Scattering of massive W bosons into gravitinos and tree unitarity in broken supergravity

TL;DR

This paper investigates how massive W bosons scatter into gravitinos in broken supergravity, revealing potential unitarity violations at high energies due to the behavior of longitudinal polarizations and the structure of scattering amplitudes.

Contribution

It demonstrates the emergence of new amplitude structures in broken supergravity that can lead to unitarity violation, highlighting differences from unbroken gauge symmetry scenarios.

Findings

Longitudinal W polarizations become strongly interacting at high energies.

Scattering amplitudes exhibit structures that can violate unitarity.

Including MSSM scalar diagrams does not cancel divergences.

Abstract

The WW scattering into gravitino and gaugino is here investigated in the broken phase, by using both gauge and mass eigenstates. Differently from what is obtained for unbroken gauge symmetry, we find in the scattering amplitudes new structures, which can lead to violation of unitarity above a certain scale. This happens because, in the annihilation diagram, the longitudinal degrees of freedom in the propagator of the gauge bosons disappear from the amplitude, by virtue of the SUGRA vertex. We show that the longitudinal polarizations of the on-shell W become strongly interacting in the high energy limit, and that the inclusion of diagrams with off-shell scalars of the MSSM does not cancel the divergences.