

FIZIKA B 8 (1999) 2, 251260 BETHESALPETER AND DYSONSCHWINGER EQUATIONS IN A WILSON LOOP CONTEXT IN QCD, EFFECTIVE MASS OPERATOR, q`q SPECTRUMM. BALDICCHI and G. M. PROSPERI Dipartimento di Fisica, Universita di Milano I.N.F.N., sezione di Milano, via Celoria 16, I20133 Milano, Italy Received 2 February 1999; Accepted 12 July 1999We briefly discuss the quarkantiquark BetheSalpeter (BS) equation and the quark DysonSchwinger equation derived in preceding papers. We also consider the qq quadratic mass operator M^{2} = (w_{1}+w_{2})^{2}+U obtained by a threedimensional reduction of the BS equation and the related approximate centreofmass Hamiltonian or linearmassoperator H_{CM} º M = w_{1}+w_{2}+V+¼. We revue previous results on the spectrum and the Regge trajectories obtained by an approximate diagonalization of H_{CM} and report new results similarly obtained for the original M^{2}. We show that in both cases we succeed to reproduce fairly well the entire meson spectrum in the cases in which the numerical calculations were actually practicable and with the exception of the light pseudoscalar states (related to the chiral symmetry problematic). A small rearrangement of the parameters and the use of a running coupling constant is necessary in the M^{2} case. PACS numbers: 12.40.Qq, 12.38.Aw, 12.38.Lg, 11.10.St

Copyright by The Croatian Physical Society
