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Supersymmetry should cancel the radiative corrections to the Higgs mass and solve the hierarchy problem. If Supersymmetry would be unbroken, would the higgs mass be 0?

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Supersymmetry is broken by electroweak symmetry breaking, by so-called F-terms. There must be another, separate source of supersymmetry breaking, because the EWSB would result in light supersymmetric particles, with sum rules for their masses, e.g. $$ m_{e_L}^2 + m_{e_R}^2 = m_e^2. $$ This is excluded experimentally. With exact supersymmetry, EW symmetry is unbroken, and there is no Higgs as we know it.

With only EWSB and no other SUSY breaking, the Higgs mass is basicaly the tree level mass, $$ m_h \lesssim M_Z$$

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  • $\begingroup$ Also, the hierarchy problem is not with the Higgs mass, it is with the dim-2 coupling in the Higgs potential. $\endgroup$ – innisfree Apr 21 '14 at 17:21

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