Pions and excited scalars in Minkowski space DSBSE formalism

TL;DR

This paper demonstrates the feasibility of solving Schwinger-Dyson and Bethe-Salpeter equations directly in Minkowski space for light mesons, providing insights into confinement and meson spectra without Euclidean space approximation.

Contribution

It presents the first direct Minkowski space solutions of DSBSE equations for light mesons, showing non-perturbative calculations are feasible in this framework.

Findings

Minkowski space solutions are numerically accessible.

The approach describes pseudoscalar mesons reasonably well.

Scalar mesons show discrepancies with experimental data.

Abstract

We present the solution of Schwinger-Dyson and Bethe-Salpeter equation (BSE) for a light flawour non-singlet spinless meson in Minkowski space. The equations are solved in momentum space without the use of the auxiliary Euclidean space. To exhibit that Minkowski space non perturbative calculations are actually possible is the main purpose of presented paper. According to confinement, the quark propagator is regular in momentum space, which allows us to look for the BSE solution directly in the Minkowski momentum space. We find the Minkowski space solution for confining theories is not only numerically accessible, but also provides a reasonable description of the pseudoscalar meson system. However, in the case of scalar mesons, the model is less reliable and we get more extra light states then observed experimentally.