The existence of multiple non-equivalent minima of the scalar potential in SUSY models both raises technical challenges and introduces interesting physics. The technical challenges are now that one has to find several minima and evaluate which is the deepest, as well as calculate the tunneling time from a false vacuum to the true vacuum. We present here studies on the vacuum stability and color/charge breaking minima in the CMSSM and R parity violating minima in a B-L extended MSSM.
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