Papers

We evaluate quantum electrodynamics (QED) nuclear medium effects under experimental conditions at the future Electron-ion collider in China (EicC). We consider neutral-current and charged-current elastic scattering, as well as neutral-current and charged-current deep inelastic scattering. We compute cross-section corrections at first order in the opacity expansion and estimate kinematic modifications due to multiple rescattering within the nucleus. We perform the first calculations of charged-current deep inelastic scattering and polarized scattering. We present results for the anticipated $^{197}_{79}\mathrm{Au},~^{208}_{82}\mathrm{Pb},$ and $^{238}_{92}\mathrm{U}$ nuclei and extrapolate these calculations to the lighter $^{40}_{20}\mathrm{Ca}$ isotope. We find that QED nuclear medium effects are non-negligible when extracting the process-independent non-perturbative structure of nucleons and nuclei at the EicC.

We study the production of $c$ and $b$ quarks in photon-induced processes as a probe of gluon saturation, with a focus on the high-energy region accessible in ultra-peripheral collisions (UPCs) at the LHC. We compare predictions for inclusive and diffractive heavy quark production with and without saturation effects by using the nonlinear Balitsky–Kovchegov and the linear Balitsky–Fadin–Kuraev–Lipatov equations for the evolution of the dipole amplitude. The percentage of coherent diffractive events is predicted to be $~20\%$ in the saturation model, which is approximately twice as large as predictions based on parton distribution functions and shadowing. This indicates that measurements of diffractive heavy quark production in UPCs may provide a sensitive probe for distinguishing linear and nonlinear regimes of quantum chromodynamics.

Neutron stars contain several forms of quantum condensed matter whose microscopic properties control macroscopic rotational dynamics and magnetic behavior of these fascinating objects. This review surveys superfluidity and superconductivity in compact stars, with emphasis on phenomena associated with quantized vorticity and magnetic-flux structures, and the possible connections to observed phenomena. We first summarize the microphysics of nucleonic pairing, including spin-singlet $^1S_0$ neutron pairing in the inner crust, proton superconductivity in the outer core, and spin-triplet $^3P_2$–$^3F_2$ neutron pairing at higher densities, together with the principal many-body uncertainties affecting the corresponding pairing gaps. We then discuss the dynamics of neutron vortices, including pinning, vortex creep, and dissipative motion, and the role of vortex dynamics in angular-momentum exchange between the superfluid and the observable crustal component. We give special attention to proton flux tubes in type-II superconducting cores, the possible realization of type-I superconductivity, and vortex–flux-tube interactions. We also review collective rotational phenomena, including Tkachenko oscillations of the vortex lattice and free precession, and their possible relation to long-term variability in pulsar timing. Finally, we discuss the possible deconfinement of hadronic matter into quark matter, the formation of color-superconducting phases, and the topological defects associated with these phases, together with their possible observational consequences. Throughout the review, we identify key open questions connecting microscopic pairing, mesoscopic defect dynamics, and observable neutron-star phenomena.

We construct a dispersive representation of the relativistic $3\to 3$ scattering amplitude for three identical spinless particles in the $S$-wave. The two-particle subenergy, instead of the total energy, is used as the dispersive variable. This choice keeps the physical dispersive contour free of the kinematical cuts that complicate total-energy dispersion relations. By separating discontinuities across the two-particle subenergy cuts from that across the three-body cut, we derive a linear integral equation with one-particle exchange as the driving term. We further show that the solution satisfies three-body unitarity as a consequence of two-body unitarity, analyticity, and crossing symmetry. For pair-wise interactions, this representation can be rewritten into the form used for isobar-spectator scattering. Finally, we give prescriptions for contour deformation and the subtraction of poles in the two-body subsystem amplitudes, which continue the amplitude onto adjacent unphysical Riemann sheets and thus provide direct access to the analytic structure relevant for three-body resonance poles.

Neutron star radius measurements, particularly using X-ray data collected with the Neutron star Interior Composition Explorer (NICER), have provided invaluable information for models of cold, catalyzed matter at densities above that of nuclear saturation. Here we present an analysis of NICER data on the 318-Hz pulsar PSR J0614-3329, which has a mass ~1.4-1.5 solar masses determined from radio observations. The best-fitting model we explore has three uniform-temperature circular hot spots and yields a symmetric 68% credible range for the equatorial circumferential radius of 9.88-12.77 km. We also explore joint fits to the NICER data and the X-ray Multi-Mirror (XMM-Newton) data on this pulsar, but find that the models that best fit both data sets systematically underpredict the XMM-Newton data when, as is standard, it is assumed that the XMM-Newton background is known from observations of surrounding fields. Finally, we discuss the implications of our results, combined with data on other neutron stars, for the properties of the dense matter in neutron star cores.

We investigate the bound and resonant states of the $\alpha+\alpha+\Omega$ and $\alpha+\alpha+\Omega_{ccc}$ three-body systems, corresponding to $^{9}_{\Omega}{\mathrm{Be}}$ and $^{9}_{\Omega_{ccc}}{\mathrm{Be}}$, within the Gaussian expansion method combined with the complex scaling method. The $\alpha\Omega$ and $\alpha\Omega_{ccc}$ interactions are constructed by folding the $N\Omega$ and $N\Omega_{ccc}$ potentials obtained from lattice QCD calculations by the HAL QCD Collaboration with the nucleon density distribution of the $\alpha$ particle. The uncertainty associated with the $\alpha$-particle matter radius is also examined. For the $\Omega$ sector, the strong $N\Omega$ attraction generates deeply bound $0_1^+$, $2_1^+$, and $4_1^+$ states in $^{9}_{\Omega}{\mathrm{Be}}$, accompanied by a pronounced contraction of the $\alpha\alpha$ core, demonstrating a strong gluelike effect of the $\Omega$ baryon. An unconventional inversion between the $0_1^+$ and $4_1^+$ levels is also predicted. In contrast, the $\Omega_{ccc}$ baryon produces considerably weaker attraction: the $0_1^+$ state of $^{9}_{\Omega_{ccc}}{\mathrm{Be}}$ is weakly bound, whereas the $2_1^+$ and $4_1^+$ states remain resonances. Their resonance energies and widths exhibit a clear dependence on the strength of the $\alpha\Omega_{ccc}$ interaction. These results reveal qualitatively different gluelike behaviors of the $\Omega$ and $\Omega_{ccc}$ baryons and provide predictions for the spectroscopy of exotic multistrange and triply charmed hypernuclei.

Femtoscopic correlations are widely regarded as precision probes of hadronic interactions through vacuum final-state interactions after kinetic freeze-out. Here we demonstrate that, in baryon-rich heavy-ion collisions, the nuclear mean field generates an additional dynamical contribution to femtoscopic correlations during the transport evolution. Using the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach, we investigate proton-proton, proton-$\Lambda$, three-proton, and proton-proton-$\Lambda$ correlations in Au+Au collisions at $\sqrt{s_{\rm NN}}=3$, 4.5, 7.7, and 19.6 GeV. We find that the nuclear mean field produces a characteristic low-$k^*$ enhancement that is strongest at the lowest beam energies and gradually disappears with increasing collision energy. Furthermore, both the stiffness and the momentum dependence of the nuclear equation of state leave distinct signatures in the femtoscopic correlation functions, with higher-order correlations exhibiting substantially enhanced sensitivity compared with conventional two-particle observables. Our results demonstrate that femtoscopy extends beyond its traditional role as a tool for studying hadronic interactions and serve as a new class of microscopic observables for the nuclear equation of state, complementary to collective flow and subthreshold strangeness production, thereby opening a new avenue for exploring dense baryonic matter in low-energy heavy-ion collisions.

We investigate cold homogeneous matter composed of neutrons, protons, and $\Lambda$ hyperons within our hyperonic extension of the lowest-order constrained variational (LOCV) method, hereafter denoted LOCVY. Our earlier LOCVY calculation, based on two-baryon interactions, is extended by supplementing the Argonne $v_{18}$ nucleonic interaction with the Urbana IX three-nucleon force, reduced within the variational framework to a correlation-weighted density-dependent effective two-nucleon interaction. The $N\Lambda$ and $\Lambda\Lambda$ interactions are kept unchanged, allowing the present calculation to isolate the competition between hyperon-induced softening and nucleonic three-body repulsion. The energy per baryon is calculated for fixed $\Lambda$ fractions $Y_{\Lambda}=0$, $0.1$, and $0.2$ in matter with a symmetric nucleonic component and in the proton-free neutron–$\Lambda$ limit. Direct differences between calculations with and without the three-body force quantify its density-dependent contribution, while a complementary decomposition into $NN$, $N\Lambda$, and $\Lambda\Lambda$ terms identifies the microscopic origin of the stiffening. The Urbana contribution becomes increasingly repulsive with density and opposes, but does not generically remove, the softening associated with a finite $\Lambda$ content. We further investigate the saturation properties for several prescribed $\Lambda$ fractions, with and without the nucleonic three-body force, to clarify how strangeness and many-body interactions modify the saturation point and the agreement with empirical nuclear-matter properties.

We extend the neural-network-based variational method for nuclear density functional theory to the Kohn–Sham scheme, representing the complex spinor components of the single-particle orbitals by multi-layer perceptrons. We show that neural-network optimization of a given energy density functional, combined with an orthonormalization post-processing step, is mathematically equivalent to the variational condition projected onto the tangent space of the wave-function manifold spanned by the network parameters, and that the training optimizes not only the expansion coefficients but also the basis functions themselves. We assess the method from three points of view. In the first place, we examine how the results depend on the number of units, the number of layers, and the arithmetic precision, and find that quantitative accuracy requires both a sufficient width and a sufficient depth, while single-precision arithmetic is sufficient to represent the nuclear density distribution. In the second place, the binding energies and charge radii of several closed-shell nuclei agree with conventional Skyrme–Hartree–Fock results, and the quadrupole deformations of open-shell nuclei are consistent with reference calculations that include pairing and with experiment. In the third place, we confirm that a neural-network single-particle basis can represent the three-dimensional configurations of the fundamental pasta phases: spheres, rods, and slabs. The framework offers a new perspective on computational nuclear theory, well suited to the forthcoming generation of GPU- and AI-oriented high-throughput supercomputers.

This introductory Chapter will try to briefly address 1. the basic physical ingredients that determine the nuclear spectrum and the associated energy scales; 2. the connection between the observed experimental results, typically in the form of cross sections, and the underlying nuclear structure presented in the previous point. The nature and scope of the present Chapter is to provide a roadmap of the field of nuclear reactions theory, and to set the stage for the more detailed discussions in the companion Chapters. The aim is to provide a conceptual framework that will allow the reader to understand how the different reaction theory approaches fit together, and how they relate to the underlying physics of nuclear reactions. The reader will find in other chapters in this volume detailed discussions about the methods addressing two seemingly quite distinct phenomena: direct and compound nuclear reactions. We hope that this brief Chapter will help them realize that whenever we are talking about either of these, we are talking about the same thing: nuclear reactions.

The spherical-to-deformed quantum phase transition of the Interacting Boson Model (IBM) is investigated using the variational quantum eigensolver (VQE). The $U(5)$–$SU(3)$ transitional Hamiltonian is studied with $\chi=-\sqrt{7}/2$. We develop a symmetry-preserving, minimum-qubit VQE framework for collective nuclear models, achieving a substantial reduction in qubit requirements without compromising the finite-size quantum-phase-transition physics. The transition is characterized through the normalized $d$-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point $\xi_c=8/17\simeq0.470588$, with an independent order-parameter extrapolation yielding $\xi_\infty=0.46986(61)$. The VQE reproduces ground-state energies and structural observables to numerical precision. These results demonstrate the potential of symmetry-reduced VQE for efficient quantum simulations of collective nuclear dynamics and quantum phase transitions.

Using the elemental abundances in 68 metal-poor (MP) stars, we present a data-driven model for $r$-process production patterns covering Sr to U. We show that essentially all the $r$-process patterns in those and other test stars can be adequately explained as mixtures of Patterns 1 and 2, which provides theoretical insights into the empirical categories of limited-$r$, $r$-I, and $r$-II stars. We carry out an extensive survey of the yield templates produced by parametric $r$-process calculations. We propose that Pattern 2 may be dominated by a single template and points to regularity in $r$-process production by a subset of neutron star mergers (NSMs), while Pattern 1 is the average superposition of multiple templates and reflects production by other NSMs and perhaps also some magneto-rotational supernovae. We raise possible systematic issues with abundance ratios for elements measured in different ionization states, and highlight the need for examining the Os, Ir, and Pt measurements for HD~122563, which is dominated by Pattern 1 with a prominent Pt peak in our model. If this result is confirmed, the meaning of the limited-$r$ category requires drastic revision. Further measurements of a wider range of $r$-process elements in a larger sample of MP stars are critical to test and improve our model.

The dipole model provides a powerful framework for describing high-energy nuclear interactions, particularly in the regime of dense gluonic matter. However, accurately evolving the dipole–nucleus scattering amplitude remains a major computational challenge because it is governed by nonlinear QCD evolution equations. To address this, we investigate a machine learning (ML) model as an efficient surrogate for the conventional numerical evolution. These ML-based approximations dramatically reduce the computational cost of global analyses while maintaining the accuracy required to describe a broad range of experimental data. We systematically evaluate the ML results for accuracy, computational efficiency, and ability to capture essential features of dipole evolution in nuclear environments. These computational advancements will enable global analyses of diverse datasets within both the dipole and parton model frameworks, providing a more rigorous probe of nuclear structure in the dense regime. Comparing both descriptions within a common fitting framework can provide precise constraints on the gluon distributions and advance our understanding of the quark and gluon structure of nuclei, particularly in the small-x region.

We study the impact of new mass-radius information from PSR J1614-2230, PSR J2124-3358, and 47 Tuc X7 in a combined equation of state inference based on chiral effective field theory constraints at nuclear densities and using different high-density extensions, including perturbative QCD constraints. The largest impact stems from the heavy-mass PSR J1614-2230 star, which shifts heavy neutron stars to smaller radii by around 0.4 km. Moreover, the combined astrophysical NICER, LIGO/Virgo, and X-ray information drives the radius posterior to a more data-driven distribution, which is less sensitive to the high-density extension. For the equation of state, the new mass-radius information significantly tightens the pressure and speed-of-sound posterior distributions, especially around three times saturation density. Finally, we make predictions for the poorly constrained masses of PSR J2124-3358 and 47 Tuc X7 based on the combined equation of state analysis and the other astrophysical sources.

Using pulse profile modeling, we obtain the mass-radius measurement of a millisecond pulsar (MSP) with data from the Neutron Star Interior Composition ExploreR, XMM-Newton and the Chandra X-ray Observatory. We report here the radius of PSR J1614$-$2230, the second most massive MSP confirmed by radio timing. All of the data sets are well described by a simple model composed of two circular hot spots. The final result yields an equatorial radius of $R_{\rm eq}=10.06 ^{+1.25}_{-0.87}\,$km, and a gravitational mass of $M=1.937^{+0.012}_{-0.013}\,M_{\odot}$ (equally tailed 68% credible intervals). Although a non-thermal component was previously reported at higher energies, we find no sign of it in either our phase-averaged or phase-resolved spectral analyses. Using new relations linking the compactness to oblateness or surface gravity, and tailored to the spin frequency of PSR J1614$-$2230, we infer a configuration with one hot spot near the pole, and another near the equator. The tight mass posterior is essentially informed by radio timing, while the radius constraint is not as tight due to the low source signal (8.5$\sigma$ X-ray pulse significance). However, over all geometries and atmosphere models tested, the radius posterior tends toward low values ($\lesssim12.08\,$km, 90th percentile in all cases).

Using first-principles field-theoretic methods, we investigate neutrino emission from strongly magnetized dense quark matter under conditions relevant to compact stars. We account for Landau-level quantization of both electron and quark states and show that it strongly modifies the kinematics of Urca processes. In particular, quark quantization restricts the available phase space in which both quark and electron energies can simultaneously lie near their respective Fermi surfaces. At moderately strong magnetic fields, before pronounced quark quantization sets in, the emission rate tends to increase on average with increasing field strength. In the regime of very strong fields, however, the increasingly restricted phase space first gives rise to Shubnikov–de Haas-type oscillations and then to resonance-like spikes near a discrete sequence of Urca-resonant magnetic field values, separated by regions of strong suppression. Finally, the emission rate becomes nearly completely quenched once $|eB| \gtrsim 6\mu_{e}\mu_{u}$, corresponding to approximately $B\gtrsim 1.5\times 10^{19}~\mbox{G}$ for the representative set of model parameters considered. We also find significant anisotropy in the longitudinal momentum emission near the Urca-resonant magnetic field values.

The longitudinal and transverse nuclear response functions encode information about the electromagnetic behavior of the nuclear target probed in inclusive electron-nucleus scattering. We present a microscopic calculation based on an independent-particle model, where a non-relativistic nuclear mean-field potential governs both the initial and final hadronic states of the interaction. We add dynamically generated short-range nucleon-nucleon correlations (SRCs), as well as meson-exchange currents (MECs) derived from one-pion exchange and intermediate $\Delta$-resonance excitation. We evaluate the contributions from one- and two-nucleon knock-out reactions to nuclear responses in inclusive electron scattering from $^{12}\mathrm{C}$ in the quasielastic and dip regions. We demonstrate that for quasielastic kinematics, SRCs quench both nuclear responses, while the MECs enhance the transverse signal, substantially improving the predicted transverse-to-longitudinal ratio. In the dip region between the quasielastic and the $\Delta$-resonance peaks, we find that the observed excess of transverse strength originates mainly from explicit two-nucleon knock-out following a $\Delta$-resonance excitation.

The chiral symmetry is a property of the fundamental theory of the strong interaction that is relevant for the hadronic physics. It is expected that at sufficiently high temperature and matter density, this symmetry becomes manifest. Within the Chiral Dual Partner Model the chiral transformation is implemented in such a way that a fermion mass term is allowed if the parity partner of each baryon is included in the framework. This model is used here to study possible manifestations of the chiral symmetry in dense nuclear matter, assuming constant isospin fraction. It is found that the onset of the odd parity baryons is associated with two branches of thermodynamical instabilities, one of them leads to a first order phase transition for temperatures below $T_c\simeq 11$ MeV. An analysis of these instabilities in the phase space is given, and neutron star matter is considered as a special case.

We study the production of the $\phi(1020)$ and $\Omega(1672)$ in heavy ion collisions at $\sqrt{s_{NN}} = 5.02$ TeV by employing two complementary approaches. In the first approach, the production of the $\phi$ and $\Omega$ is discussed in the coalescence model. In the second approach, we developed a hybrid framework that combines the recombination of shower and thermal partons with remnant string fragmentation. Thermal partons in the quark-gluon plasma are modeled using a blast-wave parameterization, while the phase space information of medium-modified parton showers is generated from Q-PYTHIA, using unquenched jet partons obtained from HIJING initial inputs. We show that both approaches agree well with the experimental measurements, and demonstrate that this hybrid framework provides deeper insight into the underlying strangeness components in the production of $\phi$ and $\Omega$ in relativistic heavy-ion collisions.

We extend the systematic study of small-$x$ Transverse Momentum Dependent (TMD) distributions, initiated in [Cougoulic:2026drr], by including the energy evolution. We use the JIMWLK evolution equation to study the energy dependence of three distributions in the quark-gluon sector, $\mathcal{F}_{qg}$, and seven distributions in the gluon-gluon sector, $\mathcal{F}_{gg}$. The initial conditions are provided by the McLerran-Venugopalan model. We study these TMD distributions in position space and with $N_c = 3$ fixed. We then compare these results to the Gaussian truncation of the Balitsky hierarchy. Although the Gaussian truncation worked very well for the TMD distributions at the initial condition, now we identify some cases where the Gaussian truncation provides a reasonably good description, but in the majority of cases it fails to fully reproduce numerical data. Using the fixed representation building blocks, $\Omega_{ag}^\omega$, we are able to partially explain the outcomes. This work constitutes the next step with the goal of understanding the interplays between the large-$N_c$ limit and Gaussian truncation as well as the BK/JIMWLK evolution equations for phenomenologically relevant observables.

Future multimessenger observations of neutron stars (NS) are expected to substantially increase both the number and precision of astrophysical constraints on the equation of state (EoS) of dense matter. This motivates inference frameworks capable of accommodating a variable, non fixed number of observations while preserving the posterior information associated with each measurement. In this work, we introduce NS-UNO, a Neural Posterior Estimation framework for NS EoS inference designed to accommodate an Unconstrained Number of Observations (UNO). NS-UNO combines a hierarchical DeepSets model with a conditional normalising flow, enabling a single trained model to perform inference from mass-radius observation sets of varying size, with each observation represented by a set of posterior samples. We demonstrate accurate and well calibrated posterior reconstructions using a model trained jointly on piecewise polytropic and non-parametric Gaussian process EoS ensembles. The reconstruction improves as observations probe a broader range of NS masses, while remaining robust to variations in the number and precision of the observations. The model also generalises to EoSs outside the families used during training. Finally, we qualitatively demonstrate the framework on current multimessenger constraints from NICER and GW170817. NS-UNO provides a flexible and scalable approach to NS EoS inference, naturally suited to the increasingly diverse observational datasets expected from next generation multimessenger astronomy.

We employ the Parton-Hadron-String Dynamics (PHSD) transport approach to investigate the influence of baryon-rich matter on charmonium production and dissociation. The Remler formalism is implemented to dynamically model charmonium formation from charm-anticharm pairs. As a validation step, the formalism is first benchmarked against experimental data from elementary pp collisions and then extended to pA systems to extract the effective nuclear absorption cross section of charmonium. This extracted cross section can subsequently be applied in heavy-ion collisions to quantify medium-induced effects. Our results demonstrate that the Remler formalism provides a quantitatively consistent description of charmonium production in pp and pA collisions at SPS energies. The approach is then extrapolated to GSI/FAIR energies, where predictions for charmonium yields and survival probabilities are presented. These findings highlight the relevance of the Remler formalism as a dynamical framework for studying heavy-quark bound-state formation in baryon-rich matter and offer theoretical guidance for future experimental programs at SPS, FAIR and NICA aimed at mapping the QCD phase structure.

The femtoscopic correlation technique in relativistic heavy-ion collisions provides a unique opportunity to investigate hadron-hadron interactions and possible exotic states. In this work, we study the $p\Lambda_c$ correlation function and its sensitivity to the low-energy $N\Lambda_c$ interaction related to possible $^3_{\Lambda_c}\mathrm{H}$ bound states. Based on the quark delocalization color screening model, three interaction scenarios with different strengths are constructed, and the corresponding spin-averaged $p\Lambda_c$ correlation functions are calculated within the Koonin–Pratt formalism. The results demonstrate that the correlation function is sensitive to the $p\Lambda_c$ interaction strength, with coupled-channel effects and $S$-$D$ wave mixing producing additional enhancements in the correlation signal. These findings suggest that future $p\Lambda_c$ femtoscopic measurements at relativistic heavy-ion collision experiments can provide valuable constraints on the interaction between charmed baryons and nucleons and offer guidance for exploring possible heavy-flavor hypernuclei.

Jets provide a powerful probe of the three-dimensional spin structure of the nucleon, a central goal of the Electron-Ion Collider. Yet the observed jet defines an axis that breaks the azimuthal isotropy of soft-gluon radiation, thereby reshaping the very asymmetries used to extract that structure. Using transverse-momentum-dependent (TMD) QCD factorization, we show for the first time that this jet-induced anisotropy imposes a parity selection rule on polarized asymmetries. Expanding the transversely polarized structure functions in harmonics $\cos(n\phi_{qJ})$, where $\phi_{qJ}$ is the angle between the jet and the lepton-jet momentum imbalance, makes this rule explicit: the symmetry of each harmonic is fixed by the parity of $n$, independently of the magnitudes of the harmonic coefficients. For the Sivers function, the canonical left-right asymmetry about the proton spin survives for even $n$ but is replaced by a counterintuitive left-right symmetry for odd $n$. The worm-gear function retains its up-down asymmetry at every harmonic while being left-right symmetric for even $n$ and asymmetric for odd $n$. At EIC kinematics, the higher harmonics studied here are predicted to be individually measurable, providing new observables for the azimuthal dynamics of soft radiation and an essential ingredient in precision extractions of nucleon structure.

We investigate meson gravitational D-form factors in the three-flavor linear sigma model and their connection to symmetry breaking in low-energy QCD. Within the scalar meson dominance picture, we examine the scalar meson exchange contributions and their relation to meson masses through scalar-meson couplings. In the three-flavor symmetric limit, we first derive analytical expressions for the D-form factors of pseudoscalar and scalar mesons. In the chiral limit, the forward-limit value of the octet pseudoscalar D-form factor is fixed to $-1$, whereas the $U(1)_A$ anomaly generates additional contributions to the singlet pseudoscalar and scalar-meson D-form factors. For realistic flavor breaking, the interaction introduced to reproduce the scalar-meson mass hierarchy below $1$ GeV significantly affects the scalar-meson D-form factors. We further compare the linear sigma model results with those obtained from a chiral perturbation theory Lagrangian including a dilatonic scalar field and show that their differences are governed by the canonical mass dimensions of the interaction terms contributing to meson mass generation. These results indicate that meson D-form factors provide sensitive probes of symmetry-breaking structures in low-energy hadron physics.

We study quantum-information aspects of neutron–proton scattering in the spin-space $M$-matrix framework. Four representative classes of input states are considered, namely diagonal mixed states, separable pure states, general two-qubit pure states, and a special Schmidt-like entangled subclass. For each class, ensemble-averaged output mutual information, reduced-state linear entropy, negativity, and geometric quantum discord are calculated in the relative momentum– scattering angle plane. The results show that the outgoing spin correlations are governed jointly by scattering kinematics and by the structure of the incoming quantum ensemble. Input states with stronger intrinsic coherence or entanglement give larger maxima and higher minima in the mutual information, negativity, and geometric quantum discord. The enhanced regions of the mutual information and geometric discord depend on the input states, while the negativity maximum remains concentrated in the high-momentum backward-scattering region. These results extend earlier studies based on product-state entanglement power and provide an ensemble-based description of how spin correlations in neutron–proton scattering arise from the interplay between input-state structure and scattering dynamics.

Searches for weak spin-dependent forces are commonly interpreted in terms of a basis of sixteen rotationally invariant two-fermion potentials, including potentials which violate parity (P) and time-reversal (T) invariance. We derive finite-range coordinate-space potentials generated by a massive spin-1 boson with vector, axial-vector, tensor, and pseudotensor couplings to Dirac fermions. In addition to the familiar vector–vector, vector–axial-vector, and axial-vector–axial-vector interactions, we obtain the mixed vector–tensor, vector–pseudotensor, axial-vector–tensor, and axial-vector–pseudotensor potentials, together with tensor–tensor, tensor–pseudotensor, and pseudotensor–pseudotensor terms. We retain the contact terms needed in atomic-scale applications and give compact expressions that include both orderings of inequivalent fermion vertices. We then extend the analysis to a massive spin-2 mediator described by a symmetric Fierz–Pauli field. Besides the conventional coupling to the conserved fermion energy–momentum tensor, we consider a symmetric axial-tensor current. Its nonconservation for massive fermions makes the longitudinal spin-2 helicities contribute to axial-tensor–axial-tensor exchange. The leading minimal spin-2 interactions are either P,T even or P odd and T even; in particular, they do not generate a T-odd potential. We map the resulting interactions onto the sixteen-potential Dobrescu–Mocioiu basis and use this mapping to translate existing experimental constraints into numerical limits on spin-1 and spin-2 coupling products in the small- and large-mediator-mass regimes, together with representative limits at finite mediator masses. The derived relations between the boson-exchange coupling constants and the coefficients of the basis potentials also allow published exclusion curves to be rescaled to arbitrary mediator masses.

Quantum resonances and black-hole quasinormal modes (QNMs) are described by closely related mathematics: radiative boundary conditions, analytic continuation of Green functions or resolvents, poles on nonphysical sheets, and non-self-adjoint spectral representations. This article does not introduce that equivalence but reconstructs its genealogy. Nuclear resonance theory grew from radioactive decay, reaction cross sections, metastable compound states, and complex energies, whereas black-hole perturbation theory grew from spacetime stability and causal response. We place the two developments on a common chronology, from Sommerfeld's radiation condition and early nuclear-decay theory through Regge–Wheeler perturbations, Vishveshwara's 1968 dissertation and 1970 papers, Press's 1971 quasi-normal terminology, and the independent Aguilar–Balslev–Combes theory of analytic dilation, then follow their later mathematical reunification in scattering-resonance theory. Alongside the chronology, we give a working dictionary relating no-incoming and horizon-ingoing/infinity-outgoing conditions, pole energy and complex frequency, width and damping rate, residues and excitation factors, and nonresonant background with branch-cut and prompt contributions. The aim is to make the cross-disciplinary equivalence operational without flattening its history, and to distinguish mathematical equivalence from historical genealogy.

We discuss several issues regarding the modern generalization of Weinberg's compositeness criterion. In particular, we demonstrate that the on-shell renormalization in NREFT reproduces Weinberg's result and provides a simple description of resonances, bound states, and coupled channel effects. Additionally, we present the complete propagator, including the charged channel for the near-threshold p-wave states.

We calculate the electromagnetic form factors of nucleons bound in finite nuclei and make predictions to the ratio between the electric ($G_E^*$) and magnetic ($G_M^*$) form factors in terms of the square of the four-momentum transfer $Q^2$. We extend our previous constant-density calculations within the covariant spectator-QMC framework by incorporating the spatial nuclear density profiles of finite nuclei and quantify the deviations from the average-density approximation used in our previous applications. The impact of the medium effects can then be observed considering the ratio between $G_E^*/G_M^*$ and the ratio in free space $G_E/G_M$, that define the proton electromagnetic double ratio associated with a given nucleus. The double ratio is expected to remove some systematic uncertainties. There is the expectation that ratios $G_E^*/G_M^*$ associated with the bound protons inside the nucleus will be measured in the near future in polarization-transfer experiments $(\vec{e} A, e'\! A' \vec{p})$. Anticipating future measurements on the subject, we make predictions for the double ratios, to be compared with the average measurements on the energy states of protons bound to nuclei. We consider the nuclei $^{12}$C, $^{16}$O and $^{40}$Ca. We conclude that the form factors calculated using nuclear density profile function $\rho(r)$ are less suppressed than in the case of the results calculated using the average nuclear density. The results indicate that the relative importance of the low-density surface region increases with $Q^2$, leading to a weaker suppression than that predicted by the average-density approximation. We also make predictions for the ratios associated with neutrons bound to nuclei.