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. (MTμμ 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.)
","abstract_html":"<p>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 |q<sup>2</sup>|→ ∞ with w=2q·p/|q<sup>2</sup>| 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|q<sup>2</sup>|. We also find the neutrino-nucleon structure functions in analogous ladder models and they exhibit the same non-scaling behavior. In all cases νW<sub>2</sub>, W<sub>1</sub> and νW<sub>3</sub> (in the case of neutrino scattering) diverge as |q<sup>2</sup>|→ ∞. 2. In a truss bridge diagram model similar to that of Bjorken and Wu νW<sub>2</sub> scales while W<sub>1</sub> 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<sub>μ</sub><sup>μ</sup> 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.)</p>","abstract_has_math":false,"creators":["Blaha, Stephen"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Mirza Beg"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1971,"date_issued":"1971-01-01T08:00:00Z","date_published":"1971-01-01T08:00:00Z","updated_at":"2026-07-24T04:11:51Z","subjects":["structure functions","ladder diagrams","scaling behavior","virtual Compton amplitude","Mellin transform","meson models","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/548","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mirza Beg"]},{"key":"dc:creator","label":"Author","values":["Blaha, Stephen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["structure functions","ladder diagrams","scaling behavior","virtual Compton amplitude","Mellin transform","meson models","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/548"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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. (MTμμ 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.)
"]},{"key":"dc:title","label":"Title","values":["Field Theoretic Models of Deep Inelastic Lepton-Nucleon Scattering"]}]}],"canonical_facts":{"dc:contributor":["Mirza Beg"],"dc:creator":["Blaha, Stephen"],"dc:description.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. (MTμμ 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.)
"],"dc:identifier":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/548"],"dc:subject":["structure functions","ladder diagrams","scaling behavior","virtual Compton amplitude","Mellin transform","meson models","Physical Sciences and Mathematics"],"dc:title":["Field Theoretic Models of Deep Inelastic Lepton-Nucleon Scattering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:11:51Z"}