{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/25733"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/25733","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An equation for meson states in the quark model and its application to a meson bootstrap","abstract":"\"A differential equation for meson states is derived from the Bethe-Salpeter equation under the conditions of the quark model. The equation is shown to imply mass relations of the form K* 2 - P2 = K2 2 - 1£ • The equation is used to attempt bootstrap calculations of the vector and pseudo-scalar meson parameters in the quark model. A bootstrap is found for the SU 3 singlet states but shown not to be possible for either the octet states or the entire QQ §ystem. The potential is the Fourier transform of the sum of one meson exchange Feynman graphs, with a hard core radius ro introdu~ed as an adjustable parameter. With the choice ro::;: ·58 F, MQuark\"\"\"\" 5.45 BeV, 0(= 2MQ fV/Sv= - .24, the self-consistent coupling constants gv2 ' Sp 2 imply in and out \"\"unmixed\"\" singlet masses that are equal and correct. With the 2 2 same Sv ' Sp , the hard core radius and are altered to produce 0-, 1- states at the 1£,13 masses. In addition to 1£, 13 and K, the s -wave states 11( 523 ), 11' (985), m('T85), cp( 1018), K* (896) are found, as well as excited states including the following: B(1018), Al (1230), A2(1401). Assuming the correct A2(13l0), the nonet structure K* (1393), f(1323), f'(1476) is found.\"","abstract_html":""A differential equation for meson states is derived from the Bethe-Salpeter equation under the conditions of the quark model. The equation is shown to imply mass relations of the form K* 2 - P2 = K2 2 - 1£ • The equation is used to attempt bootstrap calculations of the vector and pseudo-scalar meson parameters in the quark model. A bootstrap is found for the SU 3 singlet states but shown not to be possible for either the octet states or the entire QQ §ystem. The potential is the Fourier transform of the sum of one meson exchange Feynman graphs, with a hard core radius ro introdu~ed as an adjustable parameter. With the choice ro::;: ·58 F, MQuark"""" 5.45 BeV, 0(= 2MQ fV/Sv= - .24, the self-consistent coupling constants gv2 ' Sp 2 imply in and out ""unmixed"" singlet masses that are equal and correct. With the 2 2 same Sv ' Sp , the hard core radius and are altered to produce 0-, 1- states at the 1£,13 masses. In addition to 1£, 13 and K, the s -wave states 11( 523 ), 11' (985), m('T85), cp( 1018), K* (896) are found, as well as excited states including the following: B(1018), Al (1230), A2(1401). Assuming the correct A2(13l0), the nonet structure K* (1393), f(1323), f'(1476) is found."","abstract_has_math":false,"creators":["King, Lawrence Gray"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Wyld, H.W."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-07-08T18:23:28Z","date_published":"2011-07-08T18:23:28Z","updated_at":"2026-07-22T22:25:26Z","subjects":["meson states","quark model","meson bootstrap","Bethe-Salpeter equation"],"languages":["en"],"rights":["1968 Lawrence Gray King"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6082767"],"render_values":[{"text":"6082767","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/25733","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Wyld, H.W."]},{"key":"dc:creator","label":"Author","values":["King, Lawrence Gray"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-07-08T18:23:28Z","10000-01-01","1968"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["meson states","quark model","meson bootstrap","Bethe-Salpeter equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1968 Lawrence Gray King"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6082767","http://hdl.handle.net/2142/25733"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"A differential equation for meson states is derived from the Bethe-Salpeter equation under the conditions of the quark model. The equation is shown to imply mass relations of the form K* 2 - P2 = K2 2 - 1£ • The equation is used to attempt bootstrap calculations of the vector and pseudo-scalar meson parameters in the quark model. A bootstrap is found for the SU 3 singlet states but shown not to be possible for either the octet states or the entire QQ §ystem. The potential is the Fourier transform of the sum of one meson exchange Feynman graphs, with a hard core radius ro introdu~ed as an adjustable parameter. With the choice ro::;: ·58 F, MQuark\"\"\"\" 5.45 BeV, 0(= 2MQ fV/Sv= - .24, the self-consistent coupling constants gv2 ' Sp 2 imply in and out \"\"unmixed\"\" singlet masses that are equal and correct. With the 2 2 same Sv ' Sp , the hard core radius and are altered to produce 0-, 1- states at the 1£,13 masses. In addition to 1£, 13 and K, the s -wave states 11( 523 ), 11' (985), m('T85), cp( 1018), K* (896) are found, as well as excited states including the following: B(1018), Al (1230), A2(1401). Assuming the correct A2(13l0), the nonet structure K* (1393), f(1323), f'(1476) is found.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-08T18:23:28Z No. of bitstreams: 1 1968_king.pdf: 1873699 bytes, checksum: e93118dea6034cf0bdd7c6bb5498a775 (MD5)","Made available in DSpace on 2011-07-08T18:23:28Z (GMT). No. of bitstreams: 1 1968_king.pdf: 1873699 bytes, checksum: e93118dea6034cf0bdd7c6bb5498a775 (MD5) Previous issue date: 1968","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-08T18:23:28Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:32:52-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["An equation for meson states in the quark model and its application to a meson bootstrap"]}]}],"canonical_facts":{"dc:contributor":["Wyld, H.W."],"dc:creator":["King, Lawrence Gray"],"dc:date":["2011-07-08T18:23:28Z","10000-01-01","1968"],"dc:description":["\"A differential equation for meson states is derived from the Bethe-Salpeter equation under the conditions of the quark model. The equation is shown to imply mass relations of the form K* 2 - P2 = K2 2 - 1£ • The equation is used to attempt bootstrap calculations of the vector and pseudo-scalar meson parameters in the quark model. A bootstrap is found for the SU 3 singlet states but shown not to be possible for either the octet states or the entire QQ §ystem. The potential is the Fourier transform of the sum of one meson exchange Feynman graphs, with a hard core radius ro introdu~ed as an adjustable parameter. With the choice ro::;: ·58 F, MQuark\"\"\"\" 5.45 BeV, 0(= 2MQ fV/Sv= - .24, the self-consistent coupling constants gv2 ' Sp 2 imply in and out \"\"unmixed\"\" singlet masses that are equal and correct. With the 2 2 same Sv ' Sp , the hard core radius and are altered to produce 0-, 1- states at the 1£,13 masses. In addition to 1£, 13 and K, the s -wave states 11( 523 ), 11' (985), m('T85), cp( 1018), K* (896) are found, as well as excited states including the following: B(1018), Al (1230), A2(1401). Assuming the correct A2(13l0), the nonet structure K* (1393), f(1323), f'(1476) is found.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-08T18:23:28Z No. of bitstreams: 1 1968_king.pdf: 1873699 bytes, checksum: e93118dea6034cf0bdd7c6bb5498a775 (MD5)","Made available in DSpace on 2011-07-08T18:23:28Z (GMT). No. of bitstreams: 1 1968_king.pdf: 1873699 bytes, checksum: e93118dea6034cf0bdd7c6bb5498a775 (MD5) Previous issue date: 1968","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-08T18:23:28Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:32:52-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"],"dc:identifier":["6082767","http://hdl.handle.net/2142/25733"],"dc:language":["en"],"dc:rights":["1968 Lawrence Gray King"],"dc:subject":["meson states","quark model","meson bootstrap","Bethe-Salpeter equation"],"dc:title":["An equation for meson states in the quark model and its application to a meson bootstrap"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:26Z"}