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 {widetilde{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.
Highlights
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
The interest of fragmentation functions (FFs) sum rules extends beyond their application to phenomenological fits, since a few of these are sensitive to aspects of the non-perturbative Quantum Chromodynamics (QCD) dynamics, such as the dynamics of mass generation
Summary
Let us start by considering the unintegrated inclusive quarkto-jet correlator [65,69,70,71,72,78]. The correlator captures the hadronization of a quark including all the products of the hadronization process We call this the “fully inclusive” jet correlator in order to stress that none of the jet’s constituents is reconstructed – the absence of a definition for a jet axis and radius, contrary to other semi-inclusive definition of jets. It is interesting to remark that, taking into account the properties of the color trace and after a specific choice for the path of the Wilson line (to be discussed ), the correlator can be expressed as the discontinuity of the gauge-invariant quark propagator, whose spectral decomposition has been studied in Ref. We will discuss instead the spectral representation for the case of Wilson lines running along staple-like contours – which are the natural paths arising in QCD factorization theorems – and use this in applications involving correlators integrated along one light-cone direction
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