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

On the vacuum stability of SUSY models