Spurions in Anomaly Mediated Supersymmetry Breaking

Question

When studying supersymmetry breaking, people often use a spurion chiral superfield to study the soft SUSY breaking terms which enter the Lagrangian ($X=\theta^2 F$). Since we let the spurion couple to every field and assume that the messengers are at the Planck scale this is used to parametrize gravity mediated SUSY breaking. For example we can get scalar masses through, \begin{equation} \int d^4\theta \frac{X^\dagger X}{M^2} Q^\dagger Q \end{equation}

Recently I've seen papers using anomaly mediated SUSY breaking in their theories instead (one such paper can be found here). Is there a way to parametrize the SUSY breaking terms in the anomaly medaited scheme analogously to the typical gravity mediated scenario?

Answer 1

Yes, there is a way. In case you have a term in the Lagrangian that schematically looks like $$\int d^4\theta\frac{\Sigma^\dagger\Sigma}{M^2}Q^\dagger Q,$$

and the field $\Sigma$ assumes a vacuum expectation value given by

$$\langle\Sigma\rangle=M+F\theta^2,$$ gauginos for example will acquire a mass proportional to $F/M$ through a one-loop anomaly. You can read about this in detail in chapter 16 of Terning's "Modern Supersymmetry - Dynamics and Duality".