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In this paper, the analytic sufficient and necessary conditions are obtainedfor the CP conserving two-Higgs-doublet potential to be bounded from below byusing the co-positivity of tensors. This is achieved by treating the potentialas a quartic homogeneous polynomial about the moduli of the two Higgs doubletfields, where the 'angles' is described as the misalignment of the twodoublets, then solving three minimum problems with respect to the misalignment.Finally, the analytic conditions are established with the help of thecorresponding theory and methods of higher order tensors.

Co-positivity of tensors and bounded from below conditions of CP conserving two-Higgs-doublet potential