We solve the Dirac radial equation for a nucleon in a scalar Woods-Saxon potential well of depth $V_0$ and radius $r_0$. A sequence of values for the depth and radius are considered. For shallow potentials with $-1000 MeVlesssim V_0 < 0$ the wave fun
ctions for the positive-energy states $Psi _+(r)$ are dominated by their nucleon component $g(r)$. But for deeper potentials with $V_0 lesssim -1500 MeV $ the $Psi_+(r)$s begin to have dominant anti-nucleon component $f(r)$. In particular, a special intruder state enters with wave function $Psi_{1/2}(r)$ and energy $E_{1/2}$. We have considered several $r_0$ values between 2 and 8 fm. For $V_0 lesssim -2000 MeV$ and the above $r_0$ values, $Psi _{1/2}$ is the only bound positive-energy state and has its $g(r)$ closely equal to $-f(r)$, both having a narrow wave-packet shape centered around $r_0$. The $E_{1/2}$ of this state is practically independent of $V_0$ for the above $V_0$ range and obeys closely the relation $E_{1/2}=frac{hbar c}{r_0}$.
We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $lambda^2$, from $lambda^2$ to $lambda^8$. It is shown that, at the present level of accuracy, only the first three param
eters are needed to fit all available data on flavor physics.
We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. The
y are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.
Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, rea
ctor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow large electron-neutrino mixing of atmospheric neutrinos. Next generation long baseline experiments will constrain these possibilities.
The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approxim
ation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.
We show that the current bounds on the leptoquark couplings imply that if leptoquarks are produced in e p collisions, a significant fraction of them could form a leptoquark-quark bound state. The decay of the bound state has a distinct event shape wi
th rapidity gap. A possible application of this observation in the leptoquark search at HERA is discussed.
We examine the processes $e^+ e^-longrightarrow W^+ W^-$ and $Z^0 Z^0$ in the context of the $SP(6)_Lotimes U(1)_Y$ model. We find that there are significant deviations in the total cross sections $sigma (s)$ from the standard model results due to th
e presence of additional gauge bosons $Z^prime$ and $W^prime$ in the model. These deviations could be detected at LEP.
