Bethe-Salpeter qq¯ dynamics under harmonic confinement
Abstract
A Bethe-Salpeter (BS) treatment of qq¯ proposed recently for equal-mass quarks in the instantaneous approximation is extended to unequal masses. An explicit mass formula is obtained in the dimensionless form F(M)=N+const, where F(M), a nonlinear function of M, represents a central supermultiplet (mass)2 for each N excitation, formally corrected for spin and flavor variations among members. These universality features of F(M) are borne out by the data to a significant extent up to the charmed sector, in terms of a single reduced spring constant ω~ (=0.15 GeV) and the quark masses (mq). A fully covariant and transparent construction is found for the Bethe-Salpeter wave functions for P, V, and A1 mesons consistent with their equations of motion and satisfying the BS normalization without the need for a conventional decomposition into (+/-+/-) components. Tests of these wave functions are offered through the predictions of (a) P, V-->ll¯ and τ-->(π, ρ, A1)ντ decays, (b) electromagnetic radii of P mesons, and (c) weak form factor in Kl3 decay, all in excellent agreement with experiment, without extra parameters.
- Publication:
-
Physical Review D
- Pub Date:
- December 1982
- DOI:
- 10.1103/PhysRevD.26.3123
- Bibcode:
- 1982PhRvD..26.3123M