On the computation of one-loop amplitudes with external fermions in 4d heterotic superstrings

TL;DR

This paper develops computational tools for one-loop amplitudes with external fermions in 4d heterotic superstrings, demonstrating their application through a specific amplitude calculation and consistency check with supersymmetry.

Contribution

It introduces new methods for calculating one-loop amplitudes involving fermions in 4d heterotic string models, including a detailed example and verification of supersymmetry constraints.

Findings

Successfully computed a one-loop three-point amplitude with fermions and a photon.

Verified the vanishing of the anomalous magnetic moment contribution in supersymmetric models.

Provided a framework applicable to various one-loop amplitude calculations in heterotic string theory.

Abstract

We present the technical tools needed to compute any one-loop amplitude involving external spacetime fermions in a four-dimensional heterotic string model a` la Kawai-Lewellen-Tye. As an example, we compute the one-loop three-point amplitude with one "photon" and two external massive fermions ("electrons"). As a check of our computation, we verify that the one-loop contribution to the Anomalous Magnetic Moment vanishes if the model has spacetime supersymmetry, as required by the supersymmetric sum rules.