Parametrization of Fully Dressed Quark Propagator

The study of quark propagators is essential in understanding the behavior of quarks within the framework of quantum chromodynamics (QCD), the theory of strong interactions. In particular, the fully dressed quark propagator, which takes into account all possible interactions of quarks with the surrounding gluon field, plays a crucial role in describing the nonperturbative aspects of QCD. In this article, we will discuss the parametrization of the fully dressed quark propagator and its implications in QCD.

The quark propagator is a fundamental quantity in QCD that describes the propagation of quarks in space and time. It contains information about the mass, momentum, and spin of the quark, as well as its interactions with other quarks and gluons. The fully dressed quark propagator includes all possible interactions of the quark with the gluon field, which are crucial for understanding the nonperturbative aspects of QCD, such as confinement and chiral symmetry breaking.

The fully dressed quark propagator can be parametrized in terms of several form factors, which characterize the momentum dependence of the quark propagator. One common parametrization is the so-called "rainbow-ladder" approximation, which neglects higher-order corrections and simplifies the quark-gluon interaction to a simple form. In this approximation, the fully dressed quark propagator can be written as:

$S(p) = frac{i}{gamma cdot p + M(p^2)}$

where $p$ is the quark momentum, $gamma$ is the Dirac matrix, and $M(p^2)$ is the quark mass function, which encodes the momentum dependence of the quark mass due to its interaction with the gluon field.

Another common parametrization of the quark propagator is the so-called "Curtis-Pennington" form, which takes into account higher-order corrections and provides a more realistic description of the quark-gluon interaction. In this parametrization, the quark propagator is written as:

$S(p) = frac{i}{gamma cdot p + m_0 + Sigma(p^2)}$

where $m_0$ is the bare quark mass and $Sigma(p^2)$ is the self-energy term, which includes all corrections to the quark mass due to its interaction with the gluon field.

The parametrization of the fully dressed quark propagator has important implications for the study of QCD. By fitting experimental data or lattice QCD results to the parametrized form of the quark propagator, one can extract information about the quark mass function, the quark-gluon interaction strength, and other properties of the quark-gluon plasma.

Furthermore, the parametrization of the quark propagator can be used to study the phase diagram of QCD, including the transition between the hadronic phase and the quark-gluon plasma phase. By varying the parameters of the quark propagator parametrization, one can investigate the nature of this phase transition and its dependence on temperature and density.

In conclusion, the parametrization of the fully dressed quark propagator is a powerful tool for studying the nonperturbative aspects of QCD. By parametrizing the quark propagator in terms of form factors, one can extract valuable information about the quark-gluon interaction and the properties of the quark-gluon plasma. This parametrization provides important insights into the behavior of quarks in the strong interaction regime, shedding light on some of the most fundamental aspects of QCD.