Quark Mass Functions and Pion Structure in the Covariant Spectator Theory

Abstract

The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.

Quark Propagator in Minkowski Space

“…with p 0 = p 2 + κ 2 . For x 0 = y 0 , the left hand side of (18) gives the equal-time anticommutador:…”

“…Much of what is presently known in this respect was gathered with studies of the quark (and also gluon) propagator in Euclidean space, but very little is presently known on the analytic structure of the propagator in Minkowski space, although a increasingly number of studies has appeared in the literature in the last years, a list of which is given in Refs. [10,11,12,13,14,15,16,17,18,19]. One reason for this disparity in favor of the Euclidean formulation is that the analytic structure of the quark propagator (and of any other quark-gluon correlation function) in Minkowski space is more complicated than in Euclidean space.…”