More corrections to the Higgs mass in supersymmetry

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 supersymmetry 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.