Recently, it has been argued that various measures of SUSY naturalness-- electroweak, Higgs mass and EENZ/BG-- when applied consistently concur with one another and make very specific predictions for natural supersymmetric spectra. Highly natural spe
ctra are characterized by light higgsinos with mass not too far from m_h and well-mixed but TeV-scale third generation squarks. We apply the unified naturalness measure to the case of heavy Higgs bosons A, H and H^pm. We find that their masses are bounded from above by naturalness depending on tan(beta): e.g. for 10% fine-tuning and tan(beta)~ 10, we expect m_A< 2.5 TeV whilst for 3% fine-tuning and tan(beta) as high as 50, then m_A< 8 TeV. Furthermore, the presence of light higgsinos seriously alters the heavy Higgs boson branching ratios, thus diminishing prospects for usual searches into Standard Model (SM) final states, while new discovery possibilities arise due to the supersymmetric decay modes. The heavy SUSY decay modes tend to be H, A, H^pm-> W, Z, or h+MET + soft tracks so that single heavy Higgs production is characterized by the presence of high p_T W, Z or h bosons plus missing E_T. These new heavy Higgs boson signatures seem to be challenging to extract from SM backgrounds.
Recently, there are two hints arising from physics beyond the standard model. One is a possible energy loss mechanism due to emission of very weakly interacting light particles from white dwarf stars, with a coupling strength ~ 0.7x10^{-13}, and anot
her is the high energy positrons observed by the PAMELA satellite experiment. We construct a supersymmetric flipped-SU(5) model, SU(5)xU(1)_X with appropriate additional symmetries, [U(1)_H]_{gauge}x[U(1)_RxU(1)_Gamma]_{global}xZ_2, such that these are explained by a very light electrophilic axion of mass 0.5 meV from the spontaneously broken U(1)_Gamma and two component cold dark matters from Z_2 parity. We show that in the flipped-SU(5) there exists a basic mechanism for allowing excess positrons through the charged SU(2) singlet leptons, but not allowing anti-proton excess due to the absence of the SU(2) singlet quarks. We show the discovery potential of the charged SU(2) singlet E at the LHC experiments by observing the electron and positron spectrum. With these symmetries, we also comment on the mass hierarchy between the top and bottom quarks.
We improve the estimate of the axion CDM energy density by considering the new values of current quark masses, the QCD phase transition effect and a possible anharmonic effect.
