The associated production of a Higgs boson with a \(Z\) boson in the collisions of electron and positron beams at the Future Circular Collider (FCC-ee) have been studied. Here, the \(Z\) boson decays into dileptons, while the Higgs boson decays to all possible channels, mostly to the \(b\bar {b}\). The collisions provide a clean and powerful channel to probe the (\(HZZ\)) coupling at future lepton colliders. Following the event generation, the analysis is performed using the recoil mass method, which allows for the model-independent reconstruction of the Higgs boson depending on the kinematics of the final-state leptons. This method enables precise identification of the Higgs signal peak independent of its decay mode and significantly reduces systematic uncertainties. The recoil mass distributions from the signal process (\(e^+e^- \to HZ\), \(Z \to l^+l^-\)) and the main backgrounds (\(ZZ\), \(WW\), \(t\bar {t}\), and other Standard Model processes) have been analyzed using a dedicated analysis code. Monte Carlo simulations corresponding to an integrated luminosity of 5 ab\(^{-1}\) have been used for the analysis, assuming the high performance of the IDEA detector concept. The results are presented for center-of-mass energies of \(\sqrt {s} = 240\) GeV and \(\sqrt {s} = 365\) GeV to compare the sensitivities and highlight the potential of future \(e^+e^-\) colliders in probing the \(HZZ\) interaction with high precision. Abstract Published by the Jagiellonian University 2026 authors

We study the generalized Lorenz dynamical system describing convective phenomena in magnetized fluid. We employ computer algebra to effectively support the Darboux method of solving differential equations. Darboux polynomials and various types of first integrals are determined. Abstract Published by the Jagiellonian University 2025 authors

Matrix elements of the density matrix of small quantum systems have recently become experimentally accessible within the cold atoms simulations. Numerical estimation of these quantities is known to be computationally challenging. Tracing out a part of the studied system and hence accessing the reduced density matrices offers similar difficulties, but it is more interesting, as the reduced density matrix is the basis of entanglement entropy measures. In this work, we present a method of estimating the individual elements of the reduced density matrices that uses autoregressive neural networks and the path integral quantization approach. We use a hierarchy of neural networks capable of estimating conditional probabilities of consecutive spins to evaluate elements of reduced density matrices directly. Using the Ising chain as an example, we calculate the continuum limit of the ground state’s von Neumann and Rényi bipartite entanglement entropies of an interval built of up to 5 spins. We demonstrate that our architecture is able to estimate all the needed matrix elements with just a single training for a fixed temperature discretization and lattice volume. Our method can be applied to other types of spin chains, possibly with defects, as well as to estimating entanglement entropies of thermal states at non-zero temperature. Hence, it may offer an attractive computational approach as a counterpart to the experimental effort. Abstract Published by the Jagiellonian University 2025 authors

The AMPT model is used to study elliptic flow \(v_{2}\) in Au\(+\)Au collisions at \(\sqrt {s_{NN}}=200\) GeV, focusing on partonic and hadronic transport processes. By varying the partonic elastic scattering cross section \(\sigma _{p}\) and scaling hadronic cross sections \(\sigma _{H}\), we find that \(v_{2}\) is dominated by partonic interactions with larger \(\sigma _{p}\) accelerating momentum-space anisotropy conversion and suppressing residual spatial anisotropy. Hadronic rescattering minimally impacts \(v_{2}\), only emerging at reduced \(\sigma _{p}\) and higher centrality. The results highlight the critical role of partonic transport in collective flow and the limited influence of hadronic dynamics on final observables. Abstract Published by the Jagiellonian University 2025 authors

Two recent measurements of the \(^{12}\mathrm {C}(p,\gamma )^{13}\mathrm {N}\) reaction on natural carbon were performed by detecting \(\beta ^+\) decay of the \(^{13}\mathrm {N}\) residue. It is argued that the measurements at energies above the \(^{13}\mathrm {C}(p,n)^{13}\mathrm {N}\) reaction threshold of 3.24 MeV proton kinetic energy can be interpreted as a consequence of 1.06% admixture of the \(^{13}\mathrm {C}\) isotope in natural carbon, as the cross section for \(^{13}\mathrm {N}\) production raised by 3 orders of magnitude with respect to the measurements of \(^{12}\mathrm {C}(p,\gamma )^{13}\mathrm {N}\) at lower energies. Abstract Published by the Jagiellonian University 2025 authors

This paper discusses multi-particle production in QCD and in gravity at ultrarelativistic energies, their double-copy relations, and strong parallels in emergent shockwave dynamics. Dispersive techniques are applied to derive the BFKL equation for multi-gluon production in Regge asymptotics. Identical methods apply in gravity and are captured by a gravitational Lipatov equation. The building blocks in both cases are Lipatov vertices and reggeized propagators satisfying double-copy relations; in gravity, Weinberg’s soft theorem is recovered as a limit of the Lipatov framework. BFKL evolution in QCD generates wee parton states of maximal occupancy characterized by an emergent semi-hard saturation scale. Renormalization group equations in the Color Glass Condensate (CGC) EFT describe wee parton correlations and their rapidity evolution. A shockwave picture of deeply inelastic scattering and hadron–hadron collisions follows, with multi-particle production described by Cutkosky’s rules in strong time-dependent fields. Gluon radiation in the CGC EFT has a double copy in gravitational shockwave collisions, with a similar correspondence applicable between gluon and graviton shockwave propagators. Possible extensions of this semi-classical double copy are outlined for computing multi-particle production in gravitational shockwave collisions, self-force and tidal contributions, and classical and quantum noise in the focusing of geodesics.AbstractPublished by the Jagiellonian University2025authors

The possible anomalous New Physics contributions to the electric and magnetic dipole moments of the \(\tau \) lepton have brought renewed interest in development of new charge-parity violating signatures in the \(\tau \)-pair production at Belle II energies, and also at higher energies of the LHC and the FCC. In this paper, we discuss the effects of anomalous contributions to the cross section and spin correlations in the \(\gamma \gamma \to \tau ^-\tau ^+\) production processes, with \(\tau \) decays included. Such processes have been observed in the \(pp\) and PbPb collisions at CERN LHC experiments. Due to the complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular for event reweighting with studied New Physics phenomena. For the \(\gamma \gamma \) processes, extensions of the Standard Model amplitudes are implemented in the <span class="sf">TauSpinner</span> program. This is mainly with the electric and magnetic dipole moments in mind, however the algorithm can easily be extended to other New Physics interactions, provided they can be encapsulated into the similar form-factors in the Standard Model structure of matrix elements. Basic formulas and algorithm principles are presented, and numerical examples are provided for illustration. Information on how to use the program is given in Appendix of the paper.AbstractPublished by the Jagiellonian University2025authors

In this paper, we introduced two definitions of \(N\)-tuple compound synchronization (NCS) and \(N\)-tuple compound combination synchronization (NCCS) in (\(2N+2\)) and (\(3N+2\)) different chaotic models, respectively. The analytical formulas for the control functions are derived from two established theorems in order to perform these types of synchronization. These new types of synchronization are considered a generalization of various types disccussed in the literature. Numerous applications in engineering and physics may benefit from these new types of synchronization, <span class="it">e.g.</span> , image encryption and electronic circuits. Using the active control technique for the choice \(N=5\), we study two examples of 5CS and 5CCS in 12 and 17 different chaotic models. The analytical forms of the control functions are used and good agreement is found. The Runge–Kutta method of order four is used in our numerical simulations. Other examples can be similarly studied. We designed an electronic circuit for the proposed \(N\)-tuple compound synchronization in 12 different chaotic models. Using <span class="sf">MATLAB/Simulink</span>, both numerical and simulation results show good agreement. For other drive models, similar circuit implementations can be created.AbstractPublished by the Jagiellonian University2025authors

Quantization of the kinetic energy of a nucleus with deformation in curvilinear coordinates in the presence of octupole vibrations of its surface is performed. The obtained Hamiltonian differs from the previously known expression for quadrupole vibrations only in the coefficients before the differentiation operators \(\partial /\partial \gamma \) and \(\partial /\partial \eta \). This is due to the difference in the components of the moment of inertia tensor of the nucleus for quadrupole and octupole modes. An exact expression for the full Hamiltonian of an even–even nucleus is determined, taking into account both quadrupole and octupole deformations, including seven dynamic variables. Some fields of application of the proposed Hamiltonian are discussed.AbstractPublished by the Jagiellonian University2025authors

By analogy with the Ginzburg–Landau theory of multi-band superconductors with inner (interband) Josephson couplings, we formulate the three-band Glashow–Weinberg–Salam model with weak Josephson couplings between strongly asymmetrical condensates of scalar (Higgs) fields. Unlike the usual single-band model, we found three Higgs bosons corresponding to the three generations of particles. Moreover, the heaviest of these bosons corresponds to the already discovered \(H\)-boson and decays into fermions of only the third generation through the Yukawa interaction. The other two decay into fermions of the first and second generations, but they are difficult to observe due to very poor production conditions. We found two sterile ultra-light Leggett bosons, the Bose condensates of which form the dark halos of galaxies and their clusters (<span class="it">i.e.</span> so-called Dark Matter). The masses of the Leggett bosons are determined by the coefficient of the interband coupling and can be arbitrarily small (\(\sim 10^{-20}\) eV) due to non-perturbativeness of the interband coupling. Since propagation of the Leggett bosons is not accompanied by a current, these bosons are not absorbed by gauge fields, unlike the common-mode Goldstone bosons. Three coupled condensates of the scalar fields are related to the existence of three generations of leptons, where each generation interacts with the corresponding condensate getting mass. The interflavor mixing between the generations of active neutrinos and sterile right-handed neutrinos in the three-band system causes the existence of mass states of neutrino without interaction with the Higgs condensates. Abstract Published by the Jagiellonian University 2025 authors