Changes between Version 5 and Version 6 of Models/SpinTwo
 Timestamp:
 02/17/11 15:21:40 (9 years ago)
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Models/SpinTwo
v5 v6 9 9 == ADD theory == 10 10 11 Theory with D = 4 + d dimensions, with additional d spatial dimensions assumed to be compactified to be a torus with common radius R. Because only spin2 particles can propagate through D dimensions, a massive KK tower of spin2 particles appear in 4 dimensions. They can interact with the SM fields with a very weak coupling constant given by 1/ L:11 Theory with D = 4 + d dimensions, with additional d spatial dimensions assumed to be compactified to be a torus with common radius R. Because only spin2 particles can propagate through D dimensions, a massive KK tower of spin2 particles appear in 4 dimensions. They can interact with the SM fields with a very weak coupling constant given by 1/Λ: 12 12 13 L = \overline{M,,pl,,} ~ 2.4 x 10^18^ GeV 14 13 {{{ 14 #!latex 15 $\Lambda = \overline{M_{pl}} \sim 2.4 \times 10^{18} GeV$ 16 }}} 15 17 The mass gap between neighbouring modes is proportional to 1/R, hence small for d not too large. The discrete mass spectrum can be approximated by a continuum with an integrated density of states. In other words, the 4 dimensional spin2 particles appears as a infinite sum of its excited states. 16 18 … … 28 30 == RS theory == 29 31 30 Theory with D = 4 + 1 dimensions, in which the extra dimension is spatial and assumed to be compactified to be a torus with radius R. Here, the total spacetime has a warped metric and the size of the extra dimension can be at the order of the Planck length. Again, only spin2 particles can propagate through 5 dimensions, therefore, a massive KK tower of spin2 particles appear in 4 dimensions. They can interact with the SM fields with a strong coupling constant given by 1/L: 31 32 L = \overline{M,,pl,,} e^kR\pi^ 33 32 Theory with D = 4 + 1 dimensions, in which the extra dimension is spatial and assumed to be compactified to be a torus with radius R. Here, the total spacetime has a warped metric and the size of the extra dimension can be at the order of the Planck length. Again, only spin2 particles can propagate through 5 dimensions, therefore, a massive KK tower of spin2 particles appear in 4 dimensions. They can interact with the SM fields with a strong coupling constant given by 1/Λ: 33 {{{ 34 #!latex 35 $\Lambda = \overline{M_{pl}} \, e^{kR\pi}$ 36 }}} 34 37 where k is a scale of order of the Planck scale. In this model, the mass of the nth spin2 particle is given by: 35 36 m,,n,, = k x,,n,, e^kR\pi^ 37 38 {{{ 39 #!latex 40 $m_n = k \, x_n \, e^{kR\pi}$ 41 }}} 38 42 which can be ~ O(1 TeV), at the LHC reach. 39 40 43 41 44 __'''Consequence'''__: Spin2 should decay very fast and it is expected to be seem as a resonance @ hadron colliders (e.g., it decays into a pair of leptons). … … 53 56 Fourdimensional model that contains a huge number of hidden sector particles that interacts only gravitationally with the Standard Model particles. It has been suggested that gravity may be interpreted as renormalization of the effective gravity coupling due to these hidden sector particles. Therefore, the existence of M,,pl,,/TeV ~ 10^32^ such particles is required. 54 57 55 The graviton is massless in this class of theories and its coupling to the SM particles is given by 1/L: 56 57 L = \overline{M,,pl,,}(\mu*) = \mu* ~ 1 TeV. 58 58 The graviton is massless in this class of theories and its coupling to the SM particles is given by 1/Λ: 59 {{{ 60 #!latex 61 $\Lambda = \overline{M_{pl}}(\mu^{*}) \sim \mu^{*} \sim 1 \, TeV.$ 62 }}} 59 63 Notice \overline{M,,pl,,} now depends on the effective energy scale. 60 64