abstract

This paper addresses the singular 1-soliton solution of the K\((m,n)\) equation that is being considered with generalized evolution. The ansatz method will be used to extract the singular 1-soliton solution of this equation. A couple of constraint conditions will fall out in order for the singular soliton solutions to exist. Subsequently, the special cases of this equation will be studied. They are the KdV and the mKdV equations where the extended (\(G'/G\))-expansion method will be employed to extract a few nonlinear wave solutions.

abstract

In our previous study, we have investigated the behaviours of spinor-type instantons in two-dimensional conformally invariant pure spinor Thirring model in phase space. In this paper, we study the role of the coupling constant in the evolution of the four-dimensional spinor-type instantons in phase space via the Heisenberg ansatz. For this purpose, we consider the Gursey model is a four-dimensional conformally invariant pure spinor model with nonlinear self-coupled spinor term. The model proposed in 1956 as a possible basis for a unitary description of elementary particles (Heisenberg–Bohr dream). This study will also lead us to investigate the dependence of the behaviours of spinor-type instantons in phase space on quantum fractional spinor number as well as dimensions.

abstract

We present an overall empirical formula that, after specification of its free parameters, describes precisely the mass spectrum of charged leptons and is suggested to reproduce correctly also the mass spectra of neutrinos, and up and down quarks (together, twelve masses with twelve specified free parameters are presented). Imposing a priori some constraints on three parameters, we predict three of lepton and quark masses, especially the taon mass as \(m_\tau = 1776.80\) MeV. We also present a more theoretical argumentation in favor of our mass formula. In Appendix, an option of composite quarks is briefly outlined, where elementary color-triplet quark-like fermions are bound with a color-triplet isoscalar scalar boson (\({\bf 3}^*\!\times {\bf 3}^* \!\rightarrow {\bf 3}\) color coupling). This option plays here the role of a theoretical hint at imposing a constraint a priori on a free parameter in our mass formula for quarks. The possibility of leptons composed from the same preons as are quarks is considered in brief (\({\bf 3}^*\!\times {\bf 3} \rightarrow {\bf 1}\) color coupling).

abstract

In this article, the three-point QCD sum rules approach is used to investigate the rare \(h_{b}(1p)\rightarrow B_{s} \nu \overline {\nu }\) decay. The form factors relevant to this decay are calculated, considering the gluon condensate corrections to the correlation function. The total decay width of this decay is also evaluated. The predictions can be confirmed by the experimental data in future.

abstract

On the basis of extended simulations, we provide some results concerning the spectrum of Massive SU(2) Yang–Mills on the lattice. We study the “time” correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin \(I=0,1\) and internal spin \(J=0,1\) channels. No correlation is found in the \(I=1\), \(J=0\) channel. In the \(I=1\), \(J=1\) channel and far from the critical mass value \(m_{\rm c}\), the energy gap roughly follows the bare value \(m\) (vector mesons). In approaching the critical value \(m_{\rm c}\) at \(\beta \) fixed, there is a bifurcation of the energy gap: one branch follows the value \(m\), while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at \(\beta \to \infty \) implied by the low energy gap and the screening (or confining) mechanisms across the \(m=m_{\rm c}\) associated to the larger gap. The \(I=0\), \(J=0,1\) gaps are of the same order of magnitude, typically larger than the \(I=1\), \(J=1\) gap (for \(m\gg m_{\rm c}\)). For \(m\sim m_{\rm c}\), both \(I=0\) gaps have a dramatic drop with minima near the value \(m\). This behavior might correspond to the formation of \(I=0\) bound states both in the \(J=0\) and \(J=1\) channels.

abstract

Quantum electrodynamics in three dimensions in the bispinor formulation is considered. It is shown that the Dyson–Schwinger equations for fermion and boson propagators may be self-consistently solved in the infrared domain if on uses Salam’s vertex function. The parameters defining the behavior of the propagators are found numerically for different values of coupling constant and gauge parameter. For weak coupling, the approximated analytical solutions are obtained. The renormalized gauge boson propagator (transverse part) is shown in the infrared domain to be practically gauge independent.

abstract

The hadron production in heavy ion collision is treated in the framework of thermodynamic vision. Thermodynamic system formed during central collision of Pb–Pb at high energies is considered, through which binary collision is assumed among the valence quarks. The partition function of the system is calculated; accordingly the free available energy, the entropy and the chemical potential are calculated. The concept of string fragmentation and defragmentation is used to form the newly produced particles. The average multiplicity of the newly produced particles are calculated and compared with the recent experimental results.

abstract

The one-dimensional attractive Hubbard model (\(U\ll 0\)) is discussed assuming periodic boundary conditions and the half-filling case. The considered chains have \(N\) nodes, the same number of electrons, where \(N-1\) of them have the same spin projection. The discussed translational and unitary symmetries provide the exact diagonalization of the Hamiltonian for even \(N\lt 7\) via various applications of the unitary group.

abstract

In this empirical paper, we design a dynamic Kalman filtering approach to investigate time-varying relationship between spot and futures equity markets. In addition to static bounds test from statistics, we revisit the econophysics discipline, and set up a dynamic Kalman filtering process that provides an iterative process for parameter estimation. The methodology is practically tested with a growing futures market in Turkey in the crisis period. Results of empirical evidence show that the prices of futures contracts can be predicted by spot prices indicating that the markets have not got information efficiency yet. The methodology based on econophysics discipline in the paper can be applied in other financial markets and macroeconomic indicators to detect time varying dynamic relationship between economic and financial variables.