The search for new physics beyond the Standard Model can follow one of two tracks: direct searches for new particles at the collider or indirect probes for new physics from precision measurements. In the direct searches for third generation squarks in SUSY at the LHC, the common practice has been to assume a 100% decay branching fraction for a given search channel. In realistic MSSM scenarios, there is often more than one signicant decay mode present, which signicantly weakens the current search limits on third generation squarks at the LHC. On the other hand, the combination of multiple decay modes as well as the new open decay modes offer alternative discovery channels for third generation squarks searches. In this work, we present the third generation squarks decay and the collider signatures in a few representative mass parameter scenarios. We then analyze the reach of the stop/sbottom signal for the pair production in QCD at the 14 TeV LHC with 300 fb⁻¹ integrated luminosity and of the 100 TeV future collider with 3000 fb⁻¹ integrated luminosity in a few representative scenarios. In the scenario of Bino LSP with Wino NLSP, we investigate stop/sbottom pair production at the LHC with one stop/sbottom decaying via t̃ --> tu1d465[0 1], tu1d465[0 2]/b̃ --> bu1d465[0 1], bu1d465[0 2], and the other one decaying via t̃ --> bu1d465[± 1]/b̃ -->tu1d465[± 1]. With the gaugino subsequent decaying to gauge bosons or a Higgs boson u1d465[0 2] --> u1d44du1d465[0 1], hu1d465[0 1] and u1d465[± 1]--> u1d44a±u1d465[0 1], leading to u1d44fu1d44fu1d44fu1d44fu1d457u1d457u1d4c1 Ɇᴛ final states for the Higgs channel and u1d44fu1d44fu1d457u1d457u1d457u1d457u1d4c1u1d4c1Ɇᴛ final states for the u1d44d channel, we study the reach of those signals at the 14 TeV LHC with 300 fb⁻¹ integrated luminosity. Because the sbottom and stop signals in the same SUSY parameter scenario have indistinguishable final states, they are combined to obtain optimal sensitivity, which is about 150 GeV better than the individual reaches of the sbottom or stop. In the scenario of Bino LSP with Higgsino NLSP. The light stop pair production at the 14 TeV LHC, with stops decaying via t̃₁ --> tu1d465[0 2]/u1d465[0 3] and the neutralino subsequently decaying to a gauge boson or a Higgs boson u1d465[0 2]/u1d465[0 3] --> u1d465[0 1]h/u1d44d, leads to tt̄hh Ɇᴛ, tt̄hu1d44d Ɇᴛ or tt̄u1d44du1d44d Ɇᴛ final states. The above decay channels give rise to final states containing one or more leptons, therefore our search strategy is to divide the signal regions based on the multiplicity of leptons. We find that the one lepton signal region of channel tt̄hu1d44d Ɇᴛ has the best reach sensitivity of light stop searches at the 14 TeV LHC with 300 fb⁻¹ integrated luminosity. We then combine all the signal regions for a given decay channel or combine all the decay channels for a given signal region to maximize the reach sensitivity of the stop search. For the light stop pair production at the √s = 100 TeV future machine with 3000 fb⁻¹ integrated luminosity, we find that a stop with a mass up to 6 TeV can be discovered at 5u1d70e signicance, while a mass up to 6.8 TeV can be excluded at 95% C.L. for the combined results of all three channels. In the indirect probes for new physics, we utilize the u1d44d-pole Oblique Parameters u1d446,u1d447, u1d448 and Higgs precision measurements complementarily in the framework of the Two Higgs Doublet Model at current and future colliders. The u1d446, u1d447 , u1d448 is not that sensitive to the rotation angle u1d6fd-u1d6fc, while the Higgs precision measurements set strong constrains on u1d6fd-u1d6fc. Also the u1d447 is very sensitive to the mass difference of Higgs bosons, leading to the mass of charged Higgs (H±) aligning either along with the mass of neutral Higgs u1d43b or u1d434. As for the Higgs precision measurements, we consider the tree level corrections to Higgs coupling constants as well as the radiative corrections to Higgs coupling constants at one loop level for the future collider. The combination of u1d44d-pole precision measurements and Higgs precision measurements complementarily set strong constraints on the parameter space of the 2HDM, especially in the future u1d452⁺u1d452⁻ circular collider compared to the current collider due to much cleaner backgrounds and higher luminosity.
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