Bethe-Salpeter qq̅ dynamics under harmonic confinement

Abstract

A Bethe-Salpeter (BS) treatment of qq̅ 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 (m_q). 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→ll̅ and τ→(π, ρ, A₁)ν_τ decays, (b) electromagnetic radii of P mesons, and (c) weak form factor in K_l3 decay, all in excellent agreement with experiment, without extra parameters.