Explanation of theΔ5/2−(1930)as aρΔ

Plausible explanation for theΔ5/2+(2000)puzzle

“…For Λ 1/2 − (1405) the relevance of KN was first pointed out in 1977 [3] (more recently the role of πΣ has been also emphasized [4]). For ∆ 5/2 − (1930) the important role of ρ∆ has been recognized [5]. These are particular examples of a more general situation where a 3q model calculation (providing a reasonable overall description of the whole spectrum) overestimates the mass of a resonance so that a meson-baryon threshold lies in between the calculated 3q value and the experimental data [6].…”

“…Although the form of these interactions have been detailed elsewhere [5,23,24], we shall briefly revisit in Subsection A the ∆-ρ case. This will allow us to remind the general procedure of calculating the two-body amplitudes entering the FCA equations.…”

“…The ∆ρ interaction has been analyzed in the framework of the hidden gauge formalism [25] in terms of the exchange of a ρ meson in the t−channel between the ∆ and the ρ [5,15]. Under the low energy approximation of neglecting q 2 /M 2 V in the propagator of the exchanged vector meson, where q is the momentum transfer, and also the three momentum − → k of the vector meson, one obtains for the ∆ρ → ∆ρ potential the form…”

“…[5] regarding the description of ∆ 5/2 − (1930) with a mass much lower than the corresponding to the third energy band, the first available band for such a state. There the consideration of the ρ∆ channel whose threshold (2002 MeV) lies close above the experimental mass of the resonance and far below the 3q mass (∼ 2150 MeV) allowed for an explanation of ∆ 5/2 − (1930) and its partners, ∆ 3/2 − (1940) and ∆ 1/2 − (1900), as ρ∆ bound states in the I = 3/2 sector.…”

“…[6]. Since the N 5/2 − (1675) has been dynamically generated as a bound state of ρ∆(1232) in the I = 1/2 sector (the same interaction generating the ∆ 5/2 − (1930) for I = 3/2) [5], we shall investigate the three-body π-ρ-∆ system but keeping the strong correlations of the ρ∆ system which generate the N 5/2 − (1675). In such a situation the use of the Fixed Center Approximation (FCA) to the Faddeev equations is justified [8].…”