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

Abstract

Using the spectral representation of the quark propagator 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. 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 invariant propagator, that can be expressed in any gauge as the first moment of the chiral-odd quark spectral function. This is therefore revealed to be a \textit{bona fide} QCD observable encoding aspects of the dynamical mass generation in the QCD vacuum, and is furthermore experimentally measurable in specific twist-3 longitudinal-transverse asymmetries in DIS and in semi-inclusive electron-positron collisions. In light-like axial gauges, we also obtain a new sum rule for the spectral function associated with the gauge fixing vector. We finally present a gauge-dependent formula that connects the second moment of the chiral-even coefficient of the quark spectral function to invariant mass generation and final state rescattering in the hadronization of a quark. Finding twist-4 experimental observables sensitive to this quantity is left for future work.