Light stops in the MSSM parameter space

We consider the regions of the MSSM parameter space where the top squarks become light and even may be the LSP. This happens when the triple scalar coupling A becomes very big compared to m_0. We show that in this case the requirement that the LSP is neutral imposes noticeable constraint on the parameter space excluding low m_0 and m_{1/2} similar to constraint from the Higgs mass limit. In some cases these constraints overlap. This picture takes place in a wide region of \tanβ. In a narrow band close to the border line the stops are long-lived particles and decay into quarks and neutralino (chargino). The cross-section of their production at LHC via gluon fusion mechanism in this region may reach a few pb.