We discuss both MSSM and NMSSM scenarios in which the lightest Higgs boson with $m_h=98$~GeV is consistent with the small excess ($sim 2.3 sigma$) observed at the LEP in $e^+ e^-rightarrow Zh$, with $h rightarrow b {bar b}$ process and the heavier Hi
ggs boson of mass close to 125~GeV as the observed candidate of the SM Higgs like particle at the LHC. We show the allowed regions in the non-decoupling Higgs zone of MSSM parameter space which are consistent with several low energy constraints coming from heavy flavour physics, latest experimental data on Higgs signals and lower limit on superparticle masses from 7~TeV and 8~TeV LHC run. We also implement the constraints from the relic density of the cold dark matter as obtained from the recent PLANCK data. Additionally, we discuss the possibility of observing the light Higgs boson of mass 98~GeV at the 14~TeV LHC run via $pp rightarrow V h$, with $h rightarrow b bar b$ using the technique of jet substructure. Our analysis shows that at 14~TeV LHC run with 300 ${rm fb}^{-1}$ luminosity the signal efficiency of such a light Higgs boson is at most 2.5$sigma$. Finally, we make a comment on the prospect of proposed $e^+ e^-$ ILC to discover/exclude this light Higgs boson.
We revisit the issue of considering stochasticity of Grassmannian coordinates in N=1 superspace, which was analyzed previously by Kobakhidze {it et al}. In this stochastic supersymmetry(SUSY) framework, the soft SUSY breaking terms of the minimal sup
ersymmetric Standard Model(MSSM) such as the bilinear Higgs mixing, trilinear coupling as well as the gaugino mass parameters are all proportional to a single mass parameter xi, a measure of supersymmetry breaking arising out of stochasticity. While a nonvanishing trilinear coupling at the high scale is a natural outcome of the framework, a favorable signature for obtaining the lighter Higgs boson mass $m_h$ at 125 GeV, the model produces tachyonic sleptons or staus turning to be too light. The previous analyses took $Lambda$, the scale at which input parameters are given, to be larger than the gauge coupling unification scale $M_G$ in order to generate acceptable scalar masses radiatively at the electroweak scale. Still this was inadequate for obtaining $m_h$ at 125 GeV. We find that Higgs at 125 GeV is highly achievable provided we are ready to accommodate a nonvanishing scalar mass soft SUSY breaking term similar to what is done in minimal anomaly mediated SUSY breaking (AMSB) in contrast to a pure AMSB setup. Thus, the model can easily accommodate Higgs data, LHC limits of squark masses, WMAP data for dark matter relic density, flavor physics constraints and XENON100 data. In contrast to the previous analyses we consider $Lambda=M_G$, thus avoiding any ambiguities of a post-grand unified theory physics. The idea of stochastic superspace can easily be generalized to various scenarios beyond the MSSM . PACS Nos: 12.60.Jv, 04.65.+e, 95.30.Cq, 95.35.+d
