Calculation of [pi]NN and [pi]NN* resonance shifts, using the Dashen-Frautschi method

Citation

Josephson, Nora Sigrun (1967) Calculation of [pi]NN and [pi]NN* resonance shifts, using the Dashen-Frautschi method. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VKK6-0Y76. https://resolver.caltech.edu/CaltechETD:etd-09252002-121457

Abstract

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In this thesis the Dashen-Frautschi method is applied to find shifts from SU(2) symmetry of [pi]NN and [pi]NN* coupling constants. Three new features of this type of calculation are discovered. First, we observe that the same A matrix used to connect s channel and u channel residue shifts also relates u channel contributions such as those due to [gamma]N exchange to analogous processes in the s channel. Secondly, under the assumption that all photon masses are the same (for fixed [delta]I), we note that for linear D functions the A matrix has one eigenvalue exactly equal to one (for each [delta]I), but the corresponding component of the driving term vanishes. This result depends essentially only on Clebsch-Gordan and crossing coefficients. The third discovery is that when viewed in a space of larger dimension, eigenvalues near one and "no enhancement" are easy to understand. We also note that when including infrared corrections, residues are not in general proportional to products of coupling constants.

Since the driving terms are approximately orthogonal to the eigenvectors with eigenvalues near one, there is no simple dominant pattern, and thus our numerical results are sensitive to details which are poorly known. We do believe that our calculation gives correct order of magnitude estimates; the observable parts of the [delta]R/R[subscript o]'s are found to be less than one percent. The experimental data are presently unclear but at least do not decisively indicate larger residue shifts than this.

Thesis Files