The Pion Structure from the Bethe–Salpeter Equation in Minkowski Space

by Prof. Wayne de Paula (Instituto Tecnologico de Aeronautica)

Wednesday Jun 3, 2026, 9:00 PM → 10:30 PM Asia/Shanghai

ZOOM

Abstract: In this seminar, I will discuss the formation of relativistic bound states, whose dynamics are described by the solution of the Bethe–Salpeter equation. In general, the solution of this integral equation relies on the Wick rotation, which transforms it into an equation defined in Euclidean space. Owing to the presence of poles in the interaction kernel, however, establishing a direct correspondence between the Euclidean solution and the one obtained in Minkowski space can be challenging. I will discuss a method based on integral representations that allows one to obtain solutions directly in Minkowski space.
In particular, I will present the pion structure obtained from a dynamical model based on the solution of the Bethe–Salpeter equation in Minkowski space. To this end, we employ the Nakanishi integral representation for the Bethe–Salpeter amplitude. The interaction kernel incorporates the quark and gluon masses, as well as a scale parameter associated with the quark–gluon vertex. Within this framework, we compute the pion decay constant, the valence probability, light-front momentum distributions, distribution amplitudes, and probability densities both in light-front momentum space and in the three-dimensional space defined by the Cartesian product of the Ioffe time and transverse coordinates. We also calculate hadronic observables such as the pion electromagnetic form factor, the parton distribution function, and the transverse momentum distribution.

 

ZOOM: 927 1121 6089

PW: 128173

https://zoom.us/j/92711216089?pwd=AbyF2MlNb6kzBbwFb3tb56YaZXQLrq.1