Soft QCD Modeling of Meson Electromagnetic Form Factors

Abstract

We summarize recent progress in soft QCD modeling based on the set of Dyson-Schwinger equations truncated to ladder-rainbow level. We pay particular attention to electromagnetic elastic and transition form factors of the pion. This covariant approach accommodates quark confinement and implements the QCD one-loop renormalization group behavior. The dressed quark propagators are compared to the most recent lattice-QCD data.

Goldstone boson's valence-quark distribution

“…propagator predicted by the model, which underlies these condensate values, has recently been confirmed in numerical simulations of lattice-QCD [13,14].…”

“…propagator predicted by the model, which underlies these condensate values, has recently been confirmed in numerical simulations of lattice-QCD [13,14]. Fixing the single parameter at this fitted value, many observables are predicted and the model achieves a r.m.s.…”

“…(A formula without Z 2 is incorrect.) Equations (11)- (14) form an essential part of the proof [2] that if, and only if, a theory exhibits DCSB then the homogeneous, isovector, pseudoscalar Bethe-Salpeter equation has a massless, P 2 = 0, solution and the axial-vector vertex is dominated by the pion pole for P 2 ≃ 0; i.e., a proof of Goldstone's theorem in QCD.…”

Nucleon mass and pion loops

“…This behaviour was recently observed in lattice-QCD simulations [41], and Refs. [42,43] provide quantitative comparisons between those results and a modern DSE model. The infrared enhancement of M (p 2 ) is an essential consequence of dynamical chiral symmetry breaking (DCSB) and is the origin of the constituent-quark mass.…”

“…Pseudovector diquarks were omitted in the second and fourth rows. ω f 1,2 are discussed after Eq (43),. and r in and after Eq (48)…”