We present the first combined analysis of the statistical rate function f in superallowed beta decays with ab initio calculations and data. We focus on C10 to 10B, 14O to 14N and 26mAl to 26Mg, all of which are important channels for the precise determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vud. Nuclear charge form factors are obtained by combining experimental data on nuclear charge radii and theory calculations of ratios of moments with the in-medium similarity renormalization group, while the beta decay form factors are derived from exact isospin relations. This enables a rigorous study of the nuclear shape dependence in the statistical rate function f and the quantification of its uncertainties from both experiment and theory. The calculation leads to a more precise test for the first-row CKM unitarity with reduced theoretical uncertainties. This work demonstrates a reliable strategy for combining nuclear many-body calculations with high-precision nuclear data to describe beta decays at tree level for precision tests of the Standard Model.

We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction $\delta_C$ to the superallowed $\beta$ decay of $^{10}{\rm C}$. Using both phenomenological and chiral nuclear interactions, we evaluate the Fermi matrix element and quantify its deviation from the canonical $\sqrt{2}$ value. The resulting $\delta_C$ values lie in the range $\approx 0.15$--$0.25\%$ and are consistent, within sizable uncertainties (approximately $34\%$--$65\%$ relative), across Hamiltonians, indicating no statistically significant dependence on the choice of nuclear interaction. The extracted values of $V_{ud}$ are also found to be compatible with current determinations within these uncertainties.

We study the impact of symmetry energy ($S$), hyperons, and dark matter (DM) on structural and oscillatory properties of neutron stars (NSs). Uncertainty from hadronic equation of state for NSs is considered with 15 relativistic mean field models having slope parameter ($L_0$) of $S$ in range $40-120$ MeV. DM admixed NSs (DMANSs) are described with feeble interaction between light DM fermions ($\chi$) with hadronic matter in the presence of hyperons via scalar ($\eta$) and vector ($\xi$) dark mediators. The masses $m_{\chi}$, $m_{\eta}$ and $m_{\xi}$ are related by self-interaction constraints from bullet cluster. DM self-interaction couplings are related to $m_{\chi}$ by relic density constraint. The DM density is taken as an exponential function of baryon density with a free parameter $\alpha$. Uncertainty from DM model is incorporated by exploring the dependence on $m_{\chi}$ and $\alpha$. Several DM search experiments have almost ruled out the existence of massive DM ($\gtrsim$ GeV). Lately, pursuit for sub-GeV DM has attracted significant attention. Therefore, we consider $m_{\chi}<$ 1 GeV and $\alpha \leq$ 0.1 such that the contribution of DM to the total mass of the DMANSs is $<10\%$. Comparing our results with various astrophysical constraints, we find that the HESS J1731-347 and GW170817 data are very important in determining the presence of light DM in NSs in moderate amount, relevant in the range $L_0\lesssim$ 58 MeV. Employing models of DMANSs that satisfy several observational data, we infer with Bayesian analysis, the likely ranges of $m_{\chi}$ and $\alpha$ are almost independent of the underlying hadronic model within 40 MeV $\lesssim$ $L_0$ $<$ 58 MeV. In the absence of DM and with the most probable values of $m_{\chi}$ and $\alpha$ obtained from the Bayesian inference, we calculate the frequencies of non-radial $f$- and $p_1$-modes oscillation of NSs/DMANSs.

This work focuses on the fourth order correlations $\chi^{BQ}_{31}$, $\chi^{QB}_{31}$, $\chi^{BQ}_{22}$, $\chi^{BS}_{31}$, $\chi^{SB}_{31}$, $\chi^{BS}_{22}$, $\chi^{QS}_{31}$, $\chi^{SQ}_{31}$, $\chi^{QS}_{22}$, $\chi^{BQS}_{211}$, $\chi^{QBS}_{211}$, $\chi^{SBQ}_{211}$ of baryon number $B$, electric charge $Q$ and strangeness $S$ at finite temperature, magnetic field and vanishing quark chemical potential. The study is carried out in the framework of a three-flavor PNJL model, considering both cases with and without inverse magnetic catalysis effect. We find that, fourth order correlations $\chi^{BQ}_{31}$ at chiral restoration phase transition is more sensitive to the magnetic field than other second order and fourth order correlations and fluctuations, and can be served as a more effective magnetometer of QCD.

We present a theoretical study of the two-neutrino $0^+ \rightarrow 0^+$ double beta decay of $^{76}$Ge within the No-Core Configuration-Interaction framework based on the Skyrme SV density functional. We analyze three allowed decay scenarios distinguished by the $[n,m] \equiv [(\nu g_{9/2})^n, (\pi g_{9/2})^m]$ occupancy of the $0g_{9/2}$ intruder orbital, which remains conserved to high precision, as well as by the triaxiality of the daughter nucleus. The resulting $2\nu\beta\beta$ nuclear matrix element is found to depend strongly on the scenario. For the energetically favored $[4,2]$ occupancy, we obtain $|\mathcal{M}^{2\nu}| = 0.069(7)$~MeV$^{-1}$. For the $[6,0]$ occupancy, the matrix element further depends on the triaxiality parameter $\gamma$ of the two coexisting, closely lying minima in $^{76}$Se, yielding $|\mathcal{M}^{2\nu}| = 0.040(4)$~MeV$^{-1}$ at $\gamma = 17.7^\circ$ and $|\mathcal{M}^{2\nu}| = 0.22(2)$~MeV$^{-1}$ at $\gamma = 41.9^\circ$. The latter result is consistent with the empirical value reported by A. S. Barabash, $|\mathcal{M}^{2\nu}| = 0.204(14)$~MeV$^{-1}$, while the two former results are comparable to existing calculations based on energy-density-functional frameworks. Our calculations reveal challenges in the precise determination of the $|\mathcal{M}^{2\nu}|$ for the $^{76}$Ge decay. The structural complexity, triaxiality, and shape coexistence identified in the analyzed nuclei imply a strong sensitivity to fine details of the interaction and configuration mixing. This, in turn, explains the difficulties in theoretical modeling of the $|\mathcal{M}^{2\nu}|$ matrix elements for the $^{76}$Ge decay, which vary by almost an order of magnitude in the available literature.

We analyze the radiative decays of the the 1$P$, 1$D$, 2$S$, and 2$P$ $\Lambda_c$ and 1$D$, 2$S$, and 2$P$ $\Xi_c$ charmed baryons, which belong to the flavor anti-triplet ($\bf {\bar 3}_{\rm F}$), using the constituent quark model. We compute electromagnetic transitions from ground and $P$-wave states to ground states, as well as from second-shell states to both ground and $P$-wave final states. Electromagnetic decay widths are especially valuable for identifying resonances when multiple states share the same mass and total decay width. We give branching ratios which can confirm the assignment of the $\Xi_c(3055)$ reported by LHCb. We also give branching ratios that can support the assignment of the $\Xi_c(3080)$, and discuss the possibilities for the $\Xi_c(3080)$ to be the 1$D$ state with $J^P=5/2^{+}$ or the 2$S$ with $J^P=1/2^{+}$. For the first time, this work provides calculations of electromagnetic decays for $D_\rho$-wave states, $\rho-\lambda$ mixed configurations, and $\rho$-mode radially excited states in singly charmed baryons of the flavor anti-triplet. Both experimental and model-dependent uncertainties are taken into account throughout our analysis.

A comprehensive study of the phase structure of the two-flavor quark-meson-diquark model is presented within the nonperturbative functional renormalization group framework. The influence of mesonic fluctuations beyond the mean-field approximation is investigated, and two-point functions of the diquark fields are computed at finite real-time frequencies. Renormalization group consistency of the effective potential is ensured in order to avoid cutoff artifacts. Substantial modifications of the phase structure are found once mesonic fluctuations are included, and for sufficiently strong diquark couplings the dynamics become dominated by diquark condensation. These effects are elucidated through an analysis of the diquark pole mass and the Silver-Blaze property.

Collinear factorization and color-glass condensate (CGC) effective field theory are generally treated as separate approaches for calculating scattering amplitudes, valid in different kinematic regimes. For deep inelastic scattering at high photon virtuality and high center-of-mass energy, however, both of these approaches should be applicable. By expressing collinear parton distributions and generalized parton distributions in the shockwave approximation, we show that the resulting collinear-factorization amplitudes exactly reproduce the large-$Q^2$ expansion of CGC amplitudes for inclusive deep inelastic scattering, deeply virtual Compton scattering, and deeply virtual meson production. The matching holds directly at the amplitude level and includes both logarithmically enhanced and finite contributions. Our results establish the consistency between collinear factorization and the CGC in their common region of validity, clarify the origin of large momentum logarithms within the CGC framework, and provide a path toward combining high-energy and collinear evolution in a unified description of hadronic structure at small $x$ and large momentum scales.

The NA61/SHINE experiment at the CERN SPS is a multipurpose fixed-target spectrometer for charged and neutral hadron measurements. Its research program includes studies of strong interactions as well as reference measurements for neutrino and cosmic-ray physics. One major goal of its strong interaction program is to determine the existence and pinpoint the location of the QCD critical point, an object of both experimental and theoretical studies. This contribution will summarize the current status of NA61/SHINE critical point searches in nucleus-nucleus collisions, in the collision energy range $\sqrt{s_{NN}} = 5-17$~GeV. The review includes studies of fluctuations of net-electric charge, femtoscopy analysis of $\pi-\pi$ pairs, as well as intermittency of protons and negatively charged hadrons. No clear indication of the critical point has been observed so far. Finally, we report on the development of novel methods aimed at solving the long-standing problem of bin-by-bin correlations in experimental intermittency analysis, and for a more accurate handling of systematics and uncertainties.

Quantifying quantum resources for simulating the fundamental forces of Nature is sensitive to the mapping of gauge fields onto finite quantum computational architectures. When locally truncating lattice gauge theories in the irreducible representation basis, it has been proposed to further deform the theory via quantum groups. The purpose of this deformation is (1) to provide an infinite tower of finite-dimensional ($d = k+1$) groups systematically approximating the infinite-dimensional gauge links and (2) to restore the physical unitarity of a plaquette operator diagonalization procedure analytically derived from the field continuum by recontracting vertex pairs. For the SU(2)$_k$ Yang-Mills pure-gauge theory, we provide a constructive strategy of gauge-variant completions to extend this unitarity to the entire computational Hilbert space, leading to well-defined time evolution unitaries as targets for optimized circuit synthesis. Leveraging basic circuit decompositions and symmetries of the diagonalized plaquette operator, we report resource upper-bounds on the generalized-controlled-X two-qudit gates for arbitrary local truncation $d$, reducing estimates and scaling relative to the non-deformed theory by three polynomial powers from $O(d^8)$ to $O(d^5)$. Examining the stronger q-deformed gauge constraint, which softens the total flux at vertices, we show that the physical Hilbert space dimension of the deformed plaquette operator scales equivalently to its non-deformed counterpart with a constant factor $0.2563(5)$. Thus, despite affecting interactions at all scales as exemplified by the observed flux hierarchy inversion symmetry, q-deformation continues to pass scrutiny as a reliable truncation offering advantages in quantum circuit synthesis.

We perform ab initio calculations of three-point mass differences in the odd- and even-mass $^{39-49}$Ca isotopes to probe nuclear superfluidity via empirical neutron pairing gaps. We also quantify the sensitivity of those gaps to the parameters of the interaction at mean-field level. Recent studies employing accurate chiral nuclear interactions have found these gaps to be too small. We show that experimental values can be reproduced at mean-field level by substantially increasing the attraction of the singlet $S$-wave two-nucleon contact interaction, but doing so induces an unphysical bound state of the di-neutron. The sensitivity of these predictions to the full calibration of the nuclear interaction is then studied by performing Bayesian posterior sampling in a delta-full chiral effective field theory at third chiral order. We find that pairing gaps remain largely unaffected, leaving the explanation of nuclear superfluidity as a future task for improved many-body modeling and refined interactions at higher chiral orders.

This dissertation presents a unified framework for medium characterization with hard probes spanning from Cherenkov light in quantum electrodynamics (QED) to jet drift in quantum chromodynamics (QCD). We first develop a dispersive fit to the refractive index $n(\lambda)$ of liquid argon (LAr) by incorporating anomalous dispersion at the 106.6 nm resonance for the first time. We show that the angular distribution of Cherenkov radiation is highly sensitive to the peak of the refractive index and contributes a significant excess over isotropic scintillation in certain angular bins. This work is important for precision Particle Identification (PID) for experiments like DUNE and CCM. Transitioning to high-energy nuclear collisions, we utilize ``jet drift'' -- the flow-induced deflection of partons -- as a tomographic probe of the Quark-Gluon Plasma (QGP). Using the Anisotropic Parton Evolution (APE) Monte Carlo simulation across various collision systems (PbPb, AuAu, and UU), we disentangle how the jet modification depends on medium size, temperature, and geometry. We show that jet drift exhibits distinct systematics in observables like the elliptic flow ($v_2$) and dihadron acoplanarity ($\Delta\phi$), which helps disentangle it from conventional energy loss. Together, these studies demonstrate how the angular and kinematic signatures of hard probes revolutionize our ability to resolve the fundamental properties of matter.

A size-extensive, converging, black-box, ab initio coupled-cluster ($\Delta$CC) ansatz is introduced that computes the energies and wave functions of stationary states from any degenerate or nondegenerate Slater-determinant references with any numbers of $\alpha$- and $\beta$-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Rayleigh-Schrödinger perturbation ($\Delta$MP) theory. For ionized and electron-attached references, it can be viewed as a coupled-cluster Green's function, although the present theory is convergent toward the full-configuration-interaction (FCI) limits, while Feynman-Dyson many-body Green's function (MBGF) theory generally is not. Additionally, a new state-universal multireference coupled-cluster theory for general model spaces is developed by slightly modifying the $\Delta$CC ansatz. This quasidegenerate coupled-cluster (QCC) theory is size-extensive, converging, but not black-box, which is expected to be well suited for strong correlation. Determinant-based, general-order algorithms of $\Delta$CC and QCC theories are implemented, which are compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with $\Delta$MP and MBGF theories up to the nineteenth order. For transition energies, the order of performance is: QCC $\approx$ $\Delta$CC $>$ EOM-CC $>$ CI at the same excitation order or QCC $\approx$ $\Delta$CC $>$ $\Delta$MP $>$ MBGF at the same cost scaling.