Gauge singlet renormalisation in softly-broken supersymmetric theories

We consider the renormalisation of a softly-broken supersymmetric theory with singlet fields and a superpotential with a linear term. We show that there exist exact β-functions for both the linear term in the superpotential and the associated linear term in the Lagrangian. We also construct exact renormalisation group invariant trajectories for these terms, corresponding to the conformal anomaly solution for the soft masses and couplings.