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In theoretical physics, soft SUSY breaking is a supersymmetry breaking by the special kind of terms that do not invalidate certain desirable features of supersymmetry, such as the Bose-Fermi cancellation of the ultraviolet divergences contributing to the mass of the Higgs boson.
Roughly speaking, these terms are relevant operators, i.e. those whose coefficients have a positive dimension of mass.
Soft SUSY breaking is usually studied as an explicit symmetry breaking, i.e. particular terms are added to the Lagrangian, but it is assumed that such a description is just an effective treatment of a more detailed mechanism where supersymmetry is broken spontaneously.
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