The neutrino star in the bulk Universe

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1 (hf,a ψ a Lf H0 Higgs field will have only the residual form 1 0 H0 = √ 2 υ Lagrange function Lbulk = iψ ΓN ∂N ψ − mD (ψ L ψR + h.c), (14)
is connected to the string scale Ms . In the result of the comparison to (8) we have M= √ 4π (2πr4 Ms )Ms . 3 (11)
Ms
−1 M2 = r2
−1 r4
M
1.2 TeV 1.6 MeV 432.05 MeV 7.42 107 GeV 1.2 TeV 15 MeV 141.11 MeV 2.27 108 GeV TABLE I: The paremeters set of the model [15].
where g6 = det(gM N ) and M = {µ, i}, N = {ν, j } with xM = {xµ , y i}, i = 1, 2. The metrical tensor in the six-dimensional spacetime can be written: gM N =
consideration [14] gives the bound M > 100 T eV what corresponds r2 < 5.1 × 10−5 mm. If
where M - is the energy scale of the compactification (∼ 10 − 100 T eV ). Cosmological
∗ †
Electronic address: manka@.pl; URL: .pl/~manka Electronic address: dkarcz@.pl
1
Introduction
Recently there has been considerable interest in the field theories with large extra spacetime dimensions. In the comparison to the standard Kaluza-Klein theory these extra dimensions may be restricted only to the gravity sector of theory while the Standard Model (SM) fields are assumed to be localized on the 4-dimensional spacetime [1],[2],[3].This is a promising scenario from the phenomenological point of view because it shift the energy scale of unification from 1019 GeV to 1 − 100 T eV . It has been recently shown [4] that this framework can be embedded into string models, where the fundamental Planck scale can be identified with the string scale which could be as low as the weak scale. The extra dimensions have the potential to lower the unification scale as well [5]. The aim of this paper is to examine the degenerate neutrino star originated from the extra dimensional theory. The neutrino star ( neutrino ball ) was a subject of interest in the theory of the Standard Model [6]. The fermion star in the extra dimensional theory was also the a subject of interest [8].The neutrino star model is capable to explain the nature of the object in Sgr A∗ in the center of the Galaxy [7].
d2 y = (2πr2 )2 . The six-dimensional gravitional coupling κ6 = 8πG6 is convenient
1 G− 6 =
to define as 4π M 4, (2π )2
−2 we define the four-dimensional coupling constant κ = 8πGN = 8πMP l we get 2 4 2 MP l = 4πM r2 .

e
−2ξ (x)/f0
g µν
0 −δij e+2ξ(x)/f0

0 √
.
(2)
According to the above definition we can write: √ −g6 = −ge−2ξ(x)/f0 . (3)
2
We consider here the Lagrangian of the field as follows: L = Lg + LF ,
The paremeters of the model [15] are presented on the Table I. In this section we shall extend the Standard Model minimally with the bulk neutrino ψ (x, y ). The lagrangian of the neutrino sector of the model is then: Lbrane = iLf Γµ ∂µ Lf − and the fermion field are
The bulk neutrino extension of the electroweak theory
Much of the interesting phenomenology of brane-world models is associated with the Kaluza-Klein theories [9] that originate from large, gravity-only additional dimensions. The higher-dimensional bulk fermions lead to Kaluza-Klein towers of standard model singlets that may be interpreted as sterile neutrinos [10, 11, 12, 13]. In this paper we shall consider the six-dimensional Kaluza - Klein theory. Let us now consider the action in the six-dimensional spacetime: S= √ d6 x −g6 L = Sg + SF = √ d6 x −g6 (Lg + LF ), (1)
(Dated: February 1, 2008)
arXiv:astro-ph/0005116v1 6 May 2000
Abstract
Motivated by the Kaluza-Klein theory with large extra spacetime dimensions the neutrino star built from the massive sterile neutrinos core and the massless brane neutrinos envelope is presented. The six-dimensional compactification scale ∼ 15 MeV gives maximal neutrino mass Mmax = 2.3 × 104 M⊙ with radius Rmax = 1.2 × 106 km. The maximal neutrino star parameters varies with temperature. In the limit of the neutrino ball approximation the maximal sterile neutrino star is Mmax = 1.1 × 106 M⊙ .
The neutrino star in the bulk Universe
Ryszard Ma´ nka∗ and D.Karczewska† University of Silesia, Institute of Physics, Katowice 40007, ul. Uniwersytecka 4, Poland
1 Lg = − 2κ R, 6
(4) (5) (6)
LF = Lbrane δ (y ) + Lbulk ,
where κ6 is the six-dimensional gravitational coupling. Its natural interpretation originates from the distance scaling in the four-dimensional spacetime. Let us compactify the sixdimensional spacetime (M6 → M4 × S 1 × S 1 ) to the four-dimensional Minkowski one. In this paper we assume that the extra dimensions are compactified on the 2 dimensional torus with a single radius r2 . The six-dimensional action may be rewritten as: S= where d4 x √ d2 y −g6 L = √ d4 x −g L, (7)