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Using the spectral representation of the quark propagator we study the Diracdecomposition of the gauge invariant quark propagator, whose imaginary partdescribes the hadronization of a quark as this interacts with the vacuum.  We then demonstrate the formal gauge invariance of the so-called jet mass,that is of the coefficient of the chiral-odd part of the gauge invariantpropagator, that can be expressed in any gauge as the first moment of thechiral-odd quark spectral function. This is therefore revealed to be a\textit{bona fide} QCD observable encoding aspects of the dynamical massgeneration in the QCD vacuum, and is furthermore experimentally measurable inspecific twist-3 longitudinal-transverse asymmetries in DIS and insemi-inclusive electron-positron collisions. In light-like axial gauges, wealso obtain a new sum rule for the spectral function associated with the gaugefixing vector.  We finally present a gauge-dependent formula that connects the second momentof the chiral-even coefficient of the quark spectral function to invariant massgeneration and final state rescattering in the hadronization of a quark.Finding twist-4 experimental observables sensitive to this quantity is left forfuture work.

Hadronization dynamics from the spectral representation of the gauge invariant quark propagator