A review of naturalness and dark matter prediction for the Higgs mass in MSSM and beyond

Understand

Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m_h) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (Delta) of the electroweak scale and dark matter consistency.

• As a result, the Higgs mass is predicted to be just above the LEP2 bound, m_h=115.9\pm 2 GeV, corresponding to a minimal Delta=17.8, value obtained from consistency with electroweak and WMAP (3\sigma) constraints, but without the LEP2 bound.
• Due to quantum corrections (largely QCD ones for m_h above LEP2 bound), Delta grows \approx exponentially on either side of the above value of m_h, which stresses the relevance of this prediction.
• A value m_h>121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than Delta>100 (1000), respectively.