Small parameters in infrared QCD: The pion decay constant

Abstract

We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the dynamics of chiral symmetry breaking at the level of the quark propagator and, in particular, the dynamical generation of a constituent quark mass. In the present article, we study the associated Goldstone mode, the pion, and we compute the pion decay constant in the chiral limit. Our approach exploits the fact that the coupling (defined in the Taylor scheme) in the pure gauge sector is perturbative, as observed in lattice simulations which, together with a $1/N_c$-expansion, allows for a systematic, controllable approximation scheme in the low energy regime of QCD. At leading order, this leads to the well-known rainbow-ladder resummation. We study the region of parameter space of the model that gives physical values of the pion decay constant. This allows one to constrain the gluon mass parameter as a function of the coupling using a physically measured quantity.

21 pages, 11 figures

References in corpus (11)

• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Infrared propagators of Yang-Mills theory from perturbation theory
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Perspective on rainbow-ladder truncation
• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach
• Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders

Cited by in corpus (5)

• Four-gluon vertex from the Curci-Ferrari model at one-loop order
• Axial anomaly effect to the chiral-partner structure of diquarks at high temperature
• QCD phase diagram from the gluon propagator at finite temperature and density
• Proper constituent gluon mass as the final piece to construct hybrid mesons
• Parton distribution and fragmentation functions with massive gluons