Nuclear Schiff moments (NSMs) are sensitive probes for physics beyond the Standard Model of particle physics, signaling violations of time-reversal and parity-inversion symmetries in atomic nuclei. In this Letter, we report the first-ever calculation of a NSM in a nuclear ab initio framework, employing the no-core shell model to study the fluorine isotope $^{19}$F. We further perform quantum-chemistry calculations to evaluate the sensitivity of the hafnium monofluoride cation, HfF$^+$, to the NSM of $^{19}$F. Combined with recent high-precision measurements of the molecular electric dipole moment of HfF$^+$, our results enable the first experimental bound on the NSM of $^{19}$F.

The number of gross structures in the 90$^\circ$ excitation function for $^{12}$C+$^{12}$C elastic scattering, often called Airy elephants, has been of great interest. These structures are caused by refractive scattering and are separated by Airy minima. Their importance stems from their close relationship to the interaction potential between two $^{12}$C nuclei, which also describes the molecular resonances of the compound system at lower energies. Although a unique deep potential was usually determined from rainbow scattering at higher energies, a puzzling discrepancy persisted: the energy at which the Airy minimum $A1$ crosses 90$^\circ$ was $E_{c.m.}\approx$67 MeV for $^{12}$C+$^{12}$C. This is remarkably low compared to approximately 100 MeV for both the $^{16}$O+$^{12}$C and $^{16}$O+$^{16}$O systems. This question remained unanswered until the discovery of the secondary rainbow in the $^{12}$C+$^{12}$C system. We report for the first time that the highest energy at which the dynamically generated Airy minimum of the secondary rainbow crosses 90$^\circ$ is about 100 MeV. This demonstrates that the fourth Airy elephant exists between the Airy minimum $A1$ of the primary nuclear rainbow and that, $A1^{(S)}$, of the secondary rainbow. The long-standing problem concerning the Airy minima and Airy elephants has finally been resolved after decades of concern by recognizing the existence of a dynamically generated secondary rainbow in $^{12}$C+$^{12}$C scattering.

We present the first fully nonlinear causality constraints in $D = 3 + 1$ dimensions for Israel-Stewart theory in the presence of energy and number diffusion in the Eckart and Landau hydrodynamic frames, respectively. These constraints are algebraic inequalities that make no assumption on the underlying geometry of the spacetime, or the equation of state. In order to highlight the distinct physical and structural behavior of the two hydrodynamic frames, we discuss the special ultrarelativistic ideal gas equation of state considered in earlier literature in $D = 1 + 1$ dimensions, and show that our general $D = 3 + 1$ constraints reduce to their results upon an appropriate choice of angles. For this equation of state in both $D = 1 + 1$ and $D = 3 + 1$ dimensions one can show that: (i) there exists a region allowed by nonlinear causality in which the baryon current transitions into a spacelike vector in the Landau frame, and (ii) an analogous argument shows that the solutions of the Eckart frame equations of motion never violate the dominant energy condition, assuming nonlinear causality holds. We then compare our results with those from linearized Israel-Stewart theory and show that the linear causality bounds fail to capture the new physical constraints on energy and number diffusion that are successfully obtained

Low-energy vibrational excitations associated with the fluctuation of quadrupole deformed shapes are discussed within the frame of state-of-the-art Configuration Interaction calculations, actually performed via the Quasi-particle Vacua Shell Model version of the Monte Carlo Shell Model. Recently, low-lying $\gamma$ bands in heavy strongly deformed nuclei were shown to be rotational $K^P$ = 2$^+$ excitations of triaxially deformed states (see T. Otsuka \etal, Eur. Phys. J. A 61, 126 (2025)) rather than vibrational excitations as traditionally interpreted. In this context, it is important to identify possible low-lying vibrational excitations and to characterize the excitation energy at which they emerge. Focusing on two typical examples, $^{166}$Er and $^{162}$Dy, vibrational states are indeed identified above the $\gamma$ band using an extended version of the so-called T-plot. The phenomenon of shape coexistence is also shown to produce low-lying states below such vibrational band heads. These results suggest novel and rich structures in heavy deformed nuclei. While experimental counterparts are seen for some of such states, others are predictions opening doors to future dedicated experiments.

The relative correlation between the magnitudes of elliptic flow ($v_2$) and triangular flow ($v_3$) has been accurately measured in nucleus-nucleus collisions at the LHC collider. As a function of the centrality of the collision, it changes sign and varies non-monotonically. We show that this is naturally explained by two combined effects. The first effect is a skewness in initial-state fluctuations, which is quantified by the correlation between the geometry-driven elliptic deformation in the reaction plane and the fluctuation-driven triangularity $\varepsilon_3$. We introduce an intensive measure of this skewness, which is generically of order unity and depends weakly on the system size and centrality. We evaluate its magnitude using Monte Carlo simulations of the initial state, which show that it is sensitive to the nucleon width. The second effect is the fluctuation of impact parameter relative to centrality classifiers used by experiment. The ATLAS collaboration uses two different centrality classifiers, the multiplicity $N_{ch}$ and the transverse energy $E_T$. We fit both sets of results for Pb+Pb collisions up to $\approx 40\%$ centrality with a single parameter, the intensive mixed skewness. Its value inferred from experiment agrees with theoretical expectations.

In this work, we study the properties of single-flavor heavy baryons, $\Omega_{\rm ccc}$ and $\Omega_{\rm bbb}$, in a strong magnetic field. For that sake, we simply treat the baryons as quark-diquark two-body systems, and a systematic formalism is developed to deal with two-body Schr$\ddot{\text o}$dinger equations in a magnetic field. It is found that: 1. The orbital properties of $\Omega_{\rm bbb}$ are almost not affected by the magnetic field. 2. $\Omega_{\rm ccc}$ is more tightly bound in the presence of a magnetic field. 3. The magnetic-spin effect dominates over the magnetic-orbital effect. Applying to peripheral heavy ion collisions, $\Omega_{\rm ccc}$ is much better than $\Omega_{\rm bbb}$ to explore the magnetic effect, and the discovery of $\Omega_{\rm ccc}$ could be more promising.

We develop a framework that allows to calculate integrated properties of the nuclear response from first principles. Using the ab initio in-medium similarity renormalization group (IMSRG), we calculate the expectation values of moment operators that are linked to the multipole response of nuclei. This approach is applied to the isoscalar mono- and quadrupole as well as the isovector dipole response of closed-shell nuclei from $^4$He to $^{78}$Ni for different chiral two- and three-nucleon interactions. We find that the inclusion of many-body correlations in the nuclear ground state significantly impacts the multipole response when going from the random-phase approximation to the IMSRG level. Our IMSRG calculations lead to an improved description of experimental data in $^{16}$O and $^{40}$Ca, including a good reproduction of the Thomas-Reiche-Kuhn enhancement factor. These findings highlight the utility of the moment method as a benchmark for other ab initio approaches that describe nuclear response functions through the explicit treatment of excited states.

The effect of meson-exchange currents on charged-current quasielastic neutrino scattering with single-nucleon emission is computed and analyzed within the relativistic Fermi gas model. This contribution arises primarily from the interference between one-body and two-body currents, where the two-body operator excites a 1p1h state in the presence of a second, spectator nucleon. The results obtained show a reduction of the vector, axial and vector-axial transverse response functions and, consequently, a decrease in the total neutrino cross section. In addition to a comparison with the non-relativistic limit, other models are also explored, such as the relativistic mean field model for nuclear matter and the superscaling analysis with relativistic effective mass, both of which yield qualitatively similar results.

Determining the transport properties of Quark-Gluon Plasma is one of the most important aspects of relativistic heavy ion collision studies. Field-theoretical calculations of the transport coefficients such as the shear and bulk viscosities require Kubo formulae which in turn require real-time correlation functions of stress-energy tensors. Consequently, knowing the analytic structure of these correlation functions is essential in any such studies. Using the energy-conservation laws and the results from the gravity-hydrodynamics analysis, we determine the low-frequency and low-wavenumber analytic structures of all stress-energy correlation functions in the rest frame of the medium. By comparing with the diffusion and sound spectra from the second-order and the third-order relativistic hydrodynamics, various new Kubo formulae are derived in the limit where the zero-frequency limit is taken first. We also show that the meaning of the Kubo formulae for relaxation times can change when higher-order terms are added to hydrodynamics. A subtle issue of taking the zero frequency and zero wavenumber limits when using skeleton diagrams is addressed as well.

We investigate the on-shell approximation in the context of s-wave scattering for ultracold two-body collisions. Our analysis systematically covers spatial dimensions D=1,2,3 , with the aim of identifying the regimes in which the approximation remains valid when applied to commonly used model interaction potentials. Specifically, we focus on the square well and delta shell potentials, both of which admit analytical solutions for the s-wave scattering problem in all dimensions considered. By employing the exact analytical expressions for the s-wave scattering phase shift, we perform a direct comparison between the exact on-shell matrix element of the interaction potential and their corresponding approximations across a range of collision momenta. Particular attention is given to the low-energy regime. Our findings indicate that, although the on-shell approximation generally improves with increasing momentum, its accuracy also improves for weaker potentials. Remarkably, in the limit of weak interactions, we demonstrate that the on-shell approximation becomes exact at leading order. In this regime, the approximation offers a controlled means of deriving the low-momentum expansion of the potential and may serve as a useful tool in constructing effective interactions for quantum field theories.

Pion production is a major source of systematic uncertainty in neutrino oscillation measurements. We report a systematic investigation of neutrino-induced pion production using MINERvA and MicroBooNE data within the GiBUU theoretical framework. The analysis begins by establishing baseline model parameters using inclusive and pionless data from MINERvA, MicroBooNE, and T2K experiments. We then examine the role of in-medium effects, including resonance broadening and nucleon-nucleon final-state interactions. While agreement with individual datasets can be achieved through specific model configurations, we demonstrate the difficulty of a unified description across all experiments: MINERvA measurements prefer minimum in-medium modifications, whereas MicroBooNE data require the maximum in-medium enhancement, revealing the complexity and richness of the underlying nuclear dynamics.

We investigate the $S$- and $P$-wave phase shifts for the $DD^\ast$ and $BB^\ast$ scatterings using Lüscher's finite-size method under twisted boundary conditions to search for doubly charmed tetraquaks, $T_{cc}^+$, and doubly bottomed tetraquarks, $T_{bb}^-$ as the hadronic bound states. The $T_{cc}^+$ state was observed as a peak just bellow the $DD^*$ threshold by LHCb Collaboration, while the $T_{bb}^-$ state is a theoretically predicted tetraquark state having heavier quark flavors $bb\bar u \bar d$. Lüscher's finite-size method is one of the well established methods for calculating the scattering phase shifts between two hadrons in lattice QCD simulations. Several studies have used simulations under the periodic boundary condition to determine the scattering phase shifts at a few discrete momenta for the $DD^*$ system. However, the scattering phase shift has not been investigated for the $BB^*$ system. In this study, $S$- and $P$-wave scattering phase shifts for the $DD^*$ and $BB^*$ systems in both $I=0$ and $I=1$ channels under several types of partially twisted boundary conditions. The use of the partially twisted boundary conditions enables us to obtain the scattering phase shift at any momentum by continuously varying the twisting angle. It also allows us to easily access the $P$-wave scattering phase shifts through the mixing of $S$- and $P$-waves, which is induced by the imposed boundary conditions. The 2+1 flavor PACS-CS gauge ensembles at $m_\pi=295$, 411 and 569 MeV are used. For charm and bottom quarks, the relativistic heavy quark action is adopted to reduce the lattice discretization artifacts due to the heavy quark mass. We discuss the emergence of a shallow bound state with a binding energy of $\mathcal{O}(100)$ keV at the physical pion mass in the $BB^*$ system, which has the quantum number $I(J^P)=0(1^+)$.

This work investigates the impact of mirror dark matter (DM) on the global properties of rotating neutron stars (NSs) across evolutionary stages, from hot, lepton-rich proto-neutron stars (PNSs) to cold, catalyzed NSs along the Kelvin--Helmholtz timescale. The baryonic matter (BM) is modeled using a relativistic mean-field (RMF) approach with density-dependent couplings, while the dark sector mirrors the visible sector with analogous thermodynamic conditions. Using a two-fluid formalism with purely gravitational DM-BM interaction, we find that rotation enlarges the star, whereas DM admixture increases compactness and enhances gravitational stability. However, increased compactness due to DM lowers the threshold for rotational instabilities, making DM-admixed stars more susceptible. Rotation decreases temperature profiles by redistributing thermal energy over a larger volume and reducing central density, while DM raises temperatures by deepening the gravitational potential and increasing thermal energy. Stars become more prone to collapse and rotational instabilities as frequency ($\nu$) rises and the polar-to-equatorial radius ratio ($r_p/r_e$) decreases, especially near the Keplerian limit ($\nu_K$). DM-admixed stars also show higher surface gravitational redshifts due to their compactness. Our results qualitatively agree with universal relations primarily derived for rotating cold stars. These findings highlight competing effects of rotation and DM on NS thermal evolution, structure, and observables, potentially offering indirect probes of DM within NSs.

The operator product expansion (OPE) is applied in conjunction with Pionless effective field theory to study the short-rang structure of nuclei. By matching the OPE with the selected nuclear potentials for nucleon-nucleon scattering states, we obtain the Wilson coefficients. The nucleon momentum distribution in the deuteron is then used to test the OPE against the predictions of these nuclear potentials. In order to achieve a systematic separation of short-range and long-range interactions, we discuss how the OPE approximation can be improved by including higher-order EFT potentials and higher-dimension local operators.

Low-energy spectra in the isotopic chain $^{250-262}$No are systematically investigated within the fully self-consistent Quasiparticle Random-Phase-Approximation (QRPA) using Skyrme forces SLy4, SLy6, SkM* and SVbas. QRPA states of multipolarity $\lambda\mu$=20, 22, 30, 31, 32, 33, 43, 44 and 98 are considered. The main attention is paid to isotopes $^{252}$No and $^{254}$No where the most extensive experimental spectroscopic information is available. In these two nuclei, a reasonable description of $K^{\pi}=8^-, 2^-$and $3^+$ isomers is obtained with forces SLy4 and SLy6. The disputed $8^-$ isomer in $^{254}$No is assigned as neutron two-quasiparticle configuration $nn[734\uparrow,613\uparrow]$. The isomers are additionally analyzed using Skyrme functionals UNEDF1, UNEDF2 and UNEDF1$^{\rm SO}$. At the energies 1.2 - 1.4 MeV, the 2qp $K$-isomers $4^-, 7^-$ in $^{252}$No and $4^-, 6^-, 7^-$ in $^{254}$No are also predicted. In $^{254}$No, the $K^{\pi}=3^+$ isomer should be accompanied by the nearby $K^{\pi}=4^+$ counterpart. It is shown that, in the chain $^{250-262}$No, some features of $^{252}$No and $^{254}$No should exhibit essential irregularities caused by a noticeable shell gap in the neutron single-particle spectrum and corresponding reduction of the neutron pairing. In particular, low-energy pairing-vibrational $K^{\pi}=0^+$ states in $^{252,254}$No are predicted.

We use linear response theory to derive both the non-dissipative and dissipative effects of spin polarization for massive and massless interacting spin 1/2 particles in a relativistic fluid. We list and classify all the possible contributions up to first order in gradients of hydrodynamic fields including the axial chemical potential and the spin potential, and we obtain the corresponding Kubo formulas. We find that all the possible dissipative contributions, except those coming from the gradients of spin potential, require a chiral imbalance or parity violating interactions. In a fluid with chiral imbalance we find a chiral version of the spin Hall effect, i.e. a spin polarization is induced by the gradients of temperature and of axial chemical potential in the direction orthogonal to the momentum of the particle and to the gradients. Moreover, we identify several other new non-dissipative contributions that are not present for free fields.

We construct a set of unified equations of state based on the quark mean field (QMF) model, calibrated to different values of nuclear symmetry energy slope at the saturation density ($L_0$), with the aim of exploring both the static properties and dynamical behavior of neutron stars (NSs), and building a coherent picture of their internal structure. We assess the performance of these QMF models in describing the mass-radius relation, the cooling evolution of isolated NSs and X-ray transients, and the instabilities (e.g., the r-mode). In comparison to relativistic mean field (RMF) models formulated at the hadronic level, the QMF model predicts heavier nuclear clusters and larger Wigner-Seitz cell sizes in the NS crust, while the density of the free neutron gas remains largely similar between the two approaches. For the cooling of isolated NSs, the thermal evolution is found to be insensitive to both the many-body model and the symmetry energy slope in the absence of the direct Urca (dUrca) process. However, when rapid cooling via the dUrca process is allowed, in the case of large $L_0$ values (e.g., $L_0 \gtrsim 80$ MeV) in our study, the QMF model predicts a longer thermal relaxation time. Both the QMF and RMF models can reproduce cooling curves consistent with observations of X-ray transients (e.g., KS 1731--260) during their crustal cooling phase, although stellar parameters show slight variations depending on the model and symmetry energy slope. Within our unified framework, a larger $L_0$ value generally results in a wider instability window, while increasing the stellar mass tends to suppress the instability window. We also provide simple power-law parameterizations that quantify the dependence of bulk and shear viscosities on the symmetry energy slope for nuclear matter at saturation density.

Anisotropic flow and fluctuations are sensitive observables of the initial state effects in heavy ion collisions and are characterized by the medium properties and final state interactions. Using event-shape observables, one can constrain the probability distributions of anisotropic flow coefficients, thus reducing the linear and nonlinear contributions in the measured higher-order harmonics. In this paper, we use transverse spherocity as an event shape observable to study the flow coefficients and elliptic flow fluctuations. Transverse spherocity is found to have a strong correlation with elliptic flow and its fluctuations. We exploit this feature of transverse spherocity to remove the contribution to elliptic flow from higher-order harmonics. The study is performed in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using a multi-phase transport model. The multi-particle Q-cumulant method estimates the anisotropic flow coefficients, which reduces the non-flow contributions. We observe a stronger system response to the flow coefficients for the events with smaller values of elliptic flow.

We present the first microscopic description of proton radioactivity in $^{149}$Lu, the most oblate deformed proton emitter known, using a deformed microscopic optical potential derived from $ab\ initio$ nuclear matter calculations. We predict a novel angular-dependent phenomenon unprecedented in spherical proton emitters: the disappearance of classically allowed regions at small polar angles $(\theta\leq 21^\circ)$. Combining the Wentzel-Kramers-Brillouin penetration probabilities and the assault frequency of the emitted proton estimated with a new harmonic-oscillator-inspired scheme, our framework yields a half-life $T_{1/2}=467^{+143}_{-108}$ ns for $^{149}$Lu, in excellent agreement within uncertainties with the experimental value $450^{+170}_{-100}$ ns. Deformation analysis rigorously excludes configurations with $|\beta_2|\geq 0.32$. Extensions to $^{150, 151}$Lu and their isomers also achieve excellent agreement with experimental half-life data. We further predict $^{148}$Lu as another highly oblate $(\beta_2 = -0.166)$ proton emitter with a half-life of 4.42 ns. This work validates deformed microscopic optical potentials as a robust predictive tool for drip-line proton emitters and provides quantitative evidence for deformation effects in exotic decays.

Electron polarization plays a significant role in studies on nuclear scattering. Nevertheless, the development of a comprehensive approach to such a problem remains challenging, particularly at the relativistic electron-energy scale. Herein, we present a theoretical approach to investigate the impact of electron polarization in scattering off unoriented light nuclei, based on the multipole expansion for the scattering cross section at high energies. Numerical calculations for stable $^{6,7}$Li and unstable $^{7}$Be nuclei show that the longitudinal polarization and weak interaction are not explicitly correlated when electrons scatter at 0$^{\circ}$ for all energy scales. In contrast, their correlation is strongly exhibited at other scattering angles when energy exceeds 10 GeV. A comparison between stable and unstable nuclei reveals that the stability of nuclei significantly affects the electron polarization contribution to the scattering cross section. This study opens new approaches to the nuclear structure problems, in particular the EMC effect, via deep inelastic electron-nucleus scattering using the unified electroweak theory.

The present study aims at further development of covariant energy density functionals (CEDFs) towards more accurate description of binding energies across the nuclear chart. For the first time, infinite basis corrections to binding energies in the fermionic and bosonic sectors of the covariant density functional theory have been taken into account in the fitting protocol within the covariant density functional theory. In addition, total electron binding energies have been used in the conversion of atomic binding energies into nuclear ones. Their dependence on neutron excess has been investigated for the first time across the nuclear chart within atomic approach. These factors have been disregarded in previous generation of covariant energy density functionals but their neglect leads to substantial global calculation errors for physical quantities of interest. For example, these errors for binding energies are of the order of 0.8 MeV or higher for the three major classes of covariant energy density functionals.

We report directed flow ($v_1$) of multistrange baryons ($\Xi$ and $\Omega$) and improved $v_1$ data for $K^{-}$, $\bar{p}$, $\bar{\Lambda}$ and $\phi$ in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=$27 and 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). We focus on particles whose constituent quarks are not transported from the incoming nuclei but instead are produced in the collisions. At intermediate impact parameters, we examine quark coalescence behavior for particle combinations with identical quark content, and search for any departure from this behavior (``splitting'') for combinations having non-identical quark content. Under the assumption of quark coalescence for produced quarks, the splitting strength appears to increase with the electric charge difference of the constituent quarks in the combinations, consistent with electromagnetic effect expectations.

This work investigates hot quark matter under the thermodynamic conditions characteristic of a binary neutron star (BNS) merger remnants. We used the density-dependent quark mass model (DDQM) to access the microscopic nuclear equation of state (EoS) in a series of snapshots. The strange quark matter (SQM) is studied at finite temperature and entropy, in the presence of electrons and muons and their corresponding neutrinos to simulate the BNS merger conditions. For the first time, we introduced temperature into the DDQM model using a lattice QCD-motivated approach to construct both isentropic and isothermal EoSs. We observe that as the entropy of the SQM increases, the merger remnant becomes more massive and increases in size, whereas the neutrino abundance also increases. In the fixed-temperature case, on the other hand, we observe that the entropy spreads from the surface towards the center of the remnant. We determine the particle distribution in the core of the remnants, the structure of the remnant, the temperature profile, sound velocity, and the polytropic index, and discuss their effects. The strange-quark star (SQS) remnants satisfy the $2\,{\rm M_\odot}$ mass constraint associated with neutron stars (NS).

We assess the universal relations among second-order moments of relativistic stars, namely the moment of inertia, tidal deformability, and spin-induced quadrupole moment, via reformulated perturbation equations. After constructing the spherical background configuration by solving two ordinary differential equations as usual, these three moments are obtained by solving four additional ordinary differential equations. They are solved numerically from the stellar center to the surface, and we do not need to derive homogeneous solutions for obtaining the quadrupole moment. This small number of ordinary differential equations to be solved enables us to identify the primary variable for each second-order moment. Investigating the profile of these variables in the star, we speculate that their nonmonotonic behavior, enhanced typically for soft equations of state and/or high compactnesses, introduces the variety to the relations among these second-order moments unless the black-hole limit is approached. Because realistic relativistic stars are widely believed to be characterized by stiff equations of state, they enjoy the universal relation to a great extent.

The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the resulting expressions for various coefficients of the Wigner function exhibit properties that cannot be reproduced within the standard semiclassical expansion. The formula for the axial vector component of the Wigner function can be conveniently used to study spin polarization effects and illustrate connections between the spin density matrix and axial current. In particular, we find that during an adiabatic change of the periodic potential into a uniform one, the polarization vector is twisted from its original direction.

We present a comprehensive analysis of near-threshold photoproduction of $\rho^0$, $\omega$, and $\phi$ mesons on a deuterium target, utilizing published datasets from DESY and SLAC for $\rho^0$ and $\omega$ production, as well as data from the LEPS and CLAS Collaborations for $\phi$ production. In extracting the deuteron mass radius, we adopt a dipole parametrization for the scalar gravitational form factor, which effectively captures the $|t|$-dependence of the differential cross sections associated with vector meson photoproduction. In addition, results from alternative commonly used form factor parametrizations are also considered and compared. Employing the vector meson dominance (VMD) framework and invoking low-energy Quantum Chromodynamics (QCD) theorems, we extract the deuteron mass radius from near-threshold photoproduction data of $\rho^0$, $\omega$, and $\phi$ mesons. The mass radii obtained from the various datasets are found to be consistent within statistical uncertainties, yielding an average value of $2.03 \pm 0.13$ fm under the dipole form assumption. We also provide a detailed discussion of the sensitivity of the extracted radius to different choices of gravitational form factor models. Our result represents a significant improvement in precision compared to earlier estimates based solely on $\phi$ meson photoproduction, offering new constraints for theoretical models of nuclear structure and deepening our understanding of the mass distribution within the deuteron.

Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is examined in detail. It has three instanton types or flavors with distinct actions. For weak coupling and subject to there being a single large (or small) parameter, the interactive system can be handled perturbatively. The zero mode problem arising from time translation symmetry is handled via the Fadeev-Popov procedure. A diagrammatic procedure allows corrections to the fluctuation determinant to be calculated systematically. Independent instanton contributions are summed over by extending the dilute gas approximation to three flavors and energy splittings of the lowest four states is calculated. All tunneling amplitudes are concisely expressed in terms of elementary functions. While the model is possibly useful for a variety of physical systems, an application is made here to the tunneling of a composite particle in one dimension.

We present a comprehensive study of the two-flavor Quark--Meson--Diquark (QMD) model by comparing a renormalization approach with a renormalization-group (RG) consistent mean-field formulation based on the functional renormalization group (FRG). The renormalized QMD model allows analytical investigations of key quantities such as the zero-temperature diquark gap and the critical temperature for color superconductivity, ultimately reproducing the exact BCS relation in the high-density limit. We carry out the same analysis for different schemes of RG-consistent QMD models. We show that the RG-consistent approach yields a phase diagram and thermodynamic properties qualitatively similar to those of the renormalized model, provided both are embedded within a unified scheme that ensures consistent vacuum properties. In particular, both treatments recover the Stefan--Boltzmann limit at high densities. On the other hand, whether the BCS relation for the critical temperature is satisfied depends on the details of the RG-consistent setup. Our results highlight the relevance of renormalization and RG-consistent methods for accurately capturing the thermodynamics of QMD and related effective models with diquark degrees of freedom.

Widely used in atomic and superconducting qubit systems, the Jaynes-Cummings (JC) Hamiltonian is a simple, yet powerful model for a two-level system interacting with a quantum harmonic oscillator. In this paper, we focus on a system of n qubits, identically coupled to a single oscillator via JC interaction, also known as the Tavis-Cummings (TC) Hamiltonian. We show that all permutationally-invariant unitaries on an arbitrary number of qubits can be realized using this permutationally-invariant Hamiltonian, which couples the qubits to an oscillator initialized in its vacuum state, together with global uniform x and z fields on all qubits. This includes useful gates, such as controlled-Z gate with an arbitrary number of control qubits. As a corollary, we find that all permutationally invariant states -- including useful entangled states such as GHZ and Dicke states -- can be prepared using this interaction and global fields. We also characterize unitaries that can be realized on the joint Hilbert space of the qubits and oscillator with the TC interaction and global z field, and develop new methods for preparing the state of the oscillator in an arbitrary initial state. We present various examples of explicit circuits for the case of n=2 qubits. In particular, we develop new methods for implementing controlled-Z, SWAP, iSWAP, and $\sqrt{i\text{SWAP}}$ gates using only the TC interaction and a global z field. Our work also reveals an accidental symmetry in the TC Hamiltonian and shows that it can be explained using Schwinger's oscillator model of angular momentum.

We build up a complete description of QCD phase structure by applying the parametrization of the chiral and deconfinement order parameters upon the calculations from functional QCD approaches. In particular in the first order phase transition region at high chemical potential, both the phase transition line using Maxwell construction and the coexistence boundary lines from the spinodal decompostion are determined. We compute the thermodynamic quantities including the number density, the energy density, the pressure and also the free energy for both stable and unstable phases of QCD. Additionally, after applying a phenomenological description of the inhomogeneity of the QCD free energy, we obtain the surface tension of the first order phase transition of QCD.