, provides a powerful theoretical laboratory to explore the dynamics of non-Abelian gauge theories. Although $\Nc =3$ does not look a large number, the $1/\Nc$ expansion provides us with a very useful classification and book-keeping scheme for hadronic processes and sharpens conceptions otherwise obscured in real-world QCD with $\Nc = 3$. Important applications are dense QCD matter where the first principle methods for QCD are not available and many conceptual issues remain to be clarified. In this chapter we first review hadrons at large $\Nc$ from the viewpoint of quark-gluon dynamics, and then extend the discussions to hot/dense matter, focusing on confinement-deconfinement aspects. We emphasize how the large-$\Nc$ limit provides a unified organizing principle for hadronic and quark degrees of freedom in regimes where first-principle methods are limited. Two-color and isospin QCD, for which lattice simulations at finite density can be performed for a special reason, is reviewed.

We perform a systematical investigation of the existence of the deuteron-like singly bottomed dibaryon resonance states with strangeness $S=-1,~-3,~-5$ in the chiral quark model. Two resonance states with strangeness $S=-1$ are obtained in the baryon-baryon scattering process. The first candidate is $\Sigma\Sigma_b$ in the $\Lambda\Lambda_b$ and $N\Xi_b^*$ scattering process, with the resonance energy 6974.22 MeV - 6975.37 MeV and the decay width 14.450 MeV, respectively; the other one is $\Sigma \Sigma_b^*$ in the $N\Xi_b$ and $N\Xi'_b$ scattering process, with the resonance energy 6990.69 MeV - 7008.37 MeV and the decay width 43.790 MeV, respectively. The Root Mean Square (RMS) radius calculation shows that the former tends to be in a compact structure, while the latter tends to be in a molecular structure. Both of these resonance states are worthy of experimental exploration. Furthermore, it should be emphasized that the effect of channel-coupling is of great importance in exploring exotic hadron states, and investigating the scattering process may serve as an effective approach to identifying genuine resonances.

The present work reports new total photoabsorption cross sections for the $N=Z$ nuclei in the $sd$-shell $^{20}$Ne, $^{24}$Mg, $^{28}$Si, $^{32}$S, $^{36}$Ar, and for $^{26}$Mg. The results are compared to predictions of a data-driven artificial neural network application and to configuration-interaction shell-model calculations covering the excitation energy region of the isovector giant dipole resonance. Double-differential cross sections of the $(p,p^\prime)$ reaction at 295 MeV have been measured between $0^\circ$ and $14^\circ$. The angular distributions of the $E1$ parts due to Coulomb excitation have been extracted with a multipole decomposition analysis for excitation energies 12 to 24 MeV and converted to equivalent photoabsorption cross sections with the virtual photon method. Reasonable agreement of the photoabsorption cross sections with previous experiments is found for $^{24}$Mg and $^{28}$Si, while the present results diverge for $^{32}$S. For the first time, data are presented for $^{20}$Ne, $^{26}$Mg and $^{36}$Ar. Configuration-interaction shell-model calculations provide an overall satisfactory description of the fragmented $E1$ strength distributions. The same holds for absolute cross sections except for $^{26}$Mg and $^{36}$Ar, where the experimental results significantly exceed the expected exhaustion of the Thomas-Reiche-Kuhn energy-weighted sum rule. Fot light nuclei, there is a larger model dependence compared to previous analyses in heavy nuclei, in particular for excitation energies above 20 MeV, due to the need to constrain the continuum background with additional assumptions. The overall success of the shell-model approach to describe the features of the experimental photoabsorption cross sections motivates its application in large-scale reaction network calculations aiming at an understanding of the mass composition of ultrahigh-energy cosmic rays.

We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $\eta_c$ and $J/\psi$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

Collisions among heavy ions, like Pb or Au, are a great tool to study the theory of strong interactions, that is Quantum Chromodynamics (QCD). In particular, these experiments are able to give insights on all the complex phases of matter that the theory of QCD allows. In this PhD Thesis we have investigated the initial stages of proton-ion collisions: in particular, we will focus on the first $\sim 0.4$ fm/c ($\sim 10^{-24}$ s) after the collision, which are dominated by very intense gluon fields, in a state called glasma. We investigated the effect of such fields on the dynamics of heavy quarks (charm and beauty) which are created and evolve in this medium. The effect of the initial gluon fields on heavy quarks is quite substantial, in particular we observe that the glasma provokes a $50\%$ dissociation rate on quark-antiquark pairs. Moreover, glasma fields have a large momentum anisotropy, and transmit a large part of such anisotropy to the heavy quarks which evolve in this medium. Finally, we have generalized our study to a non-boost invariant medium, and shown that fluctuations in rapidity do not lead to significant isotropization within glasma timescales.

The theoretical interpretation of jet observables in heavy-ion collisions is a complex task due to the intricate interplay of perturbative and non-perturbative effects. One way to reduce this complexity is to groom away soft, wide-angle radiation so that perturbative dynamics dominates. Even in this simplified scenario, there are competing explanations for the physical origin of the measured medium-induced modifications. In this paper, we present a minimal approach to compute groomed substructure observables. The core idea is to treat medium effects as an effective energy shift of the hard, vacuum-like substructure. This energy shift includes a gradual onset of colour decoherence effects and thus depends on the jet substructure itself. We first study a NLO-exact dijet configuration in vacuum and apply radiative energy-loss to the two subjets. We find that this minimal setup already captures the narrowing trend of groomed observables but it's not able to quantitatively describe the existing data. Next, we match the NLO matrix-element to a leading-logarithm accurate parton shower and perform a clustering algorithm to recover a two-prong system to which we again apply the energy-loss distribution. Despite its simplicity, the model results in a very good theory-to-data agreement (within $10\%$) for a broad range of observables including both ALICE and ATLAS kinematics. We also examine the discriminating power of groomed jet data in terms of colour decoherence effects and find that substructure-dependent energy loss yields an overall better agreement.

As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework for addressing this question in data-driven hadronic physics problems by developing diagnostic tools - centered on a quantitative quantum qualifier - that guide model selection between classical and quantum deep neural networks based on intrinsic properties of the data. Using controlled classification and regression studies, we show how relative model performance follows systematic trends in complexity, noise, and dimensionality, and how these trends can be distilled into a predictive criterion. We then demonstrate the utility of this approach through an application to Compton form factor extraction from deeply virtual Compton scattering, where the quantum qualifier identifies kinematic regimes favorable to quantum models. Together, these results establish a principled framework for deploying quantum machine-learning tools in precision hadronic physics.

We investigate non-perturbative multi-pion contributions to nucleon flavor asymmetry within the framework of Light-Front Hamiltonian Effective Field Theory (LFHEFT). Utilizing a Fock sector expansion, we systematically incorporate pionic degrees of freedom, with the nucleon-pion interactions governed by a scalar variant of chiral effective field theory. Our results demonstrate that the non-perturbatively calculated longitudinal momentum distributions exhibit significant deviations from leading-order perturbative predictions, emphasizing the importance of higher-order Fock components in describing the proton's sea quark structure. Furthermore, we demonstrate the feasibility of extending this framework to investigate nuclear effects in light nuclei, such as the deuteron. This unified approach provides a consistent basis for analyzing the interplay between intrinsic nucleon structure and nuclear modifications, potentially offering new insights into the flavor asymmetry observed in fixed-target and collider experiments.

We study the structure of bound states appearing in systems governed by the Coulomb and short-range interactions. We analyze the binding energies and wave functions of the bound states generated by the Coulomb plus short-range potential. We demonstrate that Coulomb-induced shifts of the binding energy are closely correlated with the spatial distribution of the wave function. Furthermore, we show that the asymptotic behavior of wave functions of weakly bound states is qualitatively altered by Coulomb repulsion, leading to a modification of the near-threshold mass scaling that is otherwise universal for short-range interactions.

We calculate the 1-loop $\gamma Z$ box-graph correction to electron-quark scattering at low energy and low momentum transfer. Both electron and quark masses are kept non-zero. From our result, we extract coupling constants for the low-energy effective Lagrangian with parity-violating 4-fermion interaction terms. We study the zero-mass limits and show that a non-zero electron mass is sufficient to obtain finite, well-defined couplings which are insensitive to a hadronic mass cutoff. We finally discuss the impact of our results on the determination of the weak charge of the proton from polarized electron-proton scattering.

We present the first systematic study of rigidly rotating protoquark stars based on isentropic equations of state (EOS) within the density-dependent quark mass (DDQM) framework. Using a quasi-static equilibrium approach, we follow the Kelvin--Helmholtz evolution from hot, lepton-rich matter to a cold, catalyzed quark star. Rotation substantially enhances the maximum stable mass (by up to $\sim 40\%$), equatorial radius, and key rotational observables, with the ratio of rotational kinetic to gravitational potential energy, $T_{\rm kin}/|W|$, reaching $0.18$--$0.19$ near the Keplerian limit, indicating a heightened susceptibility to gravitational-wave--emitting instabilities. Thermal evolution introduces a clear ordering: all stellar properties peak during the lepton-rich stages and decrease monotonically as the star cools. Compared to hadronic stars, rotating protoquark stars exhibit larger radii, higher moments of inertia, and stronger quadrupolar deformation, producing a distinct signature in the mass--radius--spin plane that can accommodate objects such as HESS~J1731--347 and PSR~J0740+6620. These results demonstrate that future multimessenger observations must account for both thermal history and rotation to robustly identify quark matter in compact stars.

We investigate the frame dependence of distribution functions within the framework of generalized chiral kinetic theory. Based on the derived transformation rules governing the choice of frame, we analytically obtain the global equilibrium solution in the presence of vorticity and electromagnetic fields. Our results show that, under the assumption of a varying electromagnetic field, these equilibrium solutions can be uniquely determined.

We explore the impact of two-body currents (2BCs) at finite momentum transfer with a focus on magnetic dipole properties in $^{48}$Ca and $^{48}$Ti. To this end, we derive a multipole decomposition of 2BCs to fully include the momentum-transfer dependence in $\mathit{ab\,initio}$ calculations. As application, we investigate the effects of 2BCs on the strong M1 transition at 10.23$\,$MeV in $^{48}$Ca using the valence-space in-medium similarity renormalization group (VS-IMSRG) with a set of non-implausible interactions as well as the 1.8/2.0 (EM) interaction. Experiments, such as $(e,e')$ and $(\gamma,n)$, disagree on the magnetic dipole strength $B$(M1) for this transition. Our VS-IMSRG results favor larger $B$(M1) values similar to recent coupled-cluster calculations. However, for this transition there are larger cancellations between the leading pion-in-flight and seagull 2BCs, so that future calculations including higher-order 2BCs are important. For validation of our results, we investigate additional observables in $^{48}$Ca as well as M1 transitions in $^{48}$Ti. For these, our results agree with experiment. Finally, our results show that for medium-mass nuclei 2BC contributions to M1 and Gamow-Teller transitions are, as expected, very different. Therefore, using similar quenching factors for both in phenomenological calculations is not supported from first principles.

We investigate the equation of state (EOS) and macroscopic properties of neutron stars (NSs) and hyperonic stars within the framework of the lowest order constrained variational (LOCV) method, extended to include interacting $\Lambda$ hyperons. The nucleon-nucleon interaction is modeled using the AV18 potential supplemented by Urbana three-body forces, while $\Lambda N$ and $\Lambda \Lambda$ interactions are described by realistic spin- and parity-dependent potentials fitted to hypernuclear data. Cold, charge-neutral, and $\beta$-equilibrated matter composed of neutrons, protons, electrons, muons, and $\Lambda$ hyperons is considered. We compute particle fractions, chemical potentials, the EOS, speed of sound, tidal deformability, and stellar structure by solving the Tolman-Oppenheimer-Volkoff equations, and compare our results with recent NICER and gravitational-wave observations. The inclusion of $\Lambda$ hyperons leads to EOS softening, reducing the maximum NS mass from $2.34M_\odot$ to $2.07M_\odot$, while keeping it consistent with the $2M_\odot$ mass constraint. At $1.4M_\odot$, the model satisfies observational limits on radius and tidal deformability, with the $\Lambda$ onset occurring below this mass. Comparison with other microscopic and relativistic mean-field models shows that our EOS remains consistent with the allowed pressure-energy density range, while also permitting even canonical-mass NSs of about $1.4M_{\odot}$ to accommodate hyperons. These results suggest that hyperons can appear in NSs across the observed mass range without violating current astrophysical constraints, and that the extended LOCV method provides a consistent, microscopic approach to modeling dense hypernuclear matter.

I reexamine the perturbative renormalizability of chiral two-pion exchange in two-nucleon scattering for coupled triplets when one-pion exchange has been fully iterated at leading order. Improving over previous works, it is shown that only two counterterms are required to obtain cutoff independent results, which is one less than in naive dimensional analysis. The explanation for this reduction is the existence of an attractive and repulsive eigenchannel in the one-pion exchange potential for the coupled triplets: the attractive eigenchannel can be renormalized like a regular attractive uncoupled triplet, while the repulsive eigenchannel is always finite regardless of whether there are counterterms or not. I discuss the implications of this finding for the power counting of the $^3S_1$-$^3D_1$ and $^3P_2$-$^3F_2$ partial waves.

The first, second and third Born approximations of the Mott scattering cross section are considered. The relative error of all three Born approximations averaged by angles and energies is calculated for the first 30 elements of the Mendeleev periodic table of elements and also of the second and third-Born approximation for the first hundred elements of the Mendeleev table. The accuracy of the second and third Born approximations for calculating the normalized Mott scattering cross section are compared on the wide range of nuclei of elments. The accuracy of the Born approximations for calculating the Mott correction in the Bethe-Bloch formula for for the second Born approximation and the third approximation is analyzed. An expression is obtained for the cross section of the primary displacement of the atom in the third Born approximation. For iron, silver and lead, the cross section of the primary displacement of the atom for a number of electron energies is calculated. For a number of examples, it is calculated starting from the electron energy. The difference of the cross section is obtained by the asymptotic formula from by the McKinley-Feshbach formula, it will be less than one percent. Accuracy of the Born approximations for calculating energy-loss straggling is analyzed.

In the established paradigm of jet quenching in relativistic heavy-ion collisions, jets from initial hard parton scatterings are suppressed due to their interaction with the quark-gluon plasma (QGP) as they traverse the hot medium, serving as crucial tomographic probes of QGP properties. The QGP is also capable of absorbing and reprocessing energy deposited by the hard jets into emergent jet-like objects, providing a novel production mechanism of thermal recoil jets. These emergent thermal recoil jets exhibit distinct transverse momentum ($p_\mathrm{T}$) and jet-size ($R$) dependencies different from the hard jets, and naturally explain the puzzling observation of the enhanced yields of hadron or photon triggered jets at large azimuthal angle and solely at small $p_\mathrm{T}$ and large $R$. These thermal recoil jets are predicted to have unique substructures, such as their jet shape that increases with the radius and the thermal-like distribution of their constituents, which can be verified in future experimental analyses.

Modern nuclear data evaluation increasingly requires not only accurate scattering calculations, but also efficient methods for uncertainty quantification and parameter optimization, tasks that benefit from differentiable solvers amenable to gradient-based algorithms. I present a neural network emulator based on Bidirectional Liquid Neural Networks (BiLNN) that provides a fully differentiable mapping from optical potential parameters to scattering wave functions. The key innovation enabling generalization across the parameter space is the use of phase-space coordinates $\rho = kr$ that normalize the oscillation wavelength regardless of projectile energy, allowing a single network to span 1 to 200~MeV. Trained on Numerov solutions for twelve target nuclei (\nuc{12}{C} to \nuc{208}{Pb}), both protons and neutrons, and partial waves up to $l=30$, the network achieves an overall relative error of 1.2\%. The predicted wave functions yield accurate $S$-matrix elements and elastic scattering cross sections, reproducing diffraction patterns spanning four orders of magnitude. Importantly, the model extrapolates successfully to nuclei not included in training (\nuc{24}{Mg}, \nuc{63}{Cu}, \nuc{184}{W}) with comparable accuracy, demonstrating that it has learned the physics of the optical model rather than memorizing specific targets. The differentiable nature of the trained model opens the door to gradient-based optimization of optical model parameters and efficient uncertainty quantification.

We develop a bottom-up formulation of spin-kinetic theory for hot and/or dense plasmas. We introduce scalar and axial-vector phase-space functions as dynamical variables that parametrize both spin-averaged and spin-dependent distribution functions. Using spin-dependent Poisson brackets, we derive the corresponding kinetic equations and construct the associated Schwinger-Keldysh action. We further demonstrate how physical observables can be expressed in terms of these dynamical variables through constitutive relations. In the linear response regime, we establish a precise matching between the kinetic-theory and field-theory descriptions of vector and axial Wigner functions under electromagnetic and gravitational perturbations. Our framework provides a complementary approach to describing the dynamics of spin effects in a medium.

We calculate the electromagnetic dipole transition cross sections for the $np \rightarrow d\gamma$ and $ d\gamma \rightarrow np$ reactions over a broad range of energies. We use the LENPIC nucleon-nucleon interaction obtained from chiral effective field theory ($\chi$EFT) up to next-to-next-to-next-to-next-to-leading order (N4LO) and effective electromagnetic dipole transition operators obtained from the same $\chi$EFT up to N2LO. Our results agree with existing experiments. We get results at energies for which experimental data and/or modern theoretical calculations have not been reported. In this study, we utilize a new approach, namely, our adaptation of the Efros [V. D. Efros, Phys. Rev. C 99, 034620 (2019)] method that is prospective for future many-body applications in calculations of bound and continuum state wave functions.

Disentangling reaction mechanisms in weakly bound nuclei remains a long-standing challenge, often compounded by the treatment of absorption as an incoherent sum of channel contributions. Within the Continuum-Discretized Coupled-Channels (CDCC) framework, we apply the generalized optical theorem [Nucl.\ Phys.\ A \textbf{842}, 48 (2010)] and show that the total absorption cross section,, $\sigma_{\mathrm A}\propto -\langle\Psi|W|\Psi\rangle$, decomposes as $\sigma_{\mathrm A}=\sigma_{\mathrm D}+\sigma_{\mathrm B}+\sigma_{\mathrm{int}}$, where $\sigma_{\mathrm{int}}$ is a coherent interference term between channel components. For the systems and fragment-target optical potentials considered, $\sigma_{\mathrm{int}}$ is negative and comparable in magnitude to the direct absorption terms. The off-diagonal imaginary couplings play a dual role, redistributing flux among channels and generating $\sigma_{\mathrm{int}}$, which is required for flux-balance consistency. Calculations for $d+{}^{93}\mathrm{Nb}$ and ${}^{6}\mathrm{Li}+{}^{59}\mathrm{Co}/{}^{208}\mathrm{Pb}$ show that retaining the full non-diagonal coupling matrix substantially enhances breakup-channel absorption for heavy targets while reducing the total absorption through interference effects. Neglecting off-diagonal imaginary couplings therefore leads to a systematically biased physical picture, overestimating total absorption and severely underestimating breakup contributions, implying that experimental analyses based on incoherent-sum models inherit this bias. Full-coupling CDCC calculations are thus essential for consistent, mechanism-resolved extraction of absorption cross sections in weakly bound systems.

Accurate calculations of phase space factors (PSFs), electron energy spectra and angular correlations are essential for designing and interpreting double-beta decay (DBD) experiments. These quantities help maximize sensitivity to potential signals, distinguish between different decay modes and interpret the data. In this work we provide updated results for these kinematic factors for two-neutrino ($2\nu\beta\beta$) and neutrinoless ($0\nu\beta\beta$) decay modes, including electron-emission, positron-emission and electron capture transitions. The calculations are performed with an adapted Dirac-Hartree-Fock-Slater method which allows for orthogonality of the wave functions of electrons and positrons in bound and continuum states and incorporates relevant atomic features such us screening, finite nuclear size, exchange corrections and phase shift effects. We provide tables with updated PSFs calculated both in the closure approximation and using the Taylor expansion method, for a large number of DBD isotopes. We discuss the impact of individual atomic corrections and find that our results are in line with predictions reported in recent literature. In some specific cases we find differences between our PSF values and those previously reported which are worth considering for better prediction and interpretation of DBD data. Then, we provide numerical values for $^{76}\text{Ge}$, $^{100}\text{Mo}$, $^{130}\text{Te}$ and $^{136}\text{Xe}$, which are most investigated in current DBD experiments. Similar data for other isotopes are available upon request.

The medium modification of jet substructure in hot and dense nuclear matter has garnered significant interest from the heavy-ion physics community in recent years. Measurements of inclusive jets show an angular narrowing in nucleus-nucleus collisions, while recent CMS results for photon-tagged jets ($\gamma$+jets) suggest evidence of broadening. In this study, we conduct a theoretical analysis of the angular structure of inclusive jets and $\gamma$+jets using a transport approach that accounts for jet energy loss and the medium response in the quark-gluon plasma. We examine the girth modification of $\gamma$+jets in $0-30\%$ PbPb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, achieving satisfactory agreement with recent CMS measurements. We explore the relationship between selection bias and jet kinematics by varying the threshold for $x_{j\gamma} = p_T^{\rm jet}/p_T^{\gamma}$. Notably, we quantitatively demonstrate that $\gamma$+jets significantly reduce selection bias and can effectively select jets that have been sufficiently quenched in PbPb collisions, which is crucial for capture the jet angular broadening. Additionally, we estimate the contributions of medium-induced gluon radiation and the medium response to the broadening of the jet angular substructure. Lastly, we analyze the modification patterns of jet $R_g$ and $\Delta R_{\rm axis}$ in PbPb collisions, which indicate slight broadening for $\gamma$+jets and noticeable narrowing for inclusive jets compared to pp collisions.

In this work, we investigate the impact of the possibility of a small, subsolar mass compact star, such as the recently reported central compact object of HESS J1731-347, on the equation of state (EOS) of neutron stars. We have used a hybrid approach to the nuclear EOS developed recently where the matter around nuclear saturation density is described by a parametric expansion in terms of nuclear empirical parameters and represented in an agnostic way at higher density using piecewise polytropes. We have incorporated the inputs provided by the latest neutron skin measurement experiments from PREX-II and CREX, simultaneous mass-radius measurements of pulsars PSR J0030+0451 and PSR J0740+6620, and the gravitational wave events GW170817 and GW190425. The main results of the study show the effect of HESS J1731-347 on the nuclear parameters and neutron star observables. Our analysis yields the slope of symmetry energy $L=45.71^{+38.18}_{-22.11}$ MeV, the radius of a $1.4 M_\odot$ star, $R_{1.4}=12.18^{+0.71}_{-0.88}$ km, and the maximum mass of a static star, $M_{\rm max}= 2.14^{+0.26}_{-0.17} M_\odot$ within $90\%$ confidence interval, respectively.

The determination of whether the ground state of baryon matter in Quantum Chromodynamics (QCD) is the ordinary nucleus or a quark matter state remains a long-standing question in physics. A critical parameter in this investigation is the bag parameter $B$, which quantifies the QCD vacuum energy and can be computed using nonperturbative methods such as Lattice QCD (LQCD). By combining the equation of state derived from perturbative QCD (pQCD) with the bag parameter to fit the LQCD-simulated data for isospin-dense matter, we address the stability of quark matter within the LQCD+pQCD framework. Our findings suggest that the current data imposes an upper bound on $B^{1/4} \lesssim 160$ MeV, approaching a conclusive statement on quark matter stability. Given the lower bound on $B$ from the quark condensate contribution to the vacuum energy, the stable 2-flavor quark matter remains possible, whereas the stable 2+1-flavor quark matter is excluded, assuming complete deconfinement and chiral-symmetry restoration and the reliability of pQCD at baryon chemical potentials around the proton mass. Additionally, we derive more general thermodynamic bounds on the quark matter energy-per-baryon and $B$, which, while weaker, provide complementary insights.

We consider the rotational Brownian motion of heavy quark in QCD medium and provide analytical results for polarization of open heavy-flavor hadrons. We calculate expressions for vector and tensor polarization, corresponding to baryon spin polarization and vector meson spin alignment, respectively. Assuming that heavy quarks are initially fully spin polarized along the direction of magnetic field, we compare our results with recent experimental data from ALICE collaboration for $D^{*+}$ meson and provide predictions for spin polarization of open charm baryons. We propose that the transverse momentum dependence of heavy quark polarization may serve as a distinctive signature of the intense initial magnetic field generated in off-central relativistic heavy-ion collisions.

Dark matter may accumulate in neutron stars given its gravitational interaction and abundance. We investigate the modification of neutron star properties and confront them with the observations in the context of strongly-interacting dark matter scenario, specifically for a QCD-like theory with G$_2$ gauge group for which a first-principles equation-of-state from lattice calculations is available. We study the impact of various observational constraints and modeling of the QCD equation of state on the combined neutron stars. The results indicate that dark matter masses of a few hundred MeV to a few GeV are consistent with the latest observed neutron star properties.

We extract Compton form factors (CFFs) from deeply virtual Compton scattering measurements at the Thomas Jefferson National Accelerator Facility (JLab) using quantum-inspired deep neural networks (QDNNs). The analysis implements the twist-2 Belitsky-Kirchner-Müller formalism and employs a fitting strategy that emulates standard local fits. Using pseudodata, we benchmark QDNNs against classical deep neural networks (CDNNs) and find that QDNNs often deliver higher predictive accuracy and tighter uncertainties at comparable model complexity. Guided by these results, we introduce a quantitative selection metric that indicates when QDNNs or CDNNs are optimal for a given experimental fit. After obtaining local extractions from the JLab data, we perform a standard neural-network global CFF fit and compare with previous global analyses. The results support QDNNs as an efficient and complementary tool to CDNNs for CFF determination and for future multidimensional studies of parton distributions and hadronic structure.

We analyze the hadronic uncertainty from light-quark loops coupled to (anti)neutrino in low-energy neutral-current (anti)neutrino scattering, estimated at the $3$-$4$ permille level. This uncertainty arises from limited knowledge of the charge-isospin correlation function of quark currents. We study the charge-charge and charge-isospin correlators within $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ chiral perturbation theory (ChPT). In $\mathrm{SU}(2)$ ChPT, the two correlators are identical to all orders in the chiral and electromagnetic expansions. We further perform a leading-order $\mathrm{SU}(3)$ ChPT calculation and discuss the relevant counterterms. Our findings reduce the hadronic uncertainty in neutral-current processes such as (anti)neutrino-electron and coherent elastic (anti)neutrino-nucleus scattering by a factor $\sim 35$.

We present a new, state-of-the-art computation of the Diffuse Supernova Neutrino Background (DSNB), where we use neutrino spectra from multi-dimensional, multi-second core collapse supernova simulations - including both neutron-star and black-hole forming collapses - and binary evolution effects from modern population synthesis codes. Large sets of numerical results are processed and connected in a consistent manner, using two key quantities: the mass of the star's Carbon-Oxygen (CO) core at an advanced pre-collapse stage - which depends on binary evolution effects - and the compactness parameter, which is the main descriptor of the post-collapse neutrino emission. The method enables us to model the neutrino emission of a very diverse, binary-affected population of stars, which cannot unambiguously be mapped in detail by existing core collapse simulations. We find that including black hole-forming collapses enhances the DSNB by up to 50% at energies greater than 30-40 MeV. Binary evolution effects can change the total rate of collapses and generate a sub-population of high core mass stars that are stronger neutrino emitters. However, the net effect on the DSNB is moderate - up to a 15% increase in flux - due to the rarity of these super-massive cores and to the relatively modest dependence of the neutrino emission on the CO core mass. The methodology presented here is suitable for extensions and generalizations, and therefore it lays the foundation for modern treatments of the DSNB.

Van der Waals potentials describing interactions between color-singlet mesons and/or baryons vanish at leading order in potential nonrelativistic quantum chromodynamics (pNRQCD). This result and constraints from Gauss's law are used to prove that weakly-coupled pNRQCD van der Waals potentials in generic non-Abelian gauge theories with only heavy quarks are too weak to form bound states whose color state is a product of color-singlets. Quantum Monte Carlo calculations of four, five, and six quarks with equal masses provide numerical evidence that exotic color configurations are higher energy than products of color-singlet hadrons, suggesting that equal-mass fully-heavy tetraquark, pentaquark, and hexaquark bound states do not exist at next-to-leading order in pNRQCD and at all orders in QCD-like theories in which all quark masses are asymptotically large. Mechanisms for generating hadron-hadron bound states are identified, which necessarily involve large quark-mass hierarchies, relativistic effects arising from the presence of sufficiently light quarks, or nonperturbative effects outside the scope of weakly-coupled pNRQCD.

We revisit exact WKB quantization for radial Schrödinger problems from the modern resurgence perspective, with emphasis on how ``physically meaningful'' quantization paths should be chosen and interpreted. Using connection formulae at simple turning points and at regular singular points, we show that the nontrivial-cycle data give the spectrum. In particular, for the $3$-dimensional harmonic oscillator and the $3$-dimensional Coulomb potential, we explicitly compute a closed contour which starts at $+\infty$, bulges into the $r<0$ sector to encircle the origin, and returns to $+\infty$. Also we propose that the appropriate slice of the closed path provides a physical local basis at $r=0$, which is used by an origin-to-$\infty$ open path. Via the change of variables $r=e^x$ ($x\in(-\infty,\infty)$), the origin data are pushed to the boundary condition of convergence at $x\to-\infty$, which renders the equivalence between open-connection and closed-cycle quantization transparent. The Maslov contribution from the regular singularity is incorporated either as a small-circle monodromy which is justified in terms of renormalization group, or, equivalently, as a boundary phase; we also develop an optimized/variational perturbation theory on exact WKB. Our analysis clarifies, in radial settings, how mathematical monodromy data and physical boundary conditions dovetail, thereby addressing recent debates on path choices in resurgence-based quantization.

In the past years, a significant effort has been made with the scope of determining correlations, involving compact star properties, that are independent of the nuclear equation of state. Such universal relations are of utmost importance as they allow for the imposition of constraints on stellar properties without directly measuring them and they may also serve as a probe of General Relativity. In the present study, we investigated the possible existence of a universal relation between the binding energy of compact stars and the frequency of their non-radial oscillations. The main motivation was related to the fact that both of the aforementioned quantities might be measured in the occurrence of a supernova explosion. Interestingly, we found that there is a empirical relation between the oscillation frequency and the binding energy for both $f$ and $p_1$ modes, assuming hadronic stellar matter. The inclusion of hybrid equations of state, incorporating sharp phase transitions, was shown to result into deviations from the aforementioned quasi-universal relation.

Core-collapse supernovae, occurring at the end of massive star evolution, produce heavy elements, including those in the iron peak. Although the explosion mechanism is not yet fully understood, theoretical models can reproduce optical observations and observed elemental abundances. However, many nuclear reaction rates involved in explosive nucleosynthesis have large uncertainties, impacting the reliability of abundance predictions. To address this, we have previously developed a Monte Carlo-based nucleosynthesis code that accounts for reaction rate uncertainties and has been applied to nucleosynthesis processes beyond iron. Our framework is also well suited for studying explosive nucleosynthesis in supernovae. In this paper, we investigate 1D explosion models using the "PUSH method", focusing on progenitors with varying metallicities and initial masses around $M_\mathrm{ZAMS} = 16 M_{\odot}$. Detailed post-process nucleosynthesis calculations and Monte Carlo analyses are used to explore the effects of reaction rate uncertainties and to identify key reaction rates in explosive nucleosynthesis. We find that many reactions have little impact on the production of iron-group nuclei, as these elements are primarily synthesized in the nuclear statistical equilibrium. However, we identify a few "key reactions" that significantly influence the production of radioactive nuclei, which may affect astrophysical observables. In particular, for the production of ${}^{44}$Ti, we confirm that several traditionally studied nuclear reactions have a strong impact. However, determining a single reaction rate is insufficient to draw a definitive conclusion.