Quark Mass Functions and Pion Structure in Minkowski Space

We present a study of the dressed quark mass function and the pion structure in Minkowski space using the covariant spectator theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining \({q\bar{q}}\) potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows the Nambu–Jona–Lasinio mechanism to work. We adjust the parameters of our quark mass function calculated in Minkowski-space to agree with LQCD data obtained in Euclidean space. Results of a calculation of the pion electromagnetic form factor in the relativistic impulse approximation using the same mass function are presented and compared with experimental data.