Diagonalization of the neutralino mass matrix and boson–neutralino interaction

We analyze a connection between the neutralino mass sign, parity and structure of the neutralino–boson interaction. Correct calculation of spin-dependent and spin-independent contributions to neutralino–nuclear scattering should consider this connection. A convenient diagonalization procedure, based on the exponential parametrization of unitary matrix, is suggested. PACS  11.30.Pb; 14.80.Ly; 12.60.Jv     

Analysis of the chargino and neutralino mass parameters at one-loop level

In the minimal supersymmetric standard model (MSSM) the masses of the neutralinos and charginos depend on the gaugino and higgsino mass parameters M, M' and . If supersymmetry is realized, the extraction of these parameters from future high energy experiments will be crucial to test the underlying theory. We present a consistent method for properly defining on-shell parameters at one-loop level and determining these from precision measurements. In addition, we show how a GUT relation for the parameters M and M' can be tested at one-loop level. The numerical analysis is based on a complete one-loop calculation. The derived analytic formulae are given in the appendix.Received: 7 April 2003, Published online: 23 June 2003     

Exact solution of the four-row matrix corresponding to the variational equations for ultrasecondary quantized problems

The exact solution is presented of a four-row matrix for which only an approximate solution has previously been known.     

Exact solution for the gravitational field of a charged,magnetized, spinning mass

A family of solutions of the Einstein-Maxwell field equations is presented, corresponding to the exterior of stationaryaxisymmetric sources with charge, mass, angular momentum, and magnetic dipole moment. The Riemann tensor vanishes asymptotically for each member of the family; some solutions are asymptotically flat and some have NUT-like behavior asymptotically. For the asymptotically flat solutions, the gyromagnetic ratio may vary from zero to one. The corresponding value for the Kerr-Newman solution is one. A method for generating infinite chains of families of solutions of the Einstein-Maxwell equations is described.     

Exact solution of the Faddeev-Volkov model

The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group Uq(sl₂). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c→+∞ the model describes quantum fluctuations of discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In the strongly-coupled limit c→1 the model turns into a discrete version of the D=2 Zamolodchikov's “fishing-net” model.     

Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution

Using the spinor approach, we calculate exactly the complete spectrum of the transfer matrix for the finite-width, planar Ising model with adjustable boundary conditions. Specifically, in order to control the boundary conditions, we consider an Ising model wrapped around the cylinder, and introduce along the axis a seam of defect bonds of variable strength. Depending on the boundary conditions used, the mass gap is found to vanish algebraically or exponentially with the size of the system. These results are compared with recent numerical simulations, and with random-walk and capillary-wave arguments.     

Exact solution to the curve crossing problems of two linear diabatic potentials by transfer matrix method

In the present work we have reported a simple exact analytical solution to the curve crossing problem of two linear diabatic potentials by transfer matrix method. Our problem assumes the crossing of two linear diabatic potentials which are coupled to each other by an arbitrary coupling (in contrast to linear potentials in the vicinity of crossing points) and for numerical calculation purposes this arbitrary coupling is taken as Gaussian coupling which is further expressed as a collection of Dirac delta functions. Further we calculated the transition probability from one diabatic potential to another by the use of this method.     

Exact matrix representation of the RVB wavefunction

It is shown that the RVB wave function can be expressed as the Pfaffian of an antisymmetric matrix whose size is equal to the number of lattice points. The matrix representation helps in proper counting of all the paired states.     

Exact path-integral solution of the ring-shaped potential

The general new-time transformation method is used in obtaining the exact path-integral solution to the ring-shaped potential.     

Exact solution of the quadratic interaction Hamiltonian

We construct the exact solution for the quadratic coupling of a scalar field to an external source. With increasing dimension of space-time the perturbation becomes more and more singular, allowing us to verify the various predictions which Glimm has extracted from the perturbation theory of Møller operators.     

Impact of large mixing angle MSW solution on neutrino mass matrix

We have discussed the quark-lepton mass matrices with the U(1) and O(3) flavor symmetry in SU(5), which lead to the large mixing angle MSW solution of solar neutrinos.     

Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.     

Exact solution of the simplified hubbard model

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves nontrivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n=1), (ii) a preferred magnetic state atn=1 and largeU is a total spin singlet, (iii)U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t ²/U)-behavior at largeU. A phase diagram of the model is discussed.     

Exact solution of the generalized Kemmer oscillator

In the present work, the generalized Kemmer oscillator was introduced in one dimension. It is shown that the exact solutions of generalized Kemmer oscillator with some appropriate choices of the interactions f(x) have been obtained by using the Nikiforov–Uvarov(NU) method. Moreover, several interesting cases are discussed.