I found this term/operator in some papers that can generate masses, e.g Riva-Biggio-Pomarol(2012), Fox-Nelson-Weiner

$\int d^4\theta \frac{X^\dagger X}{M^2}Q^\dagger Q$

Could anyone explain about this term? Is there any references that explain this term?


The term give a mass for the squarks. This is easy to see by expanding the superfields, \begin{equation} \frac{ F ^4 }{ M ^4 }\int \,d^4\theta \bar{\theta} ^2 \theta ^2 \left( \tilde{q} ^\dagger + \bar{\theta} \bar{q} + ... \right) \left( \tilde{q} + \theta q + ... \right) \end{equation} Only the first squark-squark term survives giving, \begin{equation} m _{ \tilde{q} } ^2 \tilde{q} ^\dagger \tilde{q} \end{equation} where $ m _{ \tilde{q} } ^2 \equiv F ^4 / M ^4 $ (there is an implicit numerical coefficient outfront as well).

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