The quark gap equation in light-cone gauge

Abstract

We calculate the quark self-energy correction in light-cone gauge motivated by distribution amplitudes whose definition implies a Wilson line. The latter serves to preserve the gauge invariance of the hadronic amplitudes and becomes trivial in light-cone gauge. Therefore, the calculation of the distribution amplitudes simplifies significantly provided that wave functions and propagators are obtained in that gauge. In here, we explore the corresponding Dyson-Schwinger equation in its leading truncation and with a dressed vertex derived from a Ward identity in light-cone gauge. The quark's mass and wave renormalization functions, as well as a third complex-valued amplitude, are found to depend on the relative orientation of the quark momentum and a light-like four-vector, which expresses a geometric gauge dependence of the propagator.

Figures (6)

• Figure 1: The solution $A(p,n)$ and $B(p,n)$ of the quark DSE obtained with a bare vertex and with the WFGTI ansatz of Eq. \ref{['WT-vertex-LC']}.
• Figure 2: The quark-mass function $M(p,n) = B(p,n)/A(p,n)$ obtained with the bare and WFGTI vertices.
• Figure 3: Real and imaginary parts of the dressing function $C(p,n)$ obtained with the bare and WFGTI vertices.
• Figure 4: The gauge dependence of the scalar functions, $A(p,n)$ and $B(p,n)$, obtained with a bare quark-gluon vertex is due to the relative orientation of the vectors $n$ and $p$ and expressed by the angles $y_p$ and $z_p$ in Eq. \ref{['anglep']}.
• Figure 5: The dependence of the quark-mass function $M(p,n) = B(p,n)/A(p,n)$ on the quark momentum $p$ in light-cone direction, see Eq. \ref{['anglep']}.