"Naive" Quark-Pair-Creation Model of Strong-Interaction Vertices

Abstract

We explicitly formulate the vacuum quark-pair-creation model (QPC) of strong-interaction vertices (Micu, Carlitz and Kislinger) in terms of the harmonic-oscillator spatial-SU(6) wave functions and an explicit vacuum quark-antiquark-pair transition matrix (both displaying the quark internal momenta). The coupling constants are expressed as functions of masses and the oscillator radius. The structure of the formulas is in agreement with the expressions coming from VMD (vector-meson dominance) and PCAC (partial conservation of axial-vector current), and the quark-model calculation of leptonic decays. We carefully investigate the relation of this QPC model with the additive quark model with elementary meson emission, which is known to explain most of the hadronic decays. We show that we recover this model in a given limit. It is shown that in this limit, a term $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{i})$ (depending on the internal quark momentum) appears in place of the usual $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}$ term; the additional contribution is similar to the well-known "recoil" term of Mitra and Ross. The main limits of the model lie (i) in the presence of a phenomenological pair-creation constant and (ii) in the nonrelativistic character of the treatment. A critical test of our model is provided by prediction of the decay-products polarization. We find a striking agreement with experiment for the crucial ${A}_{1}$ and $B$ decays. We make a comparison with the parameter-dependent model of Colglazier and Rosner.