Hadronic form factors for the rare weak transitions Λb→ Λ(*)are calculated using a nonrelativistic quark model. The form factors are extracted in two ways. An analytic extraction using single-component wave functions (SCA) with the quark current being reduced to its nonrelativistic Pauli form is employed in the first method. In the second method, the form factors are extracted numerically using the full quark model wave function (MCN) with the full relativistic form of the quark current. Although there are differences between the two sets of form factors, both sets satisfy the relationships expected from the heavy quark effective theory (HQET). Differential decay rates, branching ratios (BRs) and forward–backward asymmetries (FBAs) are calculated for the dileptonic decays Λb→ Λ(*)ℓ+ℓ-, for transitions to both ground state and excited daughter baryons. Inclusion of the long distance contributions from charmonium resonances significantly enhances the decay rates. In the MCN model the Λ(1600) mode is the dominant mode in the μ channel when charmonium resonances are considered; the Λ(1520) mode is also found to have a comparable BR to that of the ground state in the μ channel.

Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states a torus with minor radius a and major radius R can support is obtained. A condition for mapping constrained particle wave functions on the torus into free particle wave functions is established. Pacs number(s): 03.65Ge, 68.65.-k 1. Introduction.

The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint q → 0 limit, with q the degree of freedom normal to the surface. In this work the hard constraint is relaxed, and eigenvalues and wave functions are numerically determined for a particle confined to a thin layer in the neighborhood of a toroidal surface. The hard constraint and finite layer (or soft constraint) quantities are comparable, but both differ markedly from those of the corresponding two dimensional system, indicating that the curvature potential continues to influence the dynamics when the particle is confined to a finite layer. This effect is potentially of consequence to the modelling of curved nanostructures.

Branching ratios, lepton forward-backward asymmetries, and lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of the Λ b baryon to the ground state and a number of excited state Λ baryons are calculated using form factors extracted using wave functions from a constituent quark model. The SM branching ratios for the transition to the ground state calculated using these quark model form factors are consistent with the recent measurement reported by the LHCb collaboration. It is shown that the lepton polarization asymmetries are largely insensitive to the transition form factors and, therefore, to the effects of QCD in the nonperturbative regime. These observables can therefore provide somewhat model independent ways of extracting various combinations of the Wilson coefficients.