Field Theoretic Models of Deep Inelastic Lepton-Nucleon Scattering

Author

Stephen Blaha

Date of Award

1971

Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Thesis Advisor

Mirza Beg

Related Theses

View more theses from the Mirza Beg Laboratory

Keywords

structure functions, ladder diagrams, scaling behavior, virtual Compton amplitude, Mellin transform, meson models

Abstract

We investigate the asymptotic behavior of the inelastic electron-nucleon structure functions within the framework of ladder models of the virtual Compton amplitude in the limit |q²|→ ∞ with w=2q·p/|q²| large and fixed. (q is the electron four-momentum transfer and p the target nucleon momentum.) The leading logarithmic behavior of the ladder diagrams is obtained by Mellin transform techniques. Our results are: 1. The structure functions do not scale (i.e. become non-trivial functions of ω) in our neutral vector meson ladder model and our pseusoscalar meson model because of the appearance of factors of ln|q²|. We also find the neutrino-nucleon structure functions in analogous ladder models and they exhibit the same non-scaling behavior. In all cases νW₂, W₁ and νW₃ (in the case of neutrino scattering) diverge as |q²|→ ∞. 2. In a truss bridge diagram model similar to that of Bjorken and Wu νW₂ scales while W₁ does not. 3. To fourth order in the meson-nucleon coupling constant, g, ladder diagrams are the only Compton scattering diagrams contributing to the leading logarithm for each order in g in the neutral vector meson theory and pseudoscalar meson theory. Ladder diagrams with nucleon loops contribute to the leading logarithm in the neutral vector meson theory but do not contribute to the leading logarithm in the pseudoscalar meson theory. 4. The leading part of the Bethe-Salpeter for the Compton amplitude in the neutral vector meson ladder model is closely related to Jackiw's Bethe-Salpeter equation for the electromagnetic vertex. (MT_μ^μ which is the trace of the spin-averaged virtual Compton amplitude is equal to Jackiw's off-mass-shell solution for the vertex where M is the nucleon mass.)

Comments

A thesis presented to the faculty of The Rockefeller University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

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Recommended Citation

Blaha, Stephen, "Field Theoretic Models of Deep Inelastic Lepton-Nucleon Scattering" (1971). Student Theses and Dissertations. 548.
https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/548