After a nuclear decay is it a necessity that the total energy of the products is more than the energy of the original particle before decaying? (NB: by 'energy' I don't intend to include mass-energy as well, unless by definition the term 'total energy' happens to include that in the realm of particle physics)
I was told that this might depend on whether the total mass of the products is less than the mass of the decaying particle. I'm not sure of the veracity of this claim.
I've heard the Higgs Boson can decay to heavier particles than itself. But, I'm not sure about other decays, such as the one I described, which is not a Higgs Boson.
For example, is the statement "the mass energy of the original particle is equal to the total energy of the decay products" false?