Abstract
The infrared behavior of the quark propagator is studied at one loop and in the Landau gauge ($\ensuremath{\xi}=0$) using the screened massive expansion of full QCD and three different resummation schemes for the quark self-energy. The shift of the expansion point of perturbation theory, which defines the screened expansion, together with a nonstandard renormalization of the bare parameters, proves sufficient to describe the dynamical generation of an infrared quark mass also in the chiral limit. Analytically, the scale for such a mass is set by a mass parameter $M$, whose value is fixed by a fit to the lattice data for quenched QCD. The quark mass function $\mathcal{M}({p}^{2})$ is shown to be in very good agreement with the lattice results. The quark $Z$ function, on the other hand, shows the wrong qualitative behavior in all but one of the studied resummation schemes, where its behavior is qualitatively correct, but only at sufficiently high energies.
Highlights
In the Standard Model of particle physics, the light quarks acquire their masses dynamically through two separate and complementary mechanisms
Due to the strong interactions, at low energies the light quarks propagate with a mass which is greatly enhanced with respect to their treelevel (Lagrangian) value; since this effect cannot be captured by ordinary perturbation theory, some kind of nonordinary and nonperturbative resummation of the quark self-energy is needed in order to successfully describe the infrared quark dynamics
This is precisely what the shift does; by replacing the mass contained in the standard zeroorder propagator with an enhanced mass parameter, it optimizes the expansion point of perturbation theory so that the quarks propagate with an effective infrared mass of the order of the QCD scale ΛQCD, rather than with the mass contained in the Lagrangian, which would be more relevant to the high energy regime
Summary
In the Standard Model of particle physics, the light quarks acquire their masses dynamically through two separate and complementary mechanisms. Due to the strong interactions, at low energies the light quarks propagate with a mass which is greatly enhanced with respect to their treelevel (Lagrangian) value; since this effect cannot be captured by ordinary perturbation theory, some kind of nonordinary and nonperturbative resummation of the quark self-energy is needed in order to successfully describe the infrared quark dynamics. This is precisely what the shift does; by replacing the mass contained in the standard zeroorder propagator with an enhanced mass parameter, it optimizes the expansion point of perturbation theory so that the quarks propagate with an effective infrared mass of the order of the QCD scale ΛQCD, rather than with the mass contained in the Lagrangian, which would be more relevant to the high energy regime.
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