Small parameters in infrared QCD: The pion decay constant

TL;DR

This paper investigates the pion decay constant within a modified QCD framework using the Curci-Ferrari Lagrangian, providing insights into low-energy QCD dynamics and constraining model parameters through physical observables.

Contribution

It introduces a systematic approach to compute the pion decay constant in a modified QCD model, connecting gluon mass parameters with physical measurements.

Findings

Identifies parameter regions matching the physical pion decay constant.

Constrains the gluon mass parameter based on the decay constant.

Validates the perturbative coupling in the low-energy regime.

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.