  A Higgs boson mass $\sim 126$ GeV as determined by the LHC data requires a
large loop correction which in turn implies a large sfermion mass. Implication
of this result for the stability of the proton in supersymmetric grand unified
theories is examined including other experiments constraints along with the
most recent result on cold dark matter from Planck. It is shown that over the
allowed parameter space of supergravity unified models, proton lifetime is
highly sensitive to the Higgs boson mass and a few GeV shift in its mass can
change the proton decay lifetime for the mode $p\to \bar \nu K^+$ by as much as
two orders of magnitude or more. An analysis is also given on the nature of
radiative breaking of the electroweak symmetry in view of the high Higgs boson,
and it is shown that most of the parameter space of universal and non-universal
supergravity unified models lies on the Hyperbolic Branch of radiative breaking
of the electroweak symmetry, while the Ellipsoidal Branch and the Focal Point
regions are highly depleted and contain only a very small region of the allowed
parameter space. Also discussed are the naturalness criteria when the proton
stability constraints along with the electroweak symmetry breaking are
considered together. It is shown that under the assumed naturalness criteria
the overall fine tuning is improved for larger values of the scalar mass with
the inclusion of the proton stability constraint. Thus the naturalness criteria
including proton stability along with electroweak symmetry breaking constraints
tend to favor the weak scale of SUSY in the several TeV region. Implications
for the discovery of supersymmetry in view of the high Higgs mass are briefly
discussed.
