Roger Dashen

Baryon-pion couplings from large-Nc QCD

Abstract We derive a set of consistency conditions for the pion-baryon coupling constants in the large- N c limit of QCD. The consitency conditions have a unique solution which are precisely the values for the pion-baryon coupling constants in the Skyrme model. We also prove that non-relativistic SU(2 N f spin-flavor symmetry (where N f is the number of light flavors) is a symmetry of the baryon-pion couplings in the large- N c limit of QCD. The symmetry breaking corrections to the pion-baryon couplings vanish to firts order in 1 N c . Consistency conditions for the other couplings, such as the magnetic moments are also derived.

Spin flavor structure of large N(c) baryons

The spin-flavor structure of large [ital N][sub [ital c]] baryons is described in the 1/[ital N][sub [ital c]] expansion of QCD using quark operators. The complete set of quark operator identities is obtained, and used to derive an operator reduction rule which simplifies the 1/[ital N][sub [ital c]] expansion. The operator reduction rule is applied to the axial vector currents, masses, magnetic moments, and hyperon nonleptonic decay amplitudes in the SU(3) limit, to first order in SU(3) breaking, and without assuming SU(3) symmetry. The connection between the Skyrme and quark operator representations is discussed. An explicit formula is given for the quark model operators in terms of the Skyrme model operators to all orders in 1/[ital N][sub [ital c]] for the two flavor case.

1Nc corrections to the baryon axial currents in QCD

Abstract We prove that the 1 N c corrections to the baryon axial current matrix elements are proportional to their lowest order values. This implies that the first correction to axial current coupling constant ratios vanishes, and that the SU (2 N f ) spin-flavor symmetry relations are only violated at second order in 1 N c .

A new theory for scattering from a surface

A new formal approach to the problem of scattering from a rough surface is derived. The first ingredient of this approach is a formal statement of the composite model. This consists of an approximate expression for the change in the scattering amplitude corresponding to a perturbation of a reference surface. It is good to first order in the perturbation, and exact with respect to the reference surface. The derivation of this result makes use of the general asymptotic form of the scattering solution. The expression is simplified using the boundary conditions. When the formal composite model is applied to an unfinitesimal translation, a new representation of the scattering amplitude is obtained. Unlike the traditional representation, this expression depends on two full solutions to the wave equation, and it manifestly exhibits reciprocity. This article is the first in a series. Application of the results will be considered in future papers.

Approximate representations of the scattering amplitude

This is the second in a series of articles about the theory of scattering from a rough surface. A symmetric representation of the scattering amplitude and a formal statement of the composite model, both derived in the previous article, are used to approximate the scattering amplitude in terms of the known results for a reference surface. When the reference surface is a plane, the small slope approximation follows, while the traditional composite model is obtained if the curvature of the reference surface is neglected. The medium is assumed to be homogeneous, and the calculation is performed for scalar waves obeying Dirichlet or Neumann boundary conditions, electromagnetic waves obeying perfect conductor boundary conditions and the interface between two media for both types of waves. Finally, the requirement that the formal composite model must reproduce the traditional composite model in the appropriate limit is used to obtain a new approximation to the scattering amplitude. This is done for the Dirichlet...

Intensity fluctuation for waves behind a phase screen : a new asymptotic scheme

A new asymptotic scheme is presented through the computation of 〈I2〉and 〈I1I2〉 for waves behind a random phase screen with a power-law correlation. It illustrates the basic idea for an effective new expansion technique that yields a considerably faster convergent asymptotic series for intensity moments in the strong-fluctuation regime. This scheme can also be generalized to the computation of various statistical moments of intensity and log-intensity in continuous media with a power-law spectrum.

Applications of the new scattering formalism: The Dirichlet boundary condition

This is the third in a series of articles concerning the theory of scattering from a rough surface. Consideration of the scattering problem for a scalar wave obeying Dirichlet boundary conditions enables one to investigate the formalism developed in the previous work. The advantages of this new representation of the scattering amplitude is discussed. This result is supplemented with an improved integral equation for the desired solutions on the surface. This new equation not only allows one to reproduce the approximations for the scattering amplitude obtained previously, but it can also be used to extend those results to higher orders. This is illustrated with a derivation of the second‐Born approximation. The correction to the scattering amplitude due to a distribution of point scatters is also obtained. To the order under consideration, this phenomenon is shown to be equivalent to a perturbation of the surface. A similar result is found when the index of refraction is allowed to vary near the scattering...

The eigenvalues of the Laplacian on a sphere with boundary conditions specified on a segment of a great circle

We prove that the eigenvalues of the Laplacian on a sphere with a Dirichlet boundary condition specified on a segment of a great circle lie between an integer and a half-integer and for a Neumann boundary condition they lie between a half integer and an integer. These eigenvalues correspond to the eigenvalues of the angular part of the Laplacian with boundary conditions specified on a plane angular sector, which are relevant in the calculation of scattering amplitude. These eigenvalues can also be used to determine the behavior of the fields near the tip of a plane angular sector as a function of the distance to the tip. The first few eigenvalues for both Dirichlet and Neumann boundary conditions are calculated. The same eigenvalues are also calculated using the Wentzel–Kramers–Brillouin (WKB) method. There is excellent agreement between the exact and the WKB eigenvalues.

Intensity moments for waves in random media: three-order standard asymptotic calculation

The standard asymptotic approach is applied to a computation of the strong-intensity fluctuation for waves in random media. Under the framework of the path integral and cluster expansion, the first few moments of intensity are formulated to third order and further evaluated numerically for waves that travel through systems of multiple phase screens with a power-law spectrum. Finally, a global formula for all intensity moments 〈IN〉 is presented, where complete expressions for all terms up to third order are given.

Asymptotic scheme for waves in random media

A new asymptotic scheme for intensity statistics of waves in random media with a pure power-law correlation is presented. In the strong scattering regime it provides effective and accurate asymptotic expansion series for all intensity moments. The new first-order result, which is considerably more accurate than that from the existing asymptotic theory, may also serve as a starting point for useful statistical models.