F(750), We Miss You, as Bound State of 6 Top and 6 Anti top

We collect and estimate support for our long speculated "multiple point principle" saying that there should be several vacua all having (compared to the scales of high energy physics) very low energy densities. In pure Standard Model we suggest there being three by "multiple point principle" low energy density vacua, "present", "condensate" and "high field" vacuum. We fit the mass of the in our picture since long speculated bound state of six top and six anti top quarks in three quite {\em independent ways} and get remarkably within our crude accuracy the {\em same} mass in all three fits! The new point of the present article is to estimate the bound state mass in what we could call a bag model estimation. The two other fits, which we review, obtain the mass of the bound state by fitting to the multiple point principle prediction of degenerate vacua. Our remarkable agreement of our three mass-fits can be interpreted to mean, that we have calculated at the end the energy densities of the two extra speculated vacua and found that they are indeed very small!. Unfortunately the recently much discussed statistical fluctuation peak F(750) has now been revealed to be just a fluctuation, very accidentally matches our fitted mass of the bound state remarkably well with the mass of this fluctuation 750 GeV.Comment: minor corrections in calculation and commas and a few references added. arXiv admin note: text overlap with arXiv:1607.07907, adding few citation

Reality and hermiticity from maximizing overlap in the future-included complex action theory

In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator $\hat{\cal O}$ defined in terms of the future state at the latest time $T_B$ and the past state at the earliest time $T_A$ with a proper inner product that makes normal a given Hamiltonian that is non-normal at first. We present a theorem that states that, provided that the operator $\hat{\cal O}$ is $Q$-Hermitian, i.e., Hermitian with regard to the proper inner product, the normalized matrix element becomes real and time-develops under a $Q$-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the $Q$-Hermitian Hamiltonian in terms of $Q$-Hermitian coordinate and momentum operators, and construct a conserved probability current density.Comment: Latex 12 pages, typos corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phy

On the smallness of the cosmological constant

In N=1supergravity the scalar potential of the hidden sector may have degenerate supersymmetric (SUSY) and non-supersymmetric Minkowski vacua. In this case local SUSY in the second supersymmetric Minkowski phase can be broken dynamically. Assuming that such a second phase and the phase associated with the physical vacuum are exactly degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced if in the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower than ΛQCD in the physical vacuum. The presence of a third degenerate vacuum, in which local SUSY and electroweak (EW) symmetry are broken near the Planck scale, may lead to small values of the quartic Higgs self-coupling and the corresponding beta function at the Planck scale in the phase in which we live.C. D. Froggatt, R. Nevzorov, H. B. Nielsen, A. W. Thoma