Gauge invariant spectral analysis of quark hadronization dynamics

TL;DR

This paper analyzes the gauge invariant quark propagator's spectral functions, deriving new sum rules and relations to hadronization, invariant mass, and rescattering effects, advancing understanding of quark dynamics during hadronization.

Contribution

It introduces new sum rules for quark spectral functions, relates spectral moments to physical quantities like jet mass, and explores gauge dependence in hadronization processes.

Findings

Derived a new sum rule for the gauge fixing vector spectral function.

Showed the second moment of the gauge fixing vector spectral function is zero.

Connected the first moment of the chiral-odd spectral function to the inclusive jet mass.

Abstract

We study the Dirac decomposition of the gauge invariant quark propagator, whose imaginary part describes the hadronization of a quark as this interacts with the vacuum, and relate each of its coefficients to a specific sum rule for the chiral-odd and chiral-even quark spectral functions. Working at first in light-like axial gauge, we obtain a new sum rule for the spectral function associated to the gauge fixing vector, and show that its second moment is in fact equal to zero. Then, we demonstrate that the first moment of the chiral-odd quark spectral function is equal in any gauge to the so-called inclusive jet mass, which is related to the mass of the particles produced in the hadronization of a quark. Finally, we present a gauge-dependent formula that connects the second moment of the chiral-even quark spectral function to invariant mass generation and final state rescattering in the hadronization of a quark.