Papers

The Gari–Krümpelmann (GK) model provided one of the first semiphenomenological descriptions of the electromagnetic nucleon form-factors over a wide range of momentum transfer. It combined vector-meson dominance at low and intermediate momentum transfer with perturbative-QCD constraints at large momentum transfer. The present work extends this framework by including the dispersive two-pion continuum explicitly in the isovector channel. The two-pion contribution is taken from modern dispersive analyses and embedded into the intrinsic high-$Q^2$ structure of the GK ansatz. The physical $\rho$ dynamics is then interpreted as part of the correlated two-pion spectral function. Similarly, we include in the isoscalar spectral function the correlated $K\bar K$ and $\rho\pi$ continua, where the former also includes the $\phi$-meson pole. The direct coupling terms remain essential for the transition to the asymptotic regime. This gives a cleaner separation between long-range continuum dynamics, coherent vector-meson contributions, and direct quark-current dynamics. With just 7 parameters, we can describe the large body on form-factor data and differential cross sections from electron-proton scattering in the space-like region.

Using dimensional arguments and other simple estimates, it is pointed out that a branch of nuclei with mass number A>10^7 could be metastable if they have close to maximal isospin. This branch is continuous with neutron stars. The fastest decay mode of these hypothetical metastable nuclei (which we call monsters) is through neutron evaporation. We present an estimate of the lifetime and show it could be more than 100 ps for A>10^{39}. We speculate about their creation in binary neutron star mergers, where we argue that their lifetimes could be extended further, and their presence could be detectable in gravity wave experiments of the near future.

We investigate the geometrical and thermodynamical aspects of particle production in pp collisions over a broad center-of-mass energy, ranging from $\sqrt{s}=62.4$ GeV to 13 TeV using PYTHIA8. We study the azimuthal dependence of charged-particle production relative to the leading particle. This includes the study of the Tsallis–Pareto parameters extracted from the charged-particle transverse-momentum spectra in fixed $\Delta\phi$ intervals relative to the leading charged particle. The simultaneous analysis of charged-particle multiplicity and event topology demonstrates that the underlying event (UE) dominated region can be extended beyond the conventional transverse side region across RHIC and LHC energies. To further disentangle effects from soft and hard particle production mechanisms, the study is performed in different transverse spherocity and charged-particle flattenicity classes. We demonstrate that the UE region extends beyond the conventional transverse region, validating an enlarged angular interval of $40^\circ\lesssim|\Delta\phi|\lesssim140^\circ$ from RHIC to LHC energies. Event-shape selections reveal that jetty events consistently exhibit larger $q$ and lower $T_{\rm s}$ than isotropic events. The $\Delta\phi$ profiles of charged-particle multiplicity and transverse spherocity remain universal in shape across collision energies despite the strong increase in overall event activity, whereas the Tsallis parameters retain a residual, leading-particle-driven energy dependence in the near- and away-side regions.

The collective expansion and hydrodynamic evolution in heavy-ion collisions is well-established. However, whether femtometer-scale droplets of QGP are produced in small systems at high energies remains a fundamental open question. Analysis of Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, Xe$-$Xe at $\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV and O$-$O collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.36 TeV using EPOS4 is reported to make predictions and postdictions. The results are compared with ALICE data for Pb$-$Pb and Xe$-$Xe collisions. Charged particle multiplicity (d$N_{\mathrm{ch}}$/d$\eta$), transverse-momentum ($p_{\mathrm{T}}$) spectra for pions ($\pi^{\pm}$), kaons ($K^{\pm}$), and protons ($\text{p}(\overline{\text{p}})$) are studied. The inclusion of hadronic afterburner, UrQMD (Ultra-relativistic Quantum Molecular Dynamics) is found to be necessary to correctly describe baryon yields. $p_{\mathrm{T}}$-fluctuations are also studied via normalized $p_{\mathrm{T}}$ correlator, $\sqrt{\langle \langle \Delta p_{\mathrm{T},i}\Delta p_{\mathrm{T},j} \rangle \rangle}\mathrm{/} \langle \langle p_{\mathrm{T}} \rangle \rangle$. Lastly, anisotropic flow harmonics ($v_{\mathrm{2}} \{2\}$, $v_{\mathrm{3}} \{2\}$) are computed as a function of $p_{\mathrm{T}}$ and centrality. Since EPOS4 has not been extensively studied for flow observables, this study thereby provides a non-trivial assessment of its collective dynamics. The results are compared with experiment wherever data is available. Taken together, this study provides a unified description of soft observables from Pb$-$Pb through Xe$-$Xe down to O$-$O and offer quantitative guidance on how such collisions may inform of the properties of the QGP.

The dihadron fragmentation function (DiFF) of a linearly polarized gluon has not yet been accessed experimentally, leaving an important aspect of spin-dependent gluon hadronization unexplored. We show that, at leading order, the color-singlet decay channel of the $P$-wave bottomonium state $\chi_{b0}$ produces two energetic gluons with correlated linear polarizations. Within collinear factorization, their fragmentation into separate dihadron pairs generates an Artru–Collins-type angular correlation that provides the first direct probe of the linearly polarized gluon DiFF, while the corresponding semi-inclusive decay rate constrains the unpolarized gluon DiFF. A spectator-model benchmark indicates percent-level asymmetries, potentially within reach of existing Belle data. A dedicated Belle~II data set would substantially improve the statistical precision, enabling more stringent constraints on the kinematic dependence of the linearly polarized gluon DiFF.

A large vorticity produced in non-central ultra-relativistic heavy-ion collisions induces an effective chemical potential in both partonic and hadronic matter, thereby influencing the quark-hadron transition and its associated properties. In this work, we investigate the influence of rotation on hadron yields within the framework of Hadron Resonance Gas (HRG) model. Our results show that vorticity significantly modifies hadron yields and their ratios. Most notably, rotation enhances the $p/\pi^+$ ratio while suppressing the $K^+/\pi^+$ ratio, suggesting that these observables may serve as sensitive probes of the rotational properties of the medium created in heavy-ion collisions. To quantify the effect of rotation, the calculated dependence of the $p/\pi^+$ ratio on vorticity is compared with the centrality dependence of the $p/\pi$ ratio measured by the ALICE collaboration in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ = 5.02 TeV. From this comparison, we estimate the maximum vorticity produced at freeze-out for different collision centralities. In case of peripheral collisions, the freeze-out vorticity ($\omega$) is found to reach an upper bound value of approximately 0.088 GeV, whereas for central collisions it is about 0.028 GeV. Furthermore, we investigate the effect of rotation on fluctuations of conserved quantities and their correlations. This study provides a quantitative framework for assessing the role of rotation in the thermodynamics of hadronic matter and its phenomenological consequences for heavy-ion collisions.

We study the charge separation induced by chiral magnetic effect (CME) in $p^{\uparrow}$+Au collisions at $\sqrt{s_{NN}}=200$ GeV event-by-event with an improved string-melting AMPT model. In this model, an impact-parameter-dependent formation-time delay is introduced to reduce the peak Bjorken energy density from $\sim$2 to $\sim$0.3 GeV/fm$^3$ and reproduces the illiptic flow $v_2(p_T)$ measured by PHENIX in $p+$Au simultaneously. The event-by-event CME source, whose quark momentum-exchange fraction scales with $|\mathbf{B}|_{\mathrm{event}}/|\mathbf{B}|_{\mathrm{max}}$ and is capped at the 7% value from Au+Au, transmits the field geometry directly to the observable. We find that the initial correlator shows a clear scheme hierarchy tracking $B^2$. The parton cascade preserves $\sim$80–90% of the signal, while coalescence and ART hadronic rescattering dissipate the bulk, leaving $\sim$10–30% in the final state. The $\gamma_{OS}/\gamma_{SS}$ splitting remains visible. These results support the use of the inter-scheme difference $\Delta\gamma_{\mathrm{IV}}-\Delta\gamma_{\mathrm{II}}$ as an essentially background-free CME observable as we proposed in previous work.

We present, to our knowledge, the first Bayesian extraction of baryon number susceptibilities of QCD matter at finite baryon density from heavy-ion collision data on proton number cumulants. The framework embeds arbitrary equation-of-state susceptibilities $\chi_n^B$ into realistic hydrodynamic particlization hypersurfaces through maximum-entropy freeze-out, maps the resulting (anti)baryon fluctuations onto protons, applies the experimental kinematic acceptance, and accounts for exact baryon number conservation. Applying the framework to measurements of (net-)proton number fluctuations in 0–5% central Au-Au collisions from the RHIC Beam Energy Scan in the collider mode, we extract, at each collision energy, the second-order susceptibility normalized by the hadron resonance gas value, $\chi_{2}^B/\bar{\chi}_{2}^B$, and the higher-order susceptibility ratios $\chi_{3}^B/\chi_{1}^B$ and $\chi_{4}^B/\chi_{2}^B$. We obtain tight constraints on $\chi_{2}^B$, with extracted values in quantitative agreement with lattice QCD based estimates along the chemical freeze-out line for $\mu_B \lesssim 300$~MeV. At larger $\mu_B$, the extracted values indicate an enhancement of baryon number fluctuations relative to the noncritical lattice-based extrapolation and HRG baseline considered here. The third- and fourth-order susceptibilities are only weakly constrained. In particular, we find that the observed nonmonotonic collision-energy dependence of the proton factorial cumulant ratio $\hat{C}_{3}/\hat{C}_{1}$ can be described without irreducible three- or four-baryon correlations. This behavior emerges from the interplay between the energy dependence of $\chi_{2}^B$ and exact baryon number conservation.

We present constraints on the nuclear equation of state (EOS) from microscopic asymmetric matter calculations at zero temperature based on chiral nucleon-nucleon and three-nucleon interactions. The constraints include the saturation point, the isospin dependence of the incompressibility, and the symmetry energy, as well as the crust-core transition density of neutron-star matter. To quantify and propagate correlated uncertainties from noisy many-body calculations to derived observables, we introduce GPDiff, an efficient JAX-based Python package for multivariate Gaussian process (GP) regression with automatic differentiation. After training, GPDiff enables joint predictions of the EOS and derivatives of arbitrary order with respect to the input variables, including mixed partial derivatives. In this initial application, we analyze recent high-order many-body perturbation theory calculations of asymmetric matter up to about twice saturation density and explore nonstationary change-surface kernels, a class of input-dependent kernels, for modeling the EOS. GPDiff is broadly applicable to microscopic nuclear EOS calculations at zero and finite temperature and provides a versatile package for GP-based uncertainty quantification and inference of the nuclear EOS.

We assess the prospects for inclusive heavy-quark-pair electroproduction in electron-proton ($ep$) and electron-nucleus ($e$A) collisions, alongside double-charm-pair ($D^0 \bar{D}^0$ and $D^0D^0$) electroproduction in $ep$ collisions, during the early operational phase of the Electron-Ion Collider (EIC). Based on the anticipated beam energies and luminosities of the EIC, we estimate the total cross sections and differential distributions for photon virtuality $Q^2$, heavy-quark transverse momentum, and rapidity. This analysis evaluates different Bjorken-$x$ ($x_{\rm Bj}$) intervals across a range of $Q^2$ values. Expected event yields are estimated from the projected integrated luminosities of the early science programme, demonstrating the substantial improvement in statistical precision over previous HERA measurements at moderate and large $x_{{\rm Bj}}$. For electron–nucleus collisions, we compute the nuclear modification ratio $R^{e\text{A}}$ within collinear factorisation using nuclear parton distribution functions, and identify the kinematic regimes in which shadowing, anti-shadowing, and EMC-like suppression are accessible with early EIC data. These results are intended to serve as a parton-level baseline to support feasibility studies and to provide a reference for future higher-order theoretical and experimental investigations at the EIC.

Involving the charge radii of \rm Mg isotopes, as calculated using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we have extracted the neutron radii of $^{24-38}$\rm Mg isotopes by studying their reaction cross sections ($\sigma_{R}$) from $^{12}$\rm C at 240 MeV/nucleon within the framework of Glauber model. The calculations use (i) descriptions of nuclei in terms of the Slater determinant involving harmonic oscillator single-particle wave functions (SDHO), and (ii) two-parameter Fermi (2pF) shape of density distribution, with the aim to assess the density dependence of neutron skin in $^{24-38}$\rm Mg isotopes. To understand the asymptotic behavior (spread) of neutron distribution, we propose to introduce the use of core+n ($S_{n}<S_{2n}$) or core+2n ($S_{n}>S_{2n}$) description for stable as well as unstable isotopes; $S_{n}$ ($S_{2n}$) is the one-neutron (two-neutron) separation energy of the considered isotope. The core+n (core+2n) is treated semi-phenomenologically. In this work, the core+n is employed for $^{25-38}$\rm Mg isotopes, and is subjected to reproduce the same neutron radius of the given isotope, as we obtained from $\sigma_{R}$ calculations. To validate the core+n description, we have revisited the reaction cross sections of $^{25-38}$\rm Mg isotopes. The results are found to agree well with the experimental values. Moreover, the core+n neutron distributions clearly demonstrate the one-neutron halo structure of $^{37}$\rm Mg. These findings motivated us to use the core+2n description for the neutron distribution of $^{40}$\rm Mg in predicting its neutron radius, and $\sigma_{R}$ from $^{12}$\rm C at 240 and 1000 MeV/nucleon. The trend of the neutron radius and $\sigma_{R}$ suggests that $^{40}$\rm Mg exhibits two-neutron halo like structure.

Octupole deformation in atomic nuclei is of interest for both nuclear structure and precision tests of fundamental symmetries, but identifying regions of octupole collectivity remains challenging. We analyze low-energy spectra of odd-mass nuclei and uncover a previously unrecognized empirical regularity that serves as a signature of octupole collectivity in neighboring even-even systems. The observed patterns, which can be understood within a core-coupling picture, are consistent with previous theoretical studies and lead to predictions for neutron-rich and proton-deficient nuclei. These findings provide a simple empirical guide for identifying promising candidates for future experiments and microscopic calculations.

The new era of multi-messenger astronomy requires the accurate and self-consistent derivation of the nuclear equation of state at high temperature. In the present work, we focused on the calculation of hot hybrid equations of state, studying the different evolution stages of a proto-neutron star with a quark matter core (proto-hybrid star). For the hadronic matter we used two distinct Skyrme effective interactions, while for quark matter the well-known vector MIT bag model was employed. To model the era of trapped neutrinos in the system we considered the global conservation of lepton fraction which resulted in an equation of state with an extended mixed phase. For periods following the neutrino diffusion phase of a proto-neutron star, the equations of state were modelled using both the Maxwell and the Gibbs construction depending on the assumption for either local or global electric-charge conservation. With the use of the derived hybrid models, we solved the Tolman-Oppenheimer-Volkov equations to describe the corresponding hybrid star configurations. Finally, we investigated how the structure of proto-hybrid stars evolves, using constant rest mass sequences. We found that regardless of whether electric-charge is globally or locally conserved, the earlier stages of a hybrid star's life may play a crucial role on the determination of its maximum possible gravitational mass in later stages.

We present a study of transverse momentum broadening for high-energy partons propagating through the quark-gluon plasma (QGP), extending the Gyulassy-Levai-Vitev (GLV) formalism to include both all-path-length (APL) corrections and improved sub-Regge kinematics. The standard GLV framework relies on the large separation distance and large formation time approximations, which are well justified in large nuclei but may become unreliable in small collision systems, where the relevant length and coherence scales are comparable. Working to first order in the opacity expansion, we derive analytic expressions for the transverse momentum broadening distribution and the corresponding momentum transport coefficient, $\hat{q}$, while systematically relaxing these approximations. The APL correction arises from relaxing the large separation distance approximation, whereas the sub-Regge and combined sub-Regge-APL corrections are obtained using an improved set of Regge kinematics beyond the strict Regge limit. We find that these corrections can substantially modify both the transverse momentum broadening distribution and the momentum transport coefficient, particularly for short path lengths and high exchanged momentum, providing a more complete theoretical description of momentum broadening in the QGP.

In fission induced by low energy neutrons, the mother nucleus spends a significant fraction of the time in the ground state and isomer wells, eventually passing beyond the outer barrier, where the primary fission fragments properties are defined. Despite this, the dynamics of these two early stages have not been investigated using microscopic models. This study examines the evolution of the mother nucleus in both wells separately, using time-dependent density functional theory, which has been previously used to treat the saddle-to-scission stage of fission for $^{235}$U(n,f) reactions. These two early stages of fission are essential blocks in the final theory of the formation and evolution of a compound nucleus. The present study shows that the dynamics in both wells is strongly dissipative, similar to the dynamics from saddle to scission. It also reveals that while the initial mass asymmetry of the system quickly settles to very small fluctuations in the ground state well, in the isomeric well, the mass asymmetry oscillates with a rather large amplitude, in almost harmonic motion. Furthermore, with low probability, neutrons are emitted in both wells.

White dwarfs and neutron stars are unique laboratories for dense nuclear matter physics. We develop a single relativistic mean-field framework that treats both classes of compact star, and the transition between them, on the same footing: the nuclei of white-dwarf matter are solved self-consistently as Wigner-Seitz cells with the full electromagnetic interaction, while the same Lagrangian yields the uniform nuclear matter of the neutron-star interior. Within this unified description we compute light-element white dwarfs seeded by $^4$He, $^{12}$C, and $^{16}$O, following each fixed-$A$ sequence along its neutronization path and connecting it to the neutron-star branch through exact Maxwell junctions, from which the corresponding mass-radius relations are derived. The helium- and carbon-seeded white-dwarf sequences attain maximum masses of ${\sim}1.4\,M_\odot$ and ${\sim}1.0\,M_\odot$, respectively. On the neutron-star branch, the retained light-element envelope changes the predicted radii only at the percent level—by approximately $0.2~$km at $1.4\,M_\odot$, within current observational uncertainties. Providing a consistent zero-temperature equation of state from white-dwarf to neutron-star densities, this unified framework offers a natural starting point for studies of white-dwarf–neutron-star binary mergers, progenitor-star evolution, decihertz gravitational-wave sources, and related multimessenger phenomena.

Quantum computers can generate real-time correlators of field theories. By adapting the generalized eigenvalue problem to these correlators, energy eigenvalues can be extracted directly. The method is tested using both classical simulations and quantum hardware, successfully resolving several low-lying energy levels in agreement with exact diagonalization. Comparison with an alternative spectrum determination based on the Fourier transform of correlators shows that the proposed approach is substantially more efficient.

The bound and resonance states of hypernuclei $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li and $_{\Lambda}^{7}$Be are studied within a three-cluster model. Within this model, hypernuclei $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li and $_{\Lambda }^{7}$Be are considered as three-cluster systems $^{4}$He+$^2n$+$\Lambda$, $^{4}$He+$d$+$\Lambda$, $^{4}$He+$^2p$+$\Lambda$, respectively. Special attention is paid to determining resonance states in the three-cluster continuum of these hypernuclei and to study their nature. One semi-realistic nucleon-nucleon potential is employed to determine the internal structure of the clusters $^{4}$He, $^2n$, $d$ and $^2p$, and their interaction. Three versions of the nucleon-hyperon potential, known as the YNG potential, are employed to determine the interaction of the listed clusters with the lambda hyperon. A set of very narrow and fairly wide resonance states is found in the three-cluster continuum of $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li and $_{\Lambda}^{7}$Be. The narrowest resonance states were detected in $_{\Lambda}^{7}$He and $_{\Lambda}^{7}$Li and their total width does not exceed 10 keV. The dominant decay channels of these resonance states are revealed.

Solving the Tolman–Oppenheimer–Volkoff (TOV) equations, together with the tidal perturbation equations, for large numbers of equation-of-state (EOS) samples is a major computational bottleneck in Bayesian inference of the dense-matter EOS, and this will become increasingly limiting as next-generation observatories deliver far larger and more precise datasets. We develop neural-network surrogates for the forward TOV mapping that predict neutron star mass, radius, and tidal deformability simultaneously and directly from the EOS parameters and central density. We train and compare two architectures: a conventional feedforward network and a residual network, the latter of which, to our knowledge, has not previously been explored for TOV surrogate modeling. Trained on a piecewise polytropic EOS parameter space, both networks reproduce the numerical solutions to high accuracy, with the coefficient of determination exceeding 0.999 for all three observables, while accelerating the evaluation of stellar observables by roughly two orders of magnitude relative to direct numerical integration. We find that both architectures achieve excellent predictive accuracy at the network sizes considered here, with the residual network providing a modest improvement in accuracy over the feedforward network at the expense of slightly longer inference times. The overall performance differences remain small, indicating that a feedforward network already has sufficient capacity for this mapping while residual connections offer only incremental gains. Nevertheless, the residual architecture provides a robust baseline for future extensions to richer EOS parameterizations or higher-dimensional regression tasks. The resulting surrogates are well-suited to large-scale Bayesian EOS inference and population studies, where repeated TOV evaluations would otherwise dominate the computational cost.

The emergence of massless (Nambu-Goldstone) bosons in association with a dynamically global broken symmetry is a long known and widespread phenomenon in physics. However, practically nothing is known about the expressions of Nambu–Goldstone boson character on the internal structure of these bound states. Indeed, their structure is often ignored. In strong interactions, pions and kaons are the (would-be) Nambu-Goldstone bosons and experiments underway or planned at existing or anticipated high-energy, high-luminosity facilities will gather data that it is hoped will enable maps to be drawn of their internal structure. Meanwhile, theory and phenomenology find themselves in something of a quagmire. Herein, we provide a snapshot of the current status, highlighting issues under debate and identifying areas that deserve greater attention so that best use can be made of what is likely to be a huge volume of data delivered in the next decade or so.

Tidal excitations of stellar oscillation modes during binary neutron-star inspirals offer a powerful probe of the composition of dense matter at supranuclear densities. Chemical equilibration plays a crucial, but often neglected, role in stellar perturbation calculations. If the chemical equilibration timescale is comparable to the oscillation timescale, then viscous effects can damp the modes. If the reactions are fast, some modes can completely disappear since their restoring force vanishes. Typically, these calculations, however, assume either instantaneous chemical equilibrium or no equilibration (frozen composition). Motivated by this, we investigate the effects of finite reaction rates on the oscillation spectrum of neutron stars containing hyperonic matter. We calculate the dominant non-leptonic weak interaction rates and incorporate them into the relativistic perturbation equations through a complex, frequency-dependent dynamical sound speed. We show that finite-rate effects naturally manifest as bulk-viscous dissipation, modifying the properties of both the fundamental ($f$) and gravity ($g$) modes. We further examine the impact on the tidal response by matching stellar perturbations to near-zone boundary conditions, demonstrating how viscous dissipation gives rise to a tidal lag. These results provide a consistent framework connecting microscopic reaction rates and the resulting bulk viscosity to the tidal dynamics of compact binaries, and represent a step towards incorporating viscous dissipation into gravitational-wave models of binary neutron-star inspirals.

The critical dynamics of a non-conserved order parameter is generally expected to become overdamped at long distances, even when propagating modes occur at microscopic or intermediate scales. We investigate the critical dynamics of a scalar field theory in thermal equilibrium which, in addition to local friction and noise, also contains a time-dependent second-order kinetic term. We show how to build a supersymmetric field-theory formulation. Using a two-loop expansion about four spatial dimensions, we show that the propagating and strictly overdamped limits share the same static Gaussian and Wilson-Fisher fixed points but realize distinct dynamical scaling regimes. The overdamped limit reproduces Model A. On the surface where local friction and noise vanish, the theory instead supports an interacting propagating fixed point whose dynamic exponent receives corrections at two loops. We demonstrate that coarse-graining does not generate a local dissipative operator on this surface, which therefore remains invariant under the RG flow. Local dissipation is nevertheless relevant at the propagating fixed point: an arbitrarily small equilibrium friction-noise perturbation drives the flow away from propagating scaling. Propagating critical dynamics thus defines a consistent but fine-tuned regime that is unstable to local equilibrium dissipation.

The recent observation by the LHCb Collaboration of a new beauty–strange meson $B_{s0}^*(5700)^0$~\cite{LHCb:2026Bs0star}, under the conditional assignment $J^P=0^+$ provides an important new test of the chiral organization of heavy-light hadrons. More than three decades ago it was proposed that the coexistence of heavy-quark spin symmetry and spontaneously broken chiral symmetry implies that every heavy-light spin multiplet should possess an opposite-parity partner separated by a nearly universal mass gap determined primarily by the dynamics of the light degrees of freedom~\cite{Nowak:1993vc,Bardeen:1993ae}. This chiral doubling scenario was later developed into a quantitative heavy-hadron effective theory and extended to the complete charm and beauty spectra. In particular, the strange beauty sector was predicted to exhibit a parity splitting closely related to that of the strange charm sector, with only small $1/m_Q$ corrections. We briefly review the symmetry origin of chiral doubling, derive the universal parity splitting through the heavy-hadron chiral effective theory, and discuss the new LHCb observation in the context of the original theoretical predictions. Taken together with the established charm spectrum, if the new beauty-strange state is confirmed to have $J^P=0^+$, its mass is consistent with its interpretation as the chiral partner of the ground state $B_s^0$. Finally, we stress that the above confirmation of the spin and parity imposes in the chiral doubling scenario an existence of yet unobserved, very narrow beauty-strange meson with assignment $1^+$ at 5747 $\pm$ 2 MeV. This work is dedicated to the memory of our friend and collaborator Mannque Rho (1936–2026).

This last article of the trilogy focuses on the dynamical equation of the Schrodinger Collective-Intrinsic Model (SCIM). First, we motivate and discuss the need to regularize the adiabatic and excited dynamical ingredients entering the collective-intrinsic Hamiltonian, namely the collective potential, the collective inertia tensor, and the collective dissipative tensor. In particular, we introduce a Savitzky-Golay low-pass filter to remove numerical fluctuations incompatible with the second-order truncation in the Symmetric Ordered Product of Operators used to derive the SCIM equations. The diagonal and off-diagonal properties of the three dynamical ingredients are then analyzed along the asymmetric fission path in 240Pu. This study highlights the dominant role of neutron and proton excitation channels, especially in the second well and scission regions, whereas proton-neutron couplings remain essentially negligible. Furthermore, in the adiabatic limit of the SCIM, we perform a comparison with the GOA which reveals very close predictions. Second, we discuss the construction of the initial wave packet and the numerical resolution of the collective-intrinsic Schrodinger equation. Using a continuity equation, we derive the probability fluxes associated with the different components of the wave function, which provide direct access to the contribution of the different excitations to the final observables for the fission problem. The excited states are found to account for more than 80% of the total flux at scission. Finally, we evaluate, the neutron and proton fragment distributions as well as the energy balance, including the total kinetic and excitation energies. The obtained results are found to be consistent with available experimental data and demonstrate the importance of explicitly including intrinsic excitations in the description of fission dynamics.

This second article of the trilogy presents the implementation of a third protocol, referred to as Continuous Deflation, designed to construct continuous and regular excited paths within the Schrodinger Collective-Intrinsic Model (SCIM), with applications to nuclear fission. We show that the use of standard 2QP excitations, even when combined with particle-number projection, prevents a consistent application of the SCIM framework. Motivated by the central role of pair breaking in low-energy fission, we explore how to construct intrinsic excited states that incorporate this mechanism while satisfying the continuity and regularity state requirements of the SCIM. To this end, we first analyze the Deflation procedure alone, which constructs excited states through orthogonality constraints. We then extend this construction along a deformation path by introducing an additional continuity constraint, thereby defining the Continuous Deflation method, which generates continuous paths based on excited states. In particular, we construct ten such continuous paths built on top of the adiabatic and asymmetric fission path of 240Pu. The resulting excited states are systematically analyzed in terms of their microscopic structure. We then investigate several fragment properties near scission, including neutron and proton chemical potentials, neutron necking as well as fragment particle-number distributions, and compare them with their adiabatic counterparts.

This article is the first in a trilogy aimed at presenting the first practical implementation of the Schrodinger Collective-Intrinsic Model (SCIM) applied to nuclear fission. Within the SCIM framework, the many-body wave function explicitly couples collective motion to intrinsic excitations, necessitating sets of Hartree-Fock-Bogoliubov (HFB) configurations that remain continuous and regular across a broad deformation range, from the ground state to scission and beyond. This paper focuses on constructing adiabatic HFB paths suitable for subsequent SCIM dynamical calculations. Standard constrained adiabatic paths often suffer from discontinuities and irregularities, which prevent the direct application of the formalism. To address these challenges, we implement two recently proposed overlap-based protocols, the Link and Drop methods, and combine them into a new numerical procedure.A comparison with the exact Gaussian Overlap Approximation confirms that the resulting adiabatic kernels exhibit properties consistent with the assumptions of the SCIM formalism. The regularized path is then analyzed in the scission region. We identify characteristic structures in the proton and neutron chemical potentials, a pronounced neutron enrichment of the neck at scission, and fragment particle-number distributions displaying a strong odd-even staggering in the proton sector. Finally, using a microscopic fragment-separation procedure formulated in the canonical basis, we extract static scission properties including fragment deformation energies and both Coulomb and nuclear contributions to the fragment interaction energy. These results establish the adiabatic foundations required for future SCIM calculations with intrinsic excitations and provide a microscopic characterization of the scission region in 240Pu.

$q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}(\omega^2,\mathbf{k}_\perp^2,k^2_3)$ and ${\pi}^0$ meson spectral function $\rho_{\pi^0}(\omega^2,\mathbf{k}_\perp^2,k^2_3)$ under external magnetic field $eB$ and finite meson momentum $\mathbf{k}_\perp^2,k^2_3$ are studied in the framework of a two-flavor Nambu-Jona-Lasinio (NJL) model. The $q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}$ is closely related to $\pi^0$ spectral function $\rho_{\pi^0}$. We consider three situations, chiral broken phase ($T=\mu=0$), chiral restoration phase ($T>T_{pc},\ \mu=0$) and chiral restoration phase ($T=0,\ \mu>\mu_{pc}$). For $T=\mu=0$ and $T>T_{pc},\ \mu=0$ cases, ${\pi}^0$ meson spectral function $\rho_{\pi^0}$ shows a delta peak, several Breit-Wigner peaks and several non-Breit-Wigner peaks. The delta peak indicates the bound state of $\pi^0$ meson, and the Breit-Wigner peak means the resonant state of $\pi^0$ meson. For $T=0,\ \mu>\mu_{pc}$ case, Pauli blocking effect plays a role, which changes the inner structure of these Breit-Wigner peaks and non-Breit-Wigner peaks. Such multiple peak structure is caused by the external magnetic field. The $q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}$ shows a jump from $0$ to $\pi$ when $\pi^0$ meson is in bound state. When $\pi^0$ meson is in resonant state, $\Phi_{\pi^0}$ has the value $\pi/2$ and changes continuously. In large $\omega$ region, at the starting and end points of wide peaks of spectral function, $\Phi_{\pi^0}$ jumps abruptly (from $\pi$ to finite value or from finite value to $0$), and such jumps are caused by the external magnetic field. Finite momentum $\mathbf{k}_\perp^2$ or $k^2_3$ modifies the spectral function $\rho_{\pi^0}$ and scattering phase shift $\Phi_{\pi^0}$, which demonstrates the anisotropy in the system induced by external magnetic field.

Quantum computing provides a powerful framework for simulating real-time dynamics in open quantum systems, offering key advantages for modeling heavy-quarkonium transport in high-energy nuclear collisions. In this work, we perform quantum simulations of the isotropic next-to-leading-order Lindblad equation for bottomonium in the quark-gluon plasma using a reduced spherical coordinate representation. We discretize operators and wavefunctions, map the physical state onto qubits, and execute time evolution via parameterized quantum gate operations. By extracting the $\Upsilon(1S)$ survival probability, we quantitatively isolate the color-octet contribution, demonstrating that its overall impact is small in the final production of the bottomonium ground state $\Upsilon(1S)$ in the hot QCD medium at temperatures accessible at the Large Hadron Collider. Additionally, we have further optimized the quantum simulation algorithm for the Lindblad equation. The improved algorithm requires only a single ancillary qubit to realize the Lindblad evolution, thereby minimizing the circuit significantly.

Non-perturbative scattering $T$-matrix is a core input for the evaluation of transport phenomena in a strongly-coupled medium. Existing in-medium $T$-matrix calculations are typically formulated in the two-particle center-of-mass frame, where the scattering equation can be reduced to a lower-dimensional problem. However, a medium explicitly breaks Lorentz invariance and defines a preferred reference frame, entailing that physical observables be constructed from scattering amplitudes evaluated in the medium rest (laboratory) frame. In this work, by exploiting the rotational symmetry about the scattering-pair-momentum axis, we develop a practical framework for solving the in-medium two-body $T$-matrix directly in the laboratory frame while retaining the full dependence on the total pair-momentum and scattering geometry. We demonstrate that the resulting amplitudes differ significantly from conventional center-of-mass-frame results and, when applied to heavy-light quark scattering in the quark-gluon plasma (QGP), lead to 25-40% corrections to heavy-quark drag coefficients at low momenta, thereby removing a significant source of theoretical uncertainty in extracting the QGP transport properties with heavy-quark probes.

We examine the contact three-nucleon force at N4LO expressed as a density dependent potential. In Ref. [1], the necessary couplings (13, including two that appear in the leading three-nucleon force), were extracted from nd scattering observables. The contact strengths obtained through the three-nucleon continuum, without fits to the triton, seem incompatible with the energy of nuclear and neutron matter. We take the opportunity to revisit the role of the cD, cE couplings of the leading three-nucleon force in nuclear matter and nuclei. We close with a discussion about recent fittings of three-nucleon scattering observables using a spectroscopic basis for the subleading contact three-nucleon force.