Branching ratios, lepton forward-backward asymmetries, and lepton polarization asymmetries for th... more Branching ratios, lepton forward-backward asymmetries, and lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of the Λb 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.
Lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays ... more Lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of Λ b baryons are calculated using single-component analytic (SCA) and multicomponent numerical (MCN) form factors. We show that these polarization asymmetries are insensitive to the transition form factors and, thus, the effects of QCD in the nonperturbative regime. Therefore, these observables can provide somewhat model independent ways of extracting the Wilson coefficients.
Hadronic form factors for the rare weak transitions Λ b → Λ ( * ) are calculated using a nonrelat... more Hadronic form factors for the rare weak transitions Λ b → 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 and forward-backward asymmetries (FBAs) are calculated for the dileptonic decays Λ b → 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 branching ratio to that of the ground state in the µ channel. → N ( * ) were calculated using single component wave functions obtained from a variational diagonalization of a quark model Hamiltonian. In that calculation, quark operators were reduced to their nonrelativistic Pauli form. The decay rates obtained using the form factors extracted in that calculation were in reasonable agreement with experimental results for the semileptonic decays Λ b → Λ c ℓν ℓ and Λ c → Λℓν ℓ .
Bulletin of the American Physical Society, Jan 1, 2009
The exclusive rare decays $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ gamma $ and $\ Lambda_b\ rightar... more The exclusive rare decays $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ gamma $ and $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ ell^{+}\ ell^{-} $ are treated in the framework of a constituent quark model. By use of single component wavefunctions, the hadronic form ...
The curvature potential arising from confining a particle initially in threedimensional space ont... more The curvature potential arising from confining a particle initially in threedimensional 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.
Physica E: Low-dimensional Systems and …, Jan 1, 2005
The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived... more The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram-Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameter and bend location of the tube. r 2004 Published by Elsevier B.V.
Curvature-induced bound-state eigenvalues and eigenfunctions for a particle constrained to move o... more Curvature-induced bound-state 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 that 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.
It is shown that the time-dependent Hartree–Fock equations have an unexpected constraint implicit... more It is shown that the time-dependent Hartree–Fock equations have an unexpected constraint implicitly inherent in them. For the case of two electrons interacting via the Hamiltonian H(1,2)=H0(1)+H0(2)+V(1,2), and described by the time-dependent Schrödinger equation (where the over-dot stands for time derivative) it will be shown that the time-dependent orbitals defined by the ansatzΨ(1,2)=φ1(1)φ2(2)±φ1(2)φ2(1), not only must satisfy the two coupled orbital equations with the two time-dependent mean-field potentials, but also implicitly must satisfy their own one-particle equations Unlike stationary-state methods, this represents a constraint which is not consistent with a time-dependent ab initio theory, but may be appropriate for a perturbative theory.
Branching ratios, lepton forward-backward asymmetries, and lepton polarization asymmetries for th... more Branching ratios, lepton forward-backward asymmetries, and lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of the Λb 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.
Lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays ... more Lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of Λ b baryons are calculated using single-component analytic (SCA) and multicomponent numerical (MCN) form factors. We show that these polarization asymmetries are insensitive to the transition form factors and, thus, the effects of QCD in the nonperturbative regime. Therefore, these observables can provide somewhat model independent ways of extracting the Wilson coefficients.
Hadronic form factors for the rare weak transitions Λ b → Λ ( * ) are calculated using a nonrelat... more Hadronic form factors for the rare weak transitions Λ b → 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 and forward-backward asymmetries (FBAs) are calculated for the dileptonic decays Λ b → 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 branching ratio to that of the ground state in the µ channel. → N ( * ) were calculated using single component wave functions obtained from a variational diagonalization of a quark model Hamiltonian. In that calculation, quark operators were reduced to their nonrelativistic Pauli form. The decay rates obtained using the form factors extracted in that calculation were in reasonable agreement with experimental results for the semileptonic decays Λ b → Λ c ℓν ℓ and Λ c → Λℓν ℓ .
Bulletin of the American Physical Society, Jan 1, 2009
The exclusive rare decays $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ gamma $ and $\ Lambda_b\ rightar... more The exclusive rare decays $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ gamma $ and $\ Lambda_b\ rightarrow\ Lambda^{(*)}\ ell^{+}\ ell^{-} $ are treated in the framework of a constituent quark model. By use of single component wavefunctions, the hadronic form ...
The curvature potential arising from confining a particle initially in threedimensional space ont... more The curvature potential arising from confining a particle initially in threedimensional 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.
Physica E: Low-dimensional Systems and …, Jan 1, 2005
The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived... more The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram-Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameter and bend location of the tube. r 2004 Published by Elsevier B.V.
Curvature-induced bound-state eigenvalues and eigenfunctions for a particle constrained to move o... more Curvature-induced bound-state 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 that 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.
It is shown that the time-dependent Hartree–Fock equations have an unexpected constraint implicit... more It is shown that the time-dependent Hartree–Fock equations have an unexpected constraint implicitly inherent in them. For the case of two electrons interacting via the Hamiltonian H(1,2)=H0(1)+H0(2)+V(1,2), and described by the time-dependent Schrödinger equation (where the over-dot stands for time derivative) it will be shown that the time-dependent orbitals defined by the ansatzΨ(1,2)=φ1(1)φ2(2)±φ1(2)φ2(1), not only must satisfy the two coupled orbital equations with the two time-dependent mean-field potentials, but also implicitly must satisfy their own one-particle equations Unlike stationary-state methods, this represents a constraint which is not consistent with a time-dependent ab initio theory, but may be appropriate for a perturbative theory.
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Papers by Lonnie J Mott