abstract

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

This paper conducts bifurcation analysis of the extended (3+1)-dimensional nonlinear Kudryashov’s equation (EKE), classifies traveling wave solutions, and investigates the chaotic behaviors of the equations under specific perturbations. Firstly, the traveling wave transformation is introduced to reduce the EKE to a dynamical system, and then Gaussian solitons are obtained using the generalized trial equation method. In the following step, the existence of periodic and soliton solutions is confirmed through qualitative analysis provided by bifurcation theory and phase diagrams. To verify the conclusions of the qualitative analysis, the complete discrimination system for the polynomial method (CDSPM) is employed for classification, thus enabling the traveling wave solutions. Finally, sinusoidal and Gaussian perturbations are introduced, and the corresponding Lyapunov exponents are used to verify the existence of chaotic behaviors. This paper presents the first application of the CDSPM method to the EKE, yielding several novel results including Gaussian soliton solutions, prior estimates for periodic and soliton solutions. Additionally, traveling wave solutions in the form of hyper-elliptic functions and inverse trigonometric functions are also initially given. Finally, the chaotic behavior of the EKE under perturbation terms is presented.

abstract

In this study, the B3Y-Fetal \(NN\) interaction, originating from the lowest order constrained variational approach (LOCV), is applied to investigate cluster radioactivity in energetically favoured trans-lead nuclei from \(^{221}\mathrm {Fr}\) to \(^{242}\mathrm {Cm}\) within the preformed cluster model, using the Wentzel–Kramers–Brillouin (WKB) theory. Five density-dependent parametrizations are considered to ascertain the most suitable one for cluster radioactivity. The statistical cluster preformation probability is employed and compared with the well-known empirical mass-dependent preformation factor. The predictive power of the BDB3Y1 and BDB3Y0 with the statistical probability is found to give the most accurate description of decay half-lives. These findings underscore the applicability of the B3Y-Fetal interaction in cluster radioactive decays and the reliability of statistical preformation probability in exploring similar decays within the uncharted region of the nuclear landscape. Furthermore, our results demonstrate that DDB3Y1 can aptly address the peculiarity and deviations known for \(^{14}\)C clusters, which is a strongly bound nucleus with \(N/Z = 1.33\). The extension of this study to the prediction of energetically favoured but unobserved cluster radioactive decays holds prospects for future experimental endeavours.