In this paper we explore extensions of the Minimal Supersymmetric Standard
Model involving two SU(2)L triplet chiral superfields that share a
superpotential Dirac mass yet only one of which couples to the Higgs fields.
This choice is motivated by recent work using two singlet superfields with the
same superpotential requirements. We find that, as in the singlet case, the
Higgs mass in the triplet extension can easily be raised to 125GeV
without introducing large fine-tuning. For triplets that carry hypercharge, the
regions of least fine tuning are characterized by small contributions to the
T parameter, and light stop squarks, mt~1∼300−450GeV; the latter is a result of the tanβ dependence of
the triplet contribution to the Higgs mass. Despite such light stop masses,
these models are viable provided the stop-electroweakino spectrum is
sufficiently compressed.Comment: 26 pages, 4 figure