  In this study we investigate the phenomenological viability of the $Y=0$
Triplet Extended Supersymmetric Standard Model (TESSM) by comparing its
predictions with the current Higgs data from ATLAS, CMS, and Tevatron, as well
as the measured value of the $B_s\to X_s \gamma$ branching ratio. We scan
numerically the parameter space for data points generating the measured
particle mass spectrum and also satisfying current direct search constraints on
new particles. We require all the couplings to be perturbative up to the scale
$\Lambda_{\rm UV}=10^4$ TeV, by running them with newly calculated two loop
beta functions, and find that TESSM retains perturbativity as long as
$\lambda$, the triplet coupling to the two Higgs doublets, is smaller than 1.34
in absolute value. For $|\lambda|\gtrsim 0.8$ we show that the fine-tuning
associated to each viable data point can be greatly reduced as compared to
values attainable in MSSM. We also find that for perturbatively viable data
points it is possible to obtain either enhancement or suppression in
$h\rightarrow \gamma \gamma$ decay rate depending mostly on the relative sign
between $M_2$ and $\mu_D$. Finally, we perform a fit by taking into account 58
Higgs physics observables along with $\mathcal{B}r(B_s\to X_s \gamma)$, for
which we calculate the NLO prediction within TESSM. We find that, although
naturality prefers a large $|\lambda|$, the experimental data disfavors it
compared to the small $|\lambda|$ region, because of the low energy observable
$\mathcal{B}r(B_s\to X_s \gamma)$. We notice, though, that this situation might
change with the second run of LHC at 14 TeV, in case the ATLAS or CMS results
confirm, with smaller uncertainty, a large enhancement in the Higgs decay
channel to diphoton, given that this scenario strongly favours a large value of
$|\lambda|$.
