Chi-Keung Chow

Excited bound state logarithmic perturbation theory without nodes

The logarithmic perturbation theory is modified slightly in order to deal with excited states. Instead of considering a real wavefunction describing the physical stationary state, the authors consider a complex wavefunction at the same energy, by mixing in the ghost state. For excited bound states, the former has nodes, while the latter is guaranteed not to have any nodes, and can be represented simply as exp(-G), to which the logarithmic perturbation method can be applied in a straightforward manner. The physical entities (the energy corrections) are independent of the amount of mixing of the ghost state. The connection to the Green function method is also shown. The freedom to mix in the ghost state allows the authors to justify an ad hoc approach whereby the simple version of the logarithmic perturbation theory is applied to excited bound states. The formalism is illustrated with simple examples.

Quenched and partially quenched chiral perturbation theory for vector and tensor mesons

Abstract Quenched and partially quenched chiral perturbation theory for vector mesons is developed and is used to extract the chiral loop correction to the ϱ meson mass. Connections to fully quenched and totally unquenched chiral perturbation theory results are discussed. It is also shown that (partially) quenched perturbation theory for tensor mesons can be formulated analogously, and the chiral corrections for tensor meson masses are directly proportional to their counterparts in the vector meson sector. Utilizing this observation and non-relativistic quark model, we point out that the mass difference (m a 2 − 3 2 m ϱ ) is “quenching-insensitive” in the large-Nc limit. This quantity may be used for normalization of mass scale in lattice QCD calculations.

Radiative decays of excited {Lambda}{sub {ital Q}} baryons in the bound state picture

It is shown that, in the bound state picture, the {Lambda}{sub {ital c}}(2593){r_arrow}{Lambda}{sub {ital c}}{gamma} and {Lambda}{sub {ital c}}(2625){r_arrow}{Lambda}{sub {ital c}}{gamma} decays are severely suppressed. On the other hand, for their bottom counterparts, which are predicted to have masses of 5900 and 5926 MeV, respectively, they may have significant radiative branching ratios. The {Lambda}{sub {ital b}}(5926){r_arrow}{Lambda}{sub {ital b}}{gamma} mode possibly dominates over the strong decay mode, while the {Lambda}{sub {ital b}}(5900) resonance lies below the strong decay threshold and can only decay radiatively. The isospin allowed {Lambda}{sub {ital Q}}{sup {asterisk}{asterisk}}{r_arrow}{Sigma}{sub {ital Q}}{gamma} mode is expected to be small. {copyright} {ital 1996 The American Physical Society.}

Chiral perturbation theory for tensor mesons

Interactions of a2,K*2,f2 and f2 tensor-mesons with low-energy π,K,η,η pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated as heavy non-relativistic matter fields. Using 1/Nc counting, we derive relations among unknown couplings of the chiral Lagrangian. Chiral perturbation theory is applied to the tensor-meson mass matrix. At one-loop there are large corrections to the individual tensor meson masses, but the singlet-octet mixing angle remains almost unchanged. We argue that all heavy mesons of spin ≥ 1 share common feature of chiral dynamics.

Aspects of quenched chiral perturbation theory for matter fields

Three topics about the application of quenched chiral perturbation theory to matter fields are studied. It is proved that the hairpin axial current couplings in quenched chiral perturbation theories do not contribute to the quenched chiral singularities for one chiral loop renormalization of matter field properties. The modification of mass corrections in the chiral limit due to nonzero mass splittings are studied, and selection rules for hadron decays in quenched QCD are obtained.

`A new efficient method for calculating perturbative energies using functions which are not square integrable': Regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanical results.

Perturbative Scattering Phase Shifts in One-Dimension: Closed-form results

Abstract A simple closed form expression is obtained for the scattering phase shift perturbatively to any given order in effective half-line one-dimensional problems. The result is a hierarchical scheme, expressible in quadratures, requiring only knowledge of the zeroth order solution and the perturbation potential.

Charmed strange pentaquarks in the large Nc limit.

The properties of pentaquarks containing a heavy anti-quark and strange quarks are studied in the bound state picture. In the flavor SU(3) limit, there are many pentaquark states with the same binding energy. When the SU(3) symmetry breaking effects are included, however, three states become particularly stable due to a ``Gell-Mann--Okubo mechanism. They are the

Sum rules for radiative and strong decays of heavy mesons

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Self-consistent 1/{ital N}{sub {ital c}} expansion in the presence of electroweak interactions

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