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 Bethe-Salpeter 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 pseudo-scalar 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 self-consistent 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:||
|Authors:||King, Lawrence Gray|
|Other Persons:||Wyld, H. W. (contributor)|
|Subject:||meson states | quark model | meson bootstrap | Bethe-Salpeter equation|
|Type of publication:||Book / Working Paper|
|Type of publication (narrower categories):||Thesis|
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