  In supersymmetry, the Higgs quartic couplings is given by the sum in
quadrature of the weak gauge couplings. This leads to the prediction of a light
Higgs boson, which still holds when considering loop corrections from soft
supersymmetry breaking. However, another source of corrections, which
explicitly depends on the scale of the mediation of supersymmetrey breaking, is
from generic hard breaking terms. We show that these corrections can
significantly modify the Higgs mass prediction in models of low-energy
supersymmetry breaking, for example, gauge mediation. Conversely, the Higgs
mass measurement can be used to constrain the scale of mediation of
supersymmetry breaking.
