Speaker
Description
We study the analytic structure of the non-perturbative quark propagator. To this end, we solve the coupled Schwinger-Dyson equations of the quark propagator and the quark-gluon vertex over a region of the complex plane. Retaining the full tensor structure of the quark-gluon vertex, we find that, in the sub-GeV time-like momentum region, the associated quark propagator exhibits real poles with opposite-sign residues. In particular, we find no evidence of complex conjugate poles, in contrast to results obtained in widely used approximations. This behavior is governed by three dominant form factors. By gradually tuning their strength, we show that, although they contribute differently to the quark propagator, their joint action is indispensable to stabilize the system, place the sub-GeV poles onto the real axis and produce a robust constituent quark mass of $350~\textrm{MeV}$.