The real and imaginary scattering phase shifts (SPS) and potentials for $\ell=0,2,4$ partial waves have been obtained by developing a novel algorithm$^{\ref{Fig1}}$ to derive inverse potentials using a phenomenological approach. The phase equation, which is a Riccati-type non-linear differential equation, is coupled with the Variational Monte Carlo method. Comparisons between the resulting SPS for various $\ell$ channels and experimental data are made using mean absolute percentage error (MAPE) as a cost function. Model parameters are fine-tuned through an appropriate optimization technique to minimize MAPE. The results for $\ell=0^+$, $2^+$, and $4^+$ partial waves are generated to align with experimental SPS with mean absolute error (MAE) calculated with respect to experimental data is 3.19, 8.74, 13.06 respectively corresponding to real part and 0.76, 0.76, 0.59 corresponding to imaginary parts of scattering phase shifts.

In the SU3-IBM the oblate shape is described by the \textrm{SU(3)} third-order Casimir operator in the large-$N$ limit. However for finite $N$, this interaction can produce a boson number odd-even effect. In this Letter, the unique odd-even effect is really found in the nuclei $^{196-204}$Hg. This finding implies that realistic low-lying excitations are sensitive to certain boson number $N$. The IBM hypothesis is verified for the first time since the advent of the interacting boson model. This also proves the accuracy and validity of the SU3-IBM directly. The SU(3) symmetry and the higher-order interactions are both indispensable for understanding the nuclear deformations.

We present the first theoretical study of the polarization of lepton pairs produced in $\sqrts = 5.02 $ TeV Pb+Pb collisions at the LHC, using next-to-leading order (NLO) dilepton emission rates. These calculations employ a multi-stage framework to simulate the evolution of relativistic heavy-ion collisions, and to explore the sensitivity of polarization to early times. It is found that the intermediate invariant-mass dileptons are indeed probes of the thermal equilibration process, and go beyond the reach of hadronic observables. We compute the polarization anisotropy coefficient obtained with LO dilepton rates, and show that the LO and NLO results differ radically, both in trend and in magnitude, at low and intermediate lepton pair invariant masses.

We apply the method of moments to the relativistic Boltzmann-Vlasov equation and derive the equations of motion for the irreducible moments of arbitrary tensor-rank of the invariant single-particle distribution function. We study two cases, in the first of which the moments are taken to be irreducible with respect to the little group associated with the time-like fluid four-velocity, while in the second case they are assumed to be also irreducible with respect to a space-like four-vector orthogonal to the fluid four-velocity, which breaks the spatial isotropy to a rotational symmetry in the plane transverse to this vector. A systematic truncation and closure of the general moment equations leads, in the first case, to a theory of relativistic higher-order dissipative resistive magnetohydrodynamics. In the second case, we obtain a novel theory of dissipative resistive anisotropic magnetohydrodynamics, where the momentum anisotropy is in principle independent from that introduced by the external magnetic field.

We propose a new strategy to obtain a high-purity sample of gluon-initiated jets at the LHC. Our approach, inspired by the Lund jet plane picture, is to perform a dijet selection where the two jets are collinear to each other and their momentum fraction share is highly asymmetric, and to measure the primary Lund plane density of emissions of the subleading jet. The subleading jet in this topology is practically equivalent to a secondary Lund jet plane. We demonstrate by means of fixed-order calculations that such a simple setup yields gluon jet fractions of around 90% for the subleading jet for both quark- and gluon-initiated jets. This observation is confirmed using hadron-level Monte Carlo generated events. We also show that the extracted gluon purities are highly resilient to the overall colour structure of the event, to the flavour of the hard-scattering process, and to the parton distribution functions. This strategy is well-suited for constraining the radiation pattern of gluon-initiated jets using a set of fiducial cuts that can readily be tested at the LHC, without relying on taggers or statistical demixing.

Deeply inelastic scattering (DIS) is an essential process for exploring the structure of visible matter and testing the standard model. At the same time, the theoretical interpretation of DIS measurements depends on QCD factorization theorems whose validity deteriorates at the lower values of $Q^2$ and $W^2$ typical of neutrino DIS in accelerator-based oscillation searches. For this reason, progress in understanding the origin and limits of QCD factorization is invaluable to the accuracy and precision of predictions for these upcoming neutrino experiments. In these short proceedings, we introduce a novel approach based on the quantum entropy associated with continuous distributions in QCD, using it to characterize the limits of factorization theorems relevant for the description of neutrino DIS. This work suggests an additional avenue for dissecting factorization-breaking dynamics through the quantum entropy, which could also play a role in quantum simulations of related systems.

Evidences of vortical effects have been recently found by experiments in heavy ion collisions, instigating new insights into the phase diagram of quantum chromodynamics. Considering the effect of rotations, lattice QCD data shows that the temperatures for deconfinement and chiral symmetry restoration should increase with real angular velocity, and the dominant effects are related to gluonic degrees of freedom. These findings could be essential for quark models in rotating systems that lack gluonic interactions, which predicts the decreasing of the chiral temperature transition with the angular velocity. To address this issue properly, in this work we apply the two-flavor Nambu--Jona-Lasinio model to explore the phase diagram in a rotating rigid cylinder with constant angular velocity in the mean field approximation. To circumvent the absence of gluons, we propose the application of an effective coupling dependent of the angular velocity, fitted to match the pseudocritical temperature of chiral phase transition in the model through lattice QCD data. Our results indicate that the running coupling induces the enhancement of the chiral condensate as a function of angular velocity, strengthening the breaking of chiral symmetry, an effect previously dubbed as chiral vortical catalysis. For the chiral susceptibility we observe stronger fluctuations around the transition temperature when we consider the running coupling. The phase diagram is affected by these findings shifting the critical end point (CEP) to higher temperatures and chemical potentials.

We develop an analytic method of inverting the Tolman-Oppenheimer-Volkov (TOV) relations to high accuracy. This method is developed from the strong correlations that are shown to exist between the neutron star mass-radius curve and the equation of state (EOS) or pressure-energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Root-mean-square fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5\% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary mass-radius curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Building on our recent study [https://doi.org/10.1021/acs.jpclett.3c02052, J. Phys. Chem. Lett. 14, 8780 (2023)], we explore the generalization of the ground-state Kohn-Sham (KS) formalism of density-functional theory (DFT) to the (singlet) excited states of the asymmetric Hubbard dimer at half-filling. While we found that the KS-DFT framework can be straightforwardly generalized to the highest-lying doubly-excited state, the treatment of the first excited state presents significant challenges. Specifically, using a density-fixed adiabatic connection, we show that the density of the first excited state lacks non-interacting $v$-representability. However, by employing an analytic continuation of the adiabatic path, we demonstrate that the density of the first excited state can be generated by a complex-valued external potential in the non-interacting case. More practically, by performing state-specific KS calculations with exact and approximate correlation functionals -- each state possessing a distinct correlation functional -- we observe that spurious stationary solutions of the KS equations may arise due to the approximate nature of the functional.

Using a symmetry-preserving treatment of a vector $\times$ vector contact interaction (SCI) at nonzero temperature, we compute the screening masses of flavour-SU(3) ground-state $J^P=0^\pm$, $1^\pm$ mesons, and $J^P=1/2^\pm$, $3/2^\pm$ baryons. We find that all correlation channels allowed at $T=0$ persist when the temperature increases, even above the QCD phase transition. The results for mesons qualitatively agree with those obtained from the contemporary lattice-regularised quantum chromodynamics (lQCD) simulations. One of the most remarkable features is that each parity-partner-pair degenerates when $T>T_c$, with $T_c$ being the critical temperature. For each pair, the screening mass of the negative parity meson increases monotonously with temperature. In contrast, the screening mass of the meson with positive parity is almost invariant on the domain $T\lesssim T_c/2$; when $T$ gets close to $T_c$, it decreases but soon increases again and finally degenerates with its parity partner, which signals the restoration of chiral symmetry. We also find that the $T$-dependent behaviours of baryon screening masses are quite similar to those of the mesons. For baryons, the dynamical, nonpointlike diquark correlations play a crucial role in the screening mass evolution. We further calculate the evolution of the fraction of each kind of diquark within baryons respective to temperature. We observe that, at high temperatures, only $J=0$ scalar and pseudoscalar diquark correlations can survive within $J^P=1/2^\pm$ baryons.

Pseudoscalar and axial neutral and charged pion-constituent quark coupling constants are investigated with nondegenerate quark masses in different kinematical points, off shell and on shell pions and constituent quarks. For the neutral pion, mixing effects are introduced by means of the pion mixing to states $P_0$ and $P_8$, that give rise to the $\pi^0-\eta-\eta'$ meson mixing, and mixing of quark currents via corresponding mixing interactions. The relative behavior of charged and neutral pion coupling constants to quarks may be nearly the same - in the framework of the constituent quark model - as the pion-nucleon coupling constants if mixings are introduced. A very small pion coupling to strange quark current is also obtained. The dependence of the positive and negative pion-constituent quark coupling constant on the non-degeneracy of quark masses, for emission and absorption processes, is identified.

We update a previous N$^3$LL$^\prime$+${\cal O}(\alpha_s^3)$ determination of the strong coupling from a global fit to thrust data by including newly available perturbative ingredients, upgrading the renormalization scales to include a fully canonical scaling region, and implementing the log resummation in a way which ensures the integrated cross section is unaffected by the the leading $1/Q$ hadronization power corrections. Detailed discussions are provided concerning the stability of the results under variations of the fit range and the importance of summing up higher-order logarithmic terms for convergence and stability. We show that high-precision results can be achieved even when carrying out a more conservative fit by restricting the dataset to a region which is more clearly dominated by dijet events. This leads to $\alpha_s(m_Z) = 0.1136 \pm 0.0012$ with $\chi^2/{\rm dof}=0.86$, fully compatible with earlier results using a larger fit range. We also demonstrate that a number of additional effects associated to power corrections have a small impact on this fit result, including modifications to the renormalon substraction scheme for dijet power corrections and the inclusion of three-jet power correction models. The fit is also shown to provide very good agreement with data outside the fit range.