Scalar-particle self-energy amplitudes and confinement in Minkowski space

TL;DR

This paper investigates the analytic structure of scalar particle self-energy amplitudes in Minkowski space using Covariant Spectator Theory, revealing unique features like a left-hand cut and implications for confining interactions.

Contribution

It derives dispersion relations for scalar self-energy amplitudes in Minkowski space and shows that confining interactions do not contribute to the self-energy.

Findings

Dispersion relations exhibit both right- and left-hand cuts.

Left-hand cut originates from the spectator contribution in scattering.

Confining interaction kernels do not affect the self-energy amplitude.

Abstract

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a \phi^2 \chi-theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this "spectator" left-hand cut can be understood in the context of scattering for a scalar \phi^2 \chi^2-type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.