Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

TL;DR

This paper calculates the electromagnetic form factor of a relativistic two-scalar-particle system directly in Minkowski space, revealing significant errors in Euclidean space methods at high momentum transfer and demonstrating the accuracy of light-front dynamics.

Contribution

It presents a novel Minkowski space calculation of the Bethe-Salpeter amplitude and form factor, highlighting limitations of Euclidean approaches and validating light-front dynamics.

Findings

Euclidean space calculations induce ~30% errors at Q^2=10 GeV^2/c^2

Static approximation introduces larger errors

Light-front dynamics closely matches Minkowski space results

Abstract

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.