FIZIKA B 8 (1999) 2, 251-260

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BETHE-SALPETER AND DYSON-SCHWINGER EQUATIONS IN A WILSON LOOP CONTEXT IN QCD, EFFECTIVE MASS OPERATOR, q`q SPECTRUM

M. BALDICCHI and G. M. PROSPERI

Dipartimento di Fisica, Universita di Milano I.N.F.N., sezione di Milano, via Celoria 16, I-20133 Milano, Italy

Received 2 February 1999; Accepted 12 July 1999

We briefly discuss the quark-antiquark Bethe-Salpeter (BS) equation and the quark Dyson-Schwinger equation derived in preceding papers. We also consider the qq quadratic mass operator M2 = (w1+w2)2+U obtained by a three-dimensional reduction of the BS equation and the related approximate centre-of-mass Hamiltonian or linear-mass-operator HCM M = w1+w2+V+. We revue previous results on the spectrum and the Regge trajectories obtained by an approximate diagonalization of HCM and report new results similarly obtained for the original M2. 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 M2 case.

PACS numbers: 12.40.Qq, 12.38.Aw, 12.38.Lg, 11.10.St
UDC 539.126

Keywords: quark-antiquark systems, Bethe-Salpeter equation, quark Dyson-Schwinger equation, qq quadratic mass operator, meson spectrum, Regge trajectories

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