Effective lagrangian approach to vector mesons, their structure and decays

Abstract

An improved update of the structure and decays of ρ 0 , ω and φ mesons based on a chiral SU(3) Lagrangian, including anomaly terms is presented. We demonstrate that a consistent and quantitatively successful description of both pion and kaon electromagnetic form factors can be achieved. We also discuss the e + e − → π + π 0 π − cross section, the Dalitz decay ω → π 0 µ + µ − and aspects of ρ 0 ω and ωφ mixing. Relations to previous versions of the Vector Meson Dominance model will be examined.

Rho meson properties from combining QCD-based models

“…where the ρ-meson mass is taken from [36], the ρ-pion coupling from [25] and the low-energy coefficient from the IAM fit to the scattering data [12]. We observe a very good agreement between (55) and (56).…”

“…a number) we need a model lagrangian for ρ-mesons and pions. We take the standard ρππ-lagrangian [25] …”

“…The fact that the ρ-meson couples (at least approximately) with the same strength to pions and photons constitutes one important aspect of the vector meson dominance picture (e.g. [25,28,29], see also comment in [30]). Note that so far we have not used any input from the quark model calculations of Sec.…”

Dispersive analysis ofω/ϕ→3π,πγ*

“…The integral extends over the two-body ππ phase space. The partial wave expansion for the ππ → ππ scattering amplitude is given by, (16) where the isospin-1 projection operator is,…”

“…χPT has been applied to the three pion production from the η decays [14,15]. In the case of ω/φ → 3π, χP T can be extended by including light vector mesons as additional degrees of freedom [16][17][18][19]. In a perturbative study, germane to an effective field theory, unitarity is only satisfied order-by-order in the loop expansion.…”