An equation for meson states in the quark model and its application to a meson bootstrap
A differential equation for meson states is derived fromthe BetheSalpeter equation under the conditions of the quarkmodel. The equation is shown to imply mass relations of theform K* 2  P2 = K2 2  1£ • The equation is used to attemptbootstrap calculations of the vector and pseudoscalar mesonparameters in the quark model. A bootstrap is found for the SU3singlet states but shown not to be possible for either theoctet states or the entire QQ §ystem. The potential is theFourier 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 selfconsistent coupling constants gv2 ' Sp 2 imply in and out"unmixed" singlet masses that are equal and correct. With the2 2 same Sv ' Sp , the hard core radius and are altered to produce0, 1 states at the 1£,13 masses. In addition to 1£, 13 and K, thes wave states 11( 523 ), 11' (985), m('T85), cp( 1018), K* (896) arefound, 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.
Year of publication: 
1968


Authors:  King, Lawrence Gray 
Other Persons:  Wyld, H. W. (contributor) 
Subject:  meson states  quark model  meson bootstrap  BetheSalpeter equation 
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