Analytical two-loop soft mass terms of sfermions in Extended GMSB models

Analytical two-loop contributions to soft masses of sfermions are derived in the Extended GMSB (EGMSB) model with one superpotential coupling between matter and messenger superfields. Analytical results allows to study in detail the whole range of the ratio $F\mathrm{/}{M}^2$ of the spurion $F$-term, $F$, to the messenger scale $M$. It is shown that if $F\mathrm{/}{M}^2$ is of the order of $1$, then one- and two-loop contributions to soft masses are of the same magnitude and their interplay leads to novel sfermion mass patterns.