The Ωρπ COUPLING IN THE VMD MODEL REVISITED

Abstract

We determine the value of the ω − ρ − π mesons coupling (g ωρπ ), in the context of the vector meson dominance model, from radiative decays, the ω → 3π decay width and the e + e − → 3π cross section. For the last two observables we consider the effect of either a heavier resonance (ρ ′ (1450)) or a contact term. A weighted average of the results from the set of observables yields g ωρπ = 14.7 ± 0.1 GeV −1 in absence of those contributions, and g ωρπ = 11.9 ± 0.2 GeV −1 or g ωρπ = 11.7 ± 0.1 GeV −1 when including the ρ ′ or contact term respectively. The inclusion of these additional terms makes the estimates from the different observables to lay in a more reduced range.Improved measurements of these observables and the ρ ′ (1450) meson parameters are needed to give a definite answer on the pertinence of the inclusion of this last one in the considered processes.

The πρ cloud contribution to the ω width in nuclear matter

“…In Ref. [31] the partial πρ width was found to be 2.8 MeV. Rescaling our g ωρπ to obtain that value would entail an according 22% reduction of our in-medium widths reported below.…”

“…Here, we use the microscopic vacuum spectral function underlying our in-medium model [29], which describes the low-mass tail of the ρ resonance more accurately, incorporating an energy dependence of Re Π vac ρππ . With g ωρπ = 1.9/f π (f π =92 MeV) [28,30], one obtains Γ ω→ρπ = 3.6 MeV, i.e., about 1/2 of the total 3π width (2/3 when including interference effects [31]). Using a schematic Breit-Wigner ρ spectral function, Γ ω→ρπ (m ω ) is reduced by approximately 30%.…”

ρ-ω mixing in J/ψ → VP decays

“…The framework used by SND [29,[36][37][38]] is adopted in the calculation, and the ω → π + π − π 0 contact term is taken into account [30,[39][40][41][42][43].…”

“…with the VMD model of V → 3π [29,30] and the flavor parameterization method of J/ψ → VP decays [23,24]. By doing a fit, we expect to derive the mixing parameter Π ρω , and to modulate the measured Br(J/ψ → ωπ 0 )…”

“…In Section 2, using the VMD model, as applied to the e + e − → 3π process [29] and taking into account the ω → π + π − π 0 contact term [30], we describe the process e + e − → J/ψ → Vπ 0 → π + π − π 0 π 0 and give its cross section. In Section 3, by using the flavor parameterization method [23,24], we perform a fit to the existing branching ratios within the theoretical framework of J/ψ→VP decays.…”