An equation for meson states in the quark model and its application to a meson bootstrap
type: CreativeWork
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."
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."
author: King, Lawrence Gray
language: en
keywords: meson states, quark model, meson bootstrap, Bethe-Salpeter equation
date published: 2011-07-08T18:23:28Z
date modified: 2026-07-22T22:25:26Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois - Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/25733