The quark‐level linear σ model

Abstract

This review of the quark‐level linear σ model (QLLσM) is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2)× SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non‐strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low‐energy observables with only one parameter, namely the pion decay constant fπ. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. fK and <π |Hweak|K>. Links are made with the vector‐meson‐dominance model, the BCS theory of superconductivity, and chiral‐symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.

Inhomogeneous phases in the quark-meson model with vacuum fluctuations

“…(88) is obtained with Eq. (47). This demonstrates that our treatment of inhomogeneous phases is consistent with the parameter fixing in vacuum.…”

Excited scalar and pseudoscalar mesons in the extended linear sigma model

“…[6,7]; for a modern and modified version see for example Refs. [8,9]) is that the mentioned states can effectively be described in terms of constituent quarks and antiquarks -ground-stateqq resonances. In this context, we define ground states as those with the lowest mass for a given set of quantum numbers I, J, P and C. Such description is particularly successful for the lightest pseudoscalar states π, K and η.…”

Nambu's Nobel Prize, the meson and the mass of visible matter

“…also for a constituent quark where the d-quark is replaced by a s-quark. Furthermore, it has been shown [33][34][35] that (15) is valid independent of the regularization scheme.…”

“…where use is made of the fact that m d − m u has been determined to be approximately 4 MeV [35]. This leads to the magnetic moments of the constituent quarks µ u = 1.890, µ d = −0.934 (39) and to predicted magnetic moments of the nucleon µ theor p = 2.831, µ theor n = −1.875.…”