1 2 Κ ′ 2 ( Φ † Φ ′ ′ ) ( Φ ′ ′
نویسنده
چکیده
We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry. Once the mixing element |U e3 | is determined, such a relation will tell us which solution will be favored within this model. The model can also lead to interesting phenomena on lepton-flavor violations.
منابع مشابه
On Hanf numbers of the infinitary order property
We study several cardinal, and ordinal–valued functions that are relatives of Hanf numbers. Let κ be an infinite cardinal, and let T ⊆ Lκ+,ω be a theory of cardinality ≤ κ, and let γ be an ordinal ≥ κ . For example we look at 1. μ∗T (γ, κ) := min{μ ∗ : ∀φ ∈ L∞,ω, with rk(φ) < γ, if T has the (φ, μ∗)-order property then there exists a formula φ ′ (x; y) ∈ Lκ+,ω, such that for every χ ≥ κ, T has ...
متن کاملOn Hanf Numbers of the Infinitary Order Property Draft
We study several cardinal, and ordinal–valued functions that are relatives of Hanf numbers. Let κ be an infinite cardinality, and let T ⊆ Lκ+,ω be a theory of cardinality ≤ κ, and let γ be an ordinal ≥ κ. Consider (1) μT (γ, κ) := min{μ∗ : ∀φ ∈ L∞,ω , with rk(φ) < γ, if T has the (φ, μ∗)order property then there exists a formula φ ′ (x; y) ∈ Lκ+,ω , such that for every χ ≥ κ, T has the (φ , χ)-...
متن کاملOn the Fourth Moment in the Rankin-selberg Problem
where the notation is as follows. Let φ(z) be a holomorphic cusp form of weight κ with respect to the full modular group SL(2,Z), and denote by a(n) the n-th Fourier coefficient of φ(z). We suppose that φ(z) is a normalized eigenfunction for the Hecke operators T (n), that is, a(1) = 1 and T (n)φ = a(n)φ for every n ∈ N. The classical example is a(n) = τ(n) (κ = 12), the Ramanujan function defi...
متن کاملThe Benefits of Learning with Strongly Convex Approximate Inference *** Supplemental ***
Strong convexity can be characterized in a number of ways. The following facts provide some conditions that are equivalent to Definition 1. For the 2-norm, Fact 2 means that the minimum eigenvalue of the Hessian is lower-bounded by κ. Recall that˜µ(θ) and˜µ(θ) are the gradients of˜Φ(θ) and˜Φ(θ), respectively. Since the conjugate function, ˜ Φ * , is assumed to be κ-strongly convex, we have via ...
متن کاملOn φ-Connes amenability of dual Banach algebras
Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...
متن کاملGauge invariance in Chern-Simons systems.
We investigate the problem of gauge invariance of the effective potential in Chern–Simons systems. Working at the one-loop level, we show explicitly that the picture the subject of gauge invariance has already constructed in scalar electrodynamics gets unchanged in the Chern–Simons territory. PACS: 11.15.-q, 11.15.Bt * This work is supported in part by Conselho Nacional de Desenvolvimento Cient́...
متن کامل