LHC-7 has narrowed down the mass range of the light Higgs boson. This result is consistent with the supergravity unification framework, and the current Higgs boson mass window implies a rather significant loop correction to the tree value pointing to
a relatively heavy scalar sparticle spectrum with universal boundary conditions. It is shown that the largest value of the Higgs boson mass is obtained on the Hyperbolic Branch of radiative breaking. The implications of light Higgs boson in the broader mass range of 115 GeV to 131 GeV and a narrower range of 123 GeV to 127 GeV are explored in the context of the discovery of supersymmetry at LHC-7 and for the observation of dark matter in direct detection experiments.
The recent excess observed by CDF in $B^0_s to mu^{+} mu^{-}$ is interpreted in terms of a possible supersymmetric origin. An analysis is given of the parameter space of mSUGRA and non-universal SUGRA models under the combined constraints from LHC-7
with 165 pb$^{-1}$ of integrated luminosity, under the new XENON-100 limits on the neutralino-proton spin independent cross section and under the CDF $B^0_s to mu^{+} mu^{-}$ 90% C.L. limit reported to arise from an excess number of dimuon events. It is found that the predicted value of the branching ratio $B^0_s to mu^{+} mu^{-}$ consistent with all the constraints contains the following set of NLSPs: chargino, stau, stop or CP odd (even) Higgs. The lower bounds of sparticles, including those from the LHC, XENON and CDF $B^0_sto mu^+mu^-$ constraint, are exhibited and the shift in the allowed range of sparticle masses arising solely due to the extra constraint from the CDF result is given. It is pointed out that the two sided CDF 90% C.L. limit puts upper bounds on sparticle masses. An analysis of possible signatures for early discovery at the LHC is carried out corresponding to the signal region in $B^0_s to mu^{+} mu^{-}$. Implications of GUT-scale non-universalities in the gaugino and Higgs sectors are discussed. If the excess seen by the CDF Collaboration is supported by further data from LHCb or D0, this new result could be a harbinger for the discovery of supersymmetry.
Constraints on dark matter from the first CMS and ATLAS SUSY searches are investigated. It is shown that within the minimal supergravity model, the early search for supersymmetry at the LHC has depleted a large portion of the signature space in dark
matter direct detection experiments. In particular, the prospects for detecting signals of dark matter in the XENON and CDMS experiments are significantly affected in the low neutralino mass region. Here the relic density of dark matter typically arises from slepton coannihilations in the early universe. In contrast, it is found that the CMS and ATLAS analyses leave untouched the Higgs pole and the Hyperbolic Branch/Focus Point regions, which are now being probed by the most recent XENON results. Analysis is also done for supergravity models with non-universal soft breaking where one finds that a part of the dark matter signature space depleted by the CMS and ATLAS cuts in the minimal SUGRA case is repopulated. Thus, observation of dark matter in the LHC depleted region of minimal supergravity may indicate non-universalities in soft breaking.
The CMS and the ATLAS Collaborations have recently reported on the search for supersymmetry with 35 pb$^{-1}$ of data and have put independent limits on the parameter space of the supergravity unified model with universal boundary conditions at the G
UT scale for soft breaking, i.e., the mSUGRA model. We extend this study by examining other regions of the mSUGRA parameter space in $A_0$ and $tanbeta$. Further, we contrast the reach of CMS and ATLAS with 35 pb$^{-1}$ of data with the indirect constraints, i.e., the constraints from the Higgs boson mass limits, from flavor physics and from the dark matter limits from WMAP. Specifically it is found that a significant part of the parameter space excluded by CMS and ATLAS is essentially already excluded by the indirect constraints and the fertile region of parameter space has yet to be explored. We also emphasize that gluino masses as low as 400 GeV but for squark masses much larger than the gluino mass remain unconstrained and further that much of the hyperbolic branch of radiative electroweak symmetry breaking, with low values of the Higgs mixing parameter $mu$, is essentially untouched by the recent LHC analysis.
