In order to significantly reduce the fine-tuning associated with the electroweak symmetry breaking in the minimal supersymmetric standard model (MSSM), we consider not only the minimal gravity mediation effects but also the minimal gauge mediation on
es for a common supersymmetry breaking source at a hidden sector. In this Minimal Mixed Mediation model, the minimal forms for the Kahler potential and the gauge kinetic function are employed at tree level. The MSSM gaugino masses are radiatively generated through the gauge mediation. Since a focus point of the soft Higgs mass parameter, m_{h_u}^2 appears around 3-4 TeV energy scale in this case, m_{h_u}^2 is quite insensitive to stop masses. Instead, the naturalness of the small m_{h_u}^2 is more closely associated with the gluino mass rather than the stop mass unlike the conventional scenario. As a result, even a 3-4 TeV stop mass, which is known to explain the 125 GeV Higgs mass at three-loop level, can still be compatible with the naturalness of the electroweak scale. On the other hand, the requirements of various fine-tuning measures much smaller than 100 and |mu| < 600 GeV constrain the gluino mass to be 1.6 TeV < M_3 < 2.2 TeV, which is well-inside the discovery potential range of LHC RunII.
We employ both the minimal gravity- and the minimal gauge mediations of supersymmetry breaking at the grand unified theory (GUT) scale in a single supergravity framework, assuming the gaugino masses are generated dominantly by the minimal gauge media
tion effects. In such a minimal mixed mediation model, a focus point of the soft Higgs mass parameter, m_{h_u}^2 emerges at 3-4 TeV energy scale, which is exactly the stop mass scale needed for explaining the 126 GeV Higgs boson mass without the A-term at the three loop level. As a result, m_{h_u}^2 in the MSSM can be quite insensitive to various trial stop masses at low energy, reducing the fine-tuning measures to be much smaller than 100 even for a 3-4 TeV low energy stop mass and -0.5 < A_t / m_0 < +0.1 at the GUT scale. The $mu$ parameter is smaller than 600 GeV. The gluino mass is predicted to be about 1.7 TeV, which could readily be tested at LHC run2.
We employ both the minimal gravity- and the minimal gauge mediations of supersymmetry breaking at the grand unified theory (GUT) scale in a single supergravity framework, assuming the gaugino masses are generated dominantly by the minimal gauge media
tion effects. In such a minimal mixed mediation model, a focus point of the soft Higgs mass parameter, m_{h_u}^2 emerges at 3-4 TeV energy scale, which is exactly the stop mass scale needed for explaining the 126 GeV Higgs boson mass without the A-term at the three loop level. As a result, m_{h_u}^2 can be quite insensitive to various trial stop masses at low energy, reducing the fine-tuning measures to be much smaller than 100 even for a 3-4 TeV low energy stop mass and -0.5 < A_t/m_0 < +0.1 at the GUT scale. The gluino mass is predicted to be about 1.7 TeV, which could readily be tested at LHC run2.
We present a perspective on the inflation paths in 2-, 3-,,, N-flation models based on the ultraviolet completion in heterotic string theory, where a number of grand unification scale axions are used. The number of non-Abelian gauge groups for a natu
ral inflation is restricted in string compactification, and we argue that the most plausible completion of natural inflation from a theory perspective is the 2-flation.
The large tensor spectrum recently observed by the BICEP2 Collaboration requires a super-Planckian field variation of the inflaton in the single-field inflationary scenario. The required slow-roll parameter epsilon approx 0.01 would restrict the e-fo
lding number to around 7 in (sub-)Planckian inflationary models. To overcome such problems, we consider a two-field scenario based on the natural assisted supersymmetric (SUSY) hybrid model (natural SUSY hybrid inflation [1]), which combines the SUSY hybrid and the natural inflation models. The axionic inflaton field from the natural inflation sector can admit the right values for the tensor spectrum as well as a spectral index of 0.96 with a decay constant smaller than the Planck scale, f lesssim M_P. On the other hand, the vacuum energy of 2 x 10^{16} GeV with 50 e-folds is provided by the inflaton coming from the SUSY hybrid sector, avoiding the eta problem. These are achieved by introducing both the U(1)_R and a shift symmetry, and employing the minimal Kahler potential.
BICEP2 has observed a primordial gravitational wave corresponding to the tensor-to-scalar ratio of 0.16. It seems to require a super-Planckian inflationary model. In this paper, we propose a double hybrid inflation model, where the inflaton potential
dynamically changes with the evolution of the inflaton fields. During the first phase of inflation over 7 e-folds, the power spectrum can be almost constant by a large linear term in the hybrid potential, which is responsible also for the large tensor-to-scalar ratio. In the second phase of 50 e-folds, the dominant potential becomes dynamically changed to the logarithmic form as in the ordinary supersymmetric hybrid inflation, which is performed by the second inflaton field. In this model, the sub-Planckian field values (~0.9 M_P) can still yield the correct cosmic observations with the sufficient e-folds.
A small Higgs mass parameter m_{h_u}^2 can be insensitive to various trial heavy stop masses, if a universal soft squared mass is assumed for the chiral superpartners and the Higgs boson at the grand unification (GUT) scale, and a focus point (FP) of
m_{h_u}^2 appears around the stop mass scale. The challenges in the FP scenario are (1) a too heavy stop mass (~ 5 TeV) needed for the 126 GeV Higgs mass and (2) the too high gluino mass bound (> 1.4 TeV). For a successful FP scenario, we consider (1) a superheavy right-hand (RH) neutrino and (2) the first and second generations of hierarchically heavier chiral superpartners. The RH neutrino can move a FP in the higher energy direction in the space of (Q, m_{h_u}^2(Q)), where Q denotes the renormalization scale. On the other hand, the hierarchically heavier chiral superpartners can lift up a FP in that space through two-loop gauge interactions. Precise focusing of m_{h_u}^2(Q) is achieved with the RH neutrino mass of ~ 10^{14} GeV together with an order one (0.9-1.2) Dirac Yukawa coupling to the Higgs boson, and the hierarchically heavy masses of 15-20 TeV for the heavier generations of superpartners, when the U(1)_R breaking soft parameters, m_{1/2} and A_0 are set to be 1 TeV at the GUT scale. Those values can naturally explain the small neutrino mass through the seesaw mechanism, and suppress the flavor violating processes in supersymmetric models.
We introduce one pair of inert Higgs doublets {H_d, H_u} and singlets {N^c, N}, and consider their couplings with the Higgs doublets of the minimal supersymmetric standard model (MSSM), W supset y_N N^c h_u H_d + y_N N h_d H_u. We assign extra U(1)_{
Z} gauge charges only to the extra vector-like superfields, and so all the MSSM superfields remain neutral under the new U(1)_{Z}. They can be an extension of the lambda term, W supset lambda S h_u h_d in the next-to-MSSM (NMSSM). Due to the U(1)_{Z}, the maximally allowed low energy value of y_N can be lifted up to 0.85, avoiding a Landau-pole (LP) below the grand unification scale. Such colorless vector-like superfields remarkably enhance the radiative MSSM Higgs mass particularly for large tanbeta through the y_N term and the corresponding holomorphic soft term. As a result, the lower bound of lambda and the upper bound of tanbeta can be relaxed to disappear from the restricted parameter space of the original NMSSM, 0.6 < lambda < 0.7 and 1< tanbeta < 3. Thus, the valid parameter space significantly expands up to 0 < lambda < 0.7, 0 < y_N < 0.85, and 2 < tanbeta < 50, evading the LP problem and also explaining the 126 GeV Higgs mass naturally.
For explaining the AMS-02 cosmic positron excess, which was recently reported, we consider a scenario of thermally produced and decaying dark matter (DM) into the standard model (SM) leptons with an extremely small decay rate, Gamma_{DM} sim 10^{-26}
sec.^{-1}. Since the needed DM mass is relatively heavy (700 GeV < m_{DM} < 3000 GeV), we introduce another DM component apart from the lightest supersymmetric particle (LSP). For its (meta-) stability and annihilation into other particles, the new DM should be accompanied with another Z_2 symmetry apart from the R-parity. Sizable renormalizable couplings of the new DM with SM particles, which are necessary for its thermalization in the early universe, cannot destabilize the new DM because of the new Z_2 symmetry. Since the new DM was thermally produced, it can naturally explain the present energy density of the universe. The new DM can decay into the SM leptons (and the LSP) only through non-renormalizable operators suppressed by a superheavy squared mass parameter after the new symmetry is broken around TeV scale. We realize this scenario in a model of gauged vector-like leptons, which was proposed recently for the naturalness of the Higgs boson.
We propose a U(1)^prime mediated supersymmetry (SUSY) breaking, in which U(1)^prime is identified with U(1)_{B_1+B_2-2L_1}. The U(1)_{B_1+B_2-2L_1} gauge symmetry, which is anomaly-free with the field contents of the minimal supersymmetric standard m
odel, assigns pm 1/3 charges to the first and second generations of the quarks, and mp 2 to the first generation of the leptons. As a result, the first two generations of squarks acquire masses of about 7 TeV, and the first generation of the sleptons do those of 40 TeV, respectively, in the presence of one or three pairs of extra vector-like matter {{bf 5},bar{bf 5}}. Non-observation on extra colored particles below 1 TeV at the large hadron collider, and also the flavor violations such as mu^-rightarrow e^-gamma are explained. By virtue of such a gauge symmetry, proton stability can be protected. The other squarks and sleptons as well as the gauginos can obtain masses of order 10^{2-3} GeV through the conventional gravity or gauge mediated SUSY breaking mechanism. The relatively light smuon/sneutrino and the neutralino/chargino could be responsible for the (g-2)_mu deviated from the standard model prediction. The stop mass of sim 500 GeV relieves the fine-tuning problem in the Higgs sector. Two-loop effects by the relatively heavy sfermions can protect the smallness of the stop mass from the radiative correction by the heavy gluino (gtrsim 1 TeV). Extra vector-like matter can enhance the radiative corrections to the Higgs mass up to 126 GeV, and induce the desired mixing among the chiral fermions after U(1)_{B_1+B_2-2L_1} breaking.
