Supersymmetry and the Hartmann Potential of Theoretical Chemistry

The ring-shaped Hartmann potential $V = \eta \sigma^{2} \epsilon_{0} \left( \frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right)$ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed. We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number $L$ but different values of $\eta \sigma^{2}$ and quantum number $N$. This is in contrast to the first formulation, which relates states with identical values of the quantum number $N$ and $\eta \sigma^{2}$ but different values of the quantum number $L$.Comment: 24 pages; uses LaTex; to be published at the Theoretica Chimica Acta; hard copy available from the author upon request (use address: [email protected]

A Supersymmetric SpL×UY(1)Sp_{L} \times U_{Y}(1) Model

A supersymmetric $Sp_{L}(6) \times U_{Y}(1)$ model (SUSY $Sp(6)$) is proposed as an extension of the standard electroweak model. The model is applied in a phenomenological study of $B^{0}_{d} \bar{B}^{0}_{d}$ mixing. It is found that the supersymmetric (SUSY) partner $\tilde{z}^{\prime}$ of the extra $Z^{\prime}$ can significantly cancel the other contributions to bring the mixing parameter $x_{d}$ within the experimentally allowed range $0.57 \stackrel{<}{\sim} x_{d} \stackrel{<}{\sim} 0.77$ for a top mass of $158 \stackrel{<}{\sim} m_{t} \stackrel{<}{\sim} 194$ Gev. Other interesting and possibly novel features of flavor changing neutral currents (FCNC) in SUSY theories with horizontal gauge symmetries are pointed out.Comment: to be published at the Il Nuovo Cimento A; uses FEYNMAN.tex; hard copy available from G. G. Blado ([email protected]) by regular mail upon e-mail request

Studies in the Sp(6) times U(1) extension of the electroweak model

The Sp(6) $\times$ U(1) extension of the electroweak model was proposed to address the generation problem of particle physics. Contrary to traditional approaches in building models to tackle the generation problem, this model has the unique feature of unifying horizontal (or inter-generational) and electroweak interactions without the introduction of additional fermions. Since its proposal in 1984 (12), numerous phenomenological studies have been made (7), (29). In this thesis, further studies of the Sp(6) $\times$ U(1) model (Sp(6) model) are made. A phenomenological study of the tree-level contributions to BB mixing due to the extra Z\sp\prime of the Sp(6) model shows that the standard model contribution can be enhanced. A softly broken (minimal) supersymmetric Sp(6) model is proposed by writing down a workable lagrangian. Using this proposed model, a further calculation is made on its contribution to BB mixing. It is shows that flavor changing neutral currents in this supersymmetric theory can be further suppressed by considering the contributions of the Z\sp\prime-inos