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## Main Question or Discussion Point

When we discuss higgs potential energy in textbook, we mean it takes the form ## V(h)= m^2 h^2 + \lambda h^4/4##. My question is: is potential energy always defined at some specific energy scale? since the parameters depend on energy.

For instance, if I am interested in the form of higgs potential around GUT scale (10^16 GeV), what should I do? Do I need to take into account both Coleman-weinberg effective potential and RGE running to this energy scale?

For instance, if I am interested in the form of higgs potential around GUT scale (10^16 GeV), what should I do? Do I need to take into account both Coleman-weinberg effective potential and RGE running to this energy scale?