Dynamical Generation of the Gauged Su(2) Linear Sigma Model

Abstract

The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson-quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be mq = fπg, mπ = 0, mσ = 2mq, and we also find that the quark-meson coupling is g = 2π/ √ Nc, the three-meson coupling is g ′ = m 2 σ /2fπ = 2gmq and the four-meson coupling is λ = 2g 2 = g ′ /fπ, where fπ ≃ 90 MeV is the pion decay constant and Nc = 3 is the colour number. By gauging this model one can generate the couplings to the vector mesons ρ and A1, including the quark-vector coupling constant gρ = 2π, gρππ, gA 1 ρπ and the masses mρ ∼ 700 MeV, mA 1 ≃ √ 3mρ; of course the vector and axial currents remain conserved throughout.

Constituent quark masses and the electroweak standard model

“…Here, f π ≈ 93 MeV, and the meson-quark coupling is g = 2π/ √ 3, determined from infrared QCD [6], the Z = 0 compositeness condition [7], or the quark-level linear σ model (QLLσM) [8,9].…”

Pion and kaon electromagnetic form factors

“…[4,5,6,12,13]). Scadron et al [5] gives the LσM expressions for meson form factors in the chiral limit (CL),…”

Publisher’s Note: Ground-state scalarq¯qnonet: SU(3) mass splittings and strong, electromagnetic, and weak decay rates [Phys. Rev. D69, 014010 (2004)]

“…[15], where the sameqq assignments are employed as here. [3]). Thus, the σ → 2 π decay rate, for p cm = 294 MeV and φ s = ±18…”