On the connection between quark propagation and hadronization

TL;DR

This paper explores the relationship between quark propagation, hadronization, and dynamical mass generation in QCD by connecting gauge-invariant correlators to fragmentation functions and deriving new sum rules.

Contribution

It introduces a novel gauge-invariant spectral decomposition technique and establishes new sum rules linking quark hadronization to dynamical mass generation.

Findings

Derived complete set of momentum sum rules for quark fragmentation functions.

Connected gauge-invariant jet correlator mass to the spectral function and fragmentation functions.

Proposed experimental access to quark mass generation via fragmentation function measurements.

Abstract

We investigate the properties and structure of the recently discussed "fully inclusive jet correlator", namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet's gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the $E$ and $\tilde{E}$ twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.