Changes between Version 5 and Version 6 of Models/SpinTwo

Timestamp:

Feb 17, 2011, 3:21:40 PM (14 years ago)

Author:

Priscila de Aquino

Comment:

--

Models/SpinTwo

@@ -9 +9 @@
 == ADD theory ==
 
-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 spin-2 particles can propagate through D dimensions, a massive KK tower of spin-2 particles appear in 4 dimensions. They can interact with the SM fields with a very weak coupling constant given by -1/L:
+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 spin-2 particles can propagate through D dimensions, a massive KK tower of spin-2 particles appear in 4 dimensions. They can interact with the SM fields with a very weak coupling constant given by -1/Λ:
 
-L = \overline{M,,pl,,} ~ 2.4 x 10^18^ GeV
-
+{{{
+#!latex
+$\Lambda = \overline{M_{pl}} \sim 2.4 \times 10^{18} GeV$
+}}}
 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 spin-2 particles appears as a infinite sum of its excited states.
 
@@ -28 +30 @@
 == RS theory ==
 
-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 space-time has a warped metric and the size of the extra dimension  can be at the order of the Planck length. Again, only spin-2 particles can propagate through 5 dimensions, therefore, a massive KK tower of spin-2 particles appear in 4 dimensions. They can interact with the SM fields with a strong coupling constant given by -1/L:
-
-L = \overline{M,,pl,,} e^kR\pi^
-
+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 space-time has a warped metric and the size of the extra dimension  can be at the order of the Planck length. Again, only spin-2 particles can propagate through 5 dimensions, therefore, a massive KK tower of spin-2 particles appear in 4 dimensions. They can interact with the SM fields with a strong coupling constant given by -1/Λ:
+{{{
+#!latex
+$\Lambda = \overline{M_{pl}} \, e^{kR\pi}$
+}}}
 where k is a scale of order of the Planck scale. In this model, the mass of the nth spin-2 particle is given by:
-
-m,,n,, = k x,,n,, e^-kR\pi^
-
+{{{
+#!latex
+$m_n = k \, x_n \, e^{-kR\pi}$
+}}}
 which can be ~ O(1 TeV), at the LHC reach.
-
 
 __'''Consequence'''__: Spin-2 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 @@
 Four-dimensional 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.
 
-The graviton is massless in this class of theories and its coupling to the SM particles is given by -1/L:
-
-L = \overline{M,,pl,,}(\mu*) = \mu* ~ 1 TeV. 
-
+The graviton is massless in this class of theories and its coupling to the SM particles is given by -1/Λ:
+{{{
+#!latex
+$\Lambda = \overline{M_{pl}}(\mu^{*}) \sim \mu^{*} \sim 1 \, TeV.$ 
+}}}
 Notice \overline{M,,pl,,} now depends on the effective energy scale.