Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse

We propose a solution of the naturalness problem in the context of the multiverse wavefunction without the anthropic argument. If we include microscopic wormhole configurations in the path integral, the wave function becomes a superposition of universes with various values of the coupling constants such as the cosmological constant, the parameters in the Higgs potential, and so on. We analyze the quantum state of the multiverse, and evaluate the density matrix of one universe. We show that the coupling constants induced by the wormholes are fixed in such a way that the density matrix is maximized. In particular, the cosmological constant, which is in general time-dependent, is chosen such that it takes an extremely small value in the far future. We also discuss the gauge hierarchy problem and the strong CP problem in this context. Our study predicts that the Higgs mass is 140\pm20 GeV and {\theta}=0.Comment: 35 pages, 11 figures. v2: added Section 5.3 with comments on the Wick rotation of the Lorentzian gravity. v3 some comments adde

Covariance and PCA for Categorical Variables

Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated results give reasonable values for test data. A method of principal component analysis (RS-PCA) is also proposed using regular simplex expressions, which allows easy interpretation of the principal components. The proposed methods apply to variable selection problem of categorical data USCensus1990 data. The proposed methods give appropriate criterion for the variable selection problem of categoricalComment: 12 pages, 5 figure

Asymptotically Vanishing Cosmological Constant in the Multiverse

We study the problem of the cosmological constant in the context of the multiverse in Lorentzian spacetime, and show that the cosmological constant will vanish in the future. This sort of argument was started from Coleman in 1989, and he argued that the Euclidean wormholes make the multiverse partition a superposition of various values of the cosmological constant $\Lambda$, which has a sharp peak at $\Lambda=0$. However, the implication of the Euclidean analysis to our Lorentzian spacetime is unclear. With this motivation, we analyze the quantum state of the multiverse in Lorentzian spacetime by the WKB method, and calculate the density matrix of our universe by tracing out the other universes. Our result predicts vanishing cosmological constant. While Coleman obtained the enhancement at $\Lambda=0$ through the action itself, in our Lorentzian analysis the similar enhancement arises from the front factor of $e^{iS}$ in the universe wave function, which is in the next leading order in the WKB approximation.Comment: 17 pages, 7 figures; v2:minor correction

Fermionic Dark Matter in Radiative Inverse Seesaw Model with U(1)_{B-L}

We construct a radiative inverse seesaw model with local B-L symmetry, and investigate the flavor structure of the lepton sector and the fermionic Dark Matter. Neutrino masses are radiatively generated through a kind of inverse seesaw framework. The PMNS matrix is derived from each mixing matrix of the neutrino and charged lepton sector with large Dirac CP phase. We show that the annihilation processes via the interactions with Higgses which are independent on the lepton flavor violation, have to be dominant in order to satisfy the observed relic abundance by WMAP. The new interactions with Higgses allow us to be consistent with the direct detection result reported by XENON100, and it is possible to verify the model by the exposure of XENON100 (2012).Comment: 15 pages, 1 table, 5 figures; version accepted for publication in Physical Review